1.
Sun
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The Sun is the star at the center of the Solar System. It is a perfect sphere of hot plasma, with internal convective motion that generates a magnetic field via a dynamo process. It is by far the most important source of energy for life on Earth. Its diameter is about 109 times that of Earth, and its mass is about 330,000 times that of Earth, accounting for about 99. 86% of the total mass of the Solar System. About three quarters of the Suns mass consists of hydrogen, the rest is mostly helium, with smaller quantities of heavier elements, including oxygen, carbon, neon. The Sun is a G-type main-sequence star based on its spectral class and it formed approximately 4.6 billion years ago from the gravitational collapse of matter within a region of a large molecular cloud. Most of this matter gathered in the center, whereas the rest flattened into a disk that became the Solar System. The central mass became so hot and dense that it eventually initiated nuclear fusion in its core and it is thought that almost all stars form by this process. The Sun is roughly middle-aged, it has not changed dramatically for more than four billion years and it is calculated that the Sun will become sufficiently large enough to engulf the current orbits of Mercury, Venus, and probably Earth. The enormous effect of the Sun on Earth has been recognized since prehistoric times, the synodic rotation of Earth and its orbit around the Sun are the basis of the solar calendar, which is the predominant calendar in use today. The English proper name Sun developed from Old English sunne and may be related to south, all Germanic terms for the Sun stem from Proto-Germanic *sunnōn. The English weekday name Sunday stems from Old English and is ultimately a result of a Germanic interpretation of Latin dies solis, the Latin name for the Sun, Sol, is not common in general English language use, the adjectival form is the related word solar. The term sol is used by planetary astronomers to refer to the duration of a solar day on another planet. A mean Earth solar day is approximately 24 hours, whereas a mean Martian sol is 24 hours,39 minutes, and 35.244 seconds. From at least the 4th Dynasty of Ancient Egypt, the Sun was worshipped as the god Ra, portrayed as a falcon-headed divinity surmounted by the solar disk, and surrounded by a serpent. In the New Empire period, the Sun became identified with the dung beetle, in the form of the Sun disc Aten, the Sun had a brief resurgence during the Amarna Period when it again became the preeminent, if not only, divinity for the Pharaoh Akhenaton. The Sun is viewed as a goddess in Germanic paganism, Sól/Sunna, in ancient Roman culture, Sunday was the day of the Sun god. It was adopted as the Sabbath day by Christians who did not have a Jewish background, the symbol of light was a pagan device adopted by Christians, and perhaps the most important one that did not come from Jewish traditions
2.
Earth
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Earth, otherwise known as the World, or the Globe, is the third planet from the Sun and the only object in the Universe known to harbor life. It is the densest planet in the Solar System and the largest of the four terrestrial planets, according to radiometric dating and other sources of evidence, Earth formed about 4.54 billion years ago. Earths gravity interacts with objects in space, especially the Sun. During one orbit around the Sun, Earth rotates about its axis over 365 times, thus, Earths axis of rotation is tilted, producing seasonal variations on the planets surface. The gravitational interaction between the Earth and Moon causes ocean tides, stabilizes the Earths orientation on its axis, Earths lithosphere is divided into several rigid tectonic plates that migrate across the surface over periods of many millions of years. About 71% of Earths surface is covered with water, mostly by its oceans, the remaining 29% is land consisting of continents and islands that together have many lakes, rivers and other sources of water that contribute to the hydrosphere. The majority of Earths polar regions are covered in ice, including the Antarctic ice sheet, Earths interior remains active with a solid iron inner core, a liquid outer core that generates the Earths magnetic field, and a convecting mantle that drives plate tectonics. Within the first billion years of Earths history, life appeared in the oceans and began to affect the Earths atmosphere and surface, some geological evidence indicates that life may have arisen as much as 4.1 billion years ago. Since then, the combination of Earths distance from the Sun, physical properties, in the history of the Earth, biodiversity has gone through long periods of expansion, occasionally punctuated by mass extinction events. Over 99% of all species that lived on Earth are extinct. Estimates of the number of species on Earth today vary widely, over 7.4 billion humans live on Earth and depend on its biosphere and minerals for their survival. Humans have developed diverse societies and cultures, politically, the world has about 200 sovereign states, the modern English word Earth developed from a wide variety of Middle English forms, which derived from an Old English noun most often spelled eorðe. It has cognates in every Germanic language, and their proto-Germanic root has been reconstructed as *erþō, originally, earth was written in lowercase, and from early Middle English, its definite sense as the globe was expressed as the earth. By early Modern English, many nouns were capitalized, and the became the Earth. More recently, the name is simply given as Earth. House styles now vary, Oxford spelling recognizes the lowercase form as the most common, another convention capitalizes Earth when appearing as a name but writes it in lowercase when preceded by the. It almost always appears in lowercase in colloquial expressions such as what on earth are you doing, the oldest material found in the Solar System is dated to 4. 5672±0.0006 billion years ago. By 4. 54±0.04 Gya the primordial Earth had formed, the formation and evolution of Solar System bodies occurred along with the Sun
3.
Celestial sphere
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In astronomy and navigation, the celestial sphere is an imaginary sphere of arbitrarily large radius, concentric with Earth. All objects in the sky can be thought of as projected upon the inside surface of the celestial sphere. The celestial sphere is a tool for spherical astronomy, allowing observers to plot positions of objects in the sky when their distances are unknown or unimportant. Because astronomical objects are at such distances, casual observation of the sky offers no information on the actual distances. All objects seem equally far away, as if fixed to the inside of a sphere of large but unknown radius, which rotates from east to west overhead while underfoot, the celestial sphere can be considered to be infinite in radius. This means any point within it, including that occupied by the observer, all parallel planes will seem to intersect the sphere in a coincident great circle. On an infinite-radius celestial sphere, all observers see the things in the same direction. For some objects, this is over-simplified, objects which are relatively near to the observer will seem to change position against the distant celestial sphere if the observer moves far enough, say, from one side of the Earth to the other. This effect, known as parallax, can be represented as an offset from a mean position. The celestial sphere can be considered to be centered at the Earths center, the Suns center, or any convenient location. Individual observers can work out their own small offsets from the mean positions, in many cases in astronomy, the offsets are insignificant. The celestial sphere can thus be thought of as a kind of astronomical shorthand, for many rough uses, this position, as seen from the Earths center, is adequate. This greatly abbreviates the amount of detail necessary in such almanacs and these concepts are important for understanding celestial coordinate systems – frameworks for measuring the positions of objects in the sky. Certain reference lines and planes on Earth, when projected onto the celestial sphere and these include the Earths equator, axis, and the Earths orbit. At their intersections with the sphere, these form the celestial equator, the north and south celestial poles. As the celestial sphere is considered infinite in radius, all observers see the celestial equator, celestial poles, from these bases, directions toward objects in the sky can be quantified by constructing celestial coordinate systems. Similar to terrestrial longitude and latitude, the coordinate system specifies positions relative to the celestial equator and celestial poles. The ecliptic coordinate system specifies positions relative to the Earths orbit, besides the equatorial and ecliptic systems, some other celestial coordinate systems, such as the galactic coordinate system, are more appropriate for particular purposes
4.
Tropical year
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Because of the precession of the equinoxes, the seasonal cycle does not remain exactly synchronized with the position of the Earth in its orbit around the Sun. As a consequence, the year is about 20 minutes shorter than the time it takes Earth to complete one full orbit around the Sun as measured with respect to the fixed stars. Since antiquity, astronomers have progressively refined the definition of the tropical year, the entry for year, tropical in the Astronomical Almanac Online Glossary 2015 states, the period of time for the ecliptic longitude of the Sun to increase 360 degrees. The mean tropical year is approximately 365 days,5 hours,48 minutes,45 seconds, an equivalent, more descriptive, definition is The natural basis for computing passing tropical years is the mean longitude of the Sun reckoned from the precessionally moving equinox. Whenever the longitude reaches a multiple of 360 degrees the mean Sun crosses the vernal equinox, the mean tropical year in 2000 was 365.24219 ephemeris days, each ephemeris day lasting 86,400 SI seconds. This is 365.24217 mean solar days, the word tropical comes from the Greek tropikos meaning turn. Thus, the tropics of Cancer and Capricorn mark the north and south latitudes where the Sun can appear directly overhead. Because of this connection between the tropics and the cycle of the apparent position of the Sun, the word tropical also lent its name to the tropical year. The early Chinese, Hindus, Greeks, and others made approximate measures of the tropical year, in the 2nd century BC Hipparchus measured the time required for the Sun to travel from an equinox to the same equinox again. He reckoned the length of the year to be 1/300 of a day less than 365.25 days, Hipparchus used this method because he was better able to detect the time of the equinoxes, compared to that of the solstices. He reckoned the value as 1° per century, a value that was not improved upon until about 1000 years later, since this discovery a distinction has been made between the tropical year and the sidereal year. During the Middle Ages and Renaissance a number of progressively better tables were published that allowed computation of the positions of the Sun, Moon, an important application of these tables was the reform of the calendar. The length of the year was given as 365 solar days 5 hours 49 minutes 16 seconds. This length was used in devising the Gregorian calendar of 1582, in the 16th century Copernicus put forward a heliocentric cosmology. This was actually less accurate than the value of the Alfonsine Tables. Major advances in the 17th century were made by Johannes Kepler, in 1609 and 1619 Kepler published his three laws of planetary motion. In 1627, Kepler used the observations of Tycho Brahe and Waltherus to produce the most accurate tables up to that time and he evaluated the mean tropical year as 365 solar days,5 hours,48 minutes,45 seconds. Newtons three laws of dynamics and theory of gravity were published in his Philosophiæ Naturalis Principia Mathematica in 1687 and these effects did not begin to be understood until Newtons time
5.
Year
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A year is the orbital period of the Earth moving in its orbit around the Sun. Due to the Earths axial tilt, the course of a year sees the passing of the seasons, marked by changes in weather, the hours of daylight, and, consequently, vegetation and soil fertility. In temperate and subpolar regions around the globe, four seasons are recognized, spring, summer, autumn. In tropical and subtropical regions several geographical sectors do not present defined seasons, but in the seasonal tropics, a calendar year is an approximation of the number of days of the Earths orbital period as counted in a given calendar. The Gregorian, or modern, calendar, presents its calendar year to be either a common year of 365 days or a year of 366 days, as do the Julian calendars. For the Gregorian calendar the average length of the year across the complete leap cycle of 400 years is 365.2425 days. The ISO standard ISO 80000-3, Annex C, supports the symbol a to represent a year of either 365 or 366 days, in English, the abbreviations y and yr are commonly used. In astronomy, the Julian year is a unit of time, it is defined as 365.25 days of exactly 86400 seconds, totalling exactly 31557600 seconds in the Julian astronomical year. The word year is used for periods loosely associated with, but not identical to, the calendar or astronomical year, such as the seasonal year, the fiscal year. Similarly, year can mean the period of any planet, for example. The term can also be used in reference to any long period or cycle, west Saxon ġēar, Anglian ġēr continues Proto-Germanic *jǣran. Cognates are German Jahr, Old High German jār, Old Norse ár and Gothic jer, all the descendants of the Proto-Indo-European noun *yeh₁rom year, season. Cognates also descended from the same Proto-Indo-European noun are Avestan yārǝ year, Greek ὥρα year, season, period of time, Old Church Slavonic jarŭ, Latin annus is from a PIE noun *h₂et-no-, which also yielded Gothic aþn year. Both *yeh₁-ro- and *h₂et-no- are based on verbal roots expressing movement, *h₁ey- and *h₂et- respectively, the Greek word for year, ἔτος, is cognate with Latin vetus old, from the PIE word *wetos- year, also preserved in this meaning in Sanskrit vat-sa- yearling and vat-sa-ras year. Derived from Latin annus are a number of English words, such as annual, annuity, anniversary, etc. per annum means each year, anno Domini means in the year of the Lord. No astronomical year has an number of days or lunar months. Financial and scientific calculations often use a 365-day calendar to simplify daily rates, in the Julian calendar, the average length of a year is 365.25 days. In a non-leap year, there are 365 days, in a year there are 366 days
6.
Ecliptic coordinate system
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The ecliptic coordinate system is a celestial coordinate system commonly used for representing the positions and orbits of Solar System objects. Because most planets, and many small Solar System bodies have orbits with small inclinations to the ecliptic, using it as the fundamental plane is convenient. The systems origin can be either the center of the Sun or the center of the Earth, its direction is towards the vernal equinox. It may be implemented in spherical coordinates or rectangular coordinates, a slow motion of Earths axis, precession, causes a slow, continuous turning of the coordinate system westward about the poles of the ecliptic, completing one circuit in about 26,000 years. Superimposed on this is a motion of the ecliptic. The three most commonly used are, Mean equinox of an epoch is a fixed standard direction. Mean equinox of date is the intersection of the ecliptic of date with the mean equator, commonly used in planetary orbit calculation. True equinox of date is the intersection of the ecliptic of date with the true equator and this is the actual intersection of the two planes at any particular moment, with all motions accounted for. A position in the coordinate system is thus typically specified true equinox and ecliptic of date, mean equinox and ecliptic of J2000.0. Note that there is no mean ecliptic, as the ecliptic is not subject to small periodic oscillations, ecliptic longitude or celestial longitude measures the angular distance of an object along the ecliptic from the primary direction. Like right ascension in the coordinate system, the primary direction points from the Earth towards the Sun at the vernal equinox of the Northern Hemisphere. Because it is a system, ecliptic longitude is measured positive eastwards in the fundamental plane from 0° to 360°. Because of axial precession, the longitude of most fixed stars increases by about 50.3 arcseconds per year, or 83.8 arcminutes per century. Ecliptic latitude or celestial latitude, measures the distance of an object from the ecliptic towards the north or south ecliptic pole. For example, the ecliptic pole has a celestial latitude of +90°. Ecliptic latitude for fixed stars is not affected by precession, distance is also necessary for a complete spherical position. Different distance units are used for different objects, within the Solar System, astronomical units are used, and for objects near the Earth, Earth radii or kilometers are used. From antiquity through the 18th century, ecliptic longitude was measured using twelve zodiacal signs, each of 30° longitude
7.
Earth's orbit
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Earths orbit is the path through which the Earth travels around the Sun. The average distance between the Earth and the Sun is 149.60 million kilometers, and a complete orbit occurs every 365.256 days, Earths orbit has an eccentricity of 0.0167. Earths orbital motion gives an apparent movement of the Sun with respect to other stars at a rate of about 1° per day eastward as seen from Earth. Earths orbital speed averages about 30 km/s, which is fast enough to cover the planets diameter in seven minutes, viewed from a vantage point above the north poles of both the Sun and the Earth, the Earth would appear to revolve in a counterclockwise direction about the Sun. From the same point, both the Earth and the Sun would appear to rotate in a counterclockwise direction about their respective axes. Heliocentrism is the model that first placed the Sun at the center of the Solar System and put the planets, including Earth. Historically, heliocentrism is opposed to geocentrism, which placed the Earth at the center, aristarchus of Samos already proposed a heliocentric model in the 3rd century BC. This Copernican revolution resolved the issue of planetary motion by arguing that such motion was only perceived. Although Copernicuss groundbreaking book. had been over a century earlier, because of Earths axial tilt, the inclination of the Suns trajectory in the sky varies over the course of the year. For an observer at a northern latitude, when the pole is tilted toward the Sun the day lasts longer. This results in average temperatures, as additional solar radiation reaches the surface. When the north pole is tilted away from the Sun, the reverse is true, above the Arctic Circle and below the Antarctic Circle, an extreme case is reached in which there is no daylight at all for part of the year. This is called a polar night and this variation in the weather results in the seasons. The solstices and equinoxes divide the year up into four equal parts. In the northern winter solstice occurs on or about December 21, summer solstice is near June 21, spring equinox is around March 20. In modern times, Earths perihelion occurs around January 3, the changing Earth–Sun distance results in an increase of about 6. 9% in total solar energy reaching the Earth at perihelion relative to aphelion. The Hill sphere of the Earth is about 1,500,000 kilometers in radius and this is the maximal distance at which the Earths gravitational influence is stronger than the more distant Sun and planets. Objects orbiting the Earth must be within this radius, otherwise they can become unbound by the perturbation of the Sun
8.
Earth's rotation
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Earths rotation is the rotation of the planet Earth around its own axis. The Earth rotates from the west towards east, as viewed from North Star or polestar Polaris, the Earth turns counter-clockwise. The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is the point in the Northern Hemisphere where the Earths axis of rotation meets its surface and this point is distinct from the Earths North Magnetic Pole. The South Pole is the point where the Earths axis of rotation intersects its surface. The Earth rotates once in about 24 hours with respect to the sun, Earths rotation is slowing slightly with time, thus, a day was shorter in the past. This is due to the effects the Moon has on Earths rotation. Atomic clocks show that a modern-day is longer by about 1.7 milliseconds than a century ago, analysis of historical astronomical records shows a slowing trend of 2.3 milliseconds per century since the 8th century BCE. Among the ancient Greeks, several of the Pythagorean school believed in the rotation of the rather than the apparent diurnal rotation of the heavens. Perhaps the first was Philolaus, though his system was complicated, in the third century BCE, Aristarchus of Samos suggested the suns central place. However, Aristotle in the fourth century criticized the ideas of Philolaus as being based on rather than observation. He established the idea of a sphere of fixed stars that rotated about the earth and this was accepted by most of those who came after, in particular Claudius Ptolemy, who thought the earth would be devastated by gales if it rotated. In the 10th century, some Muslim astronomers accepted that the Earth rotates around its axis, treatises were written to discuss its possibility, either as refutations or expressing doubts about Ptolemys arguments against it. At the Maragha and Samarkand observatories, the Earths rotation was discussed by Tusi and Qushji, in medieval Europe, Thomas Aquinas accepted Aristotles view and so, reluctantly, did John Buridan and Nicole Oresme in the fourteenth century. Not until Nicolaus Copernicus in 1543 adopted a heliocentric world system did the earths rotation begin to be established, Copernicus pointed out that if the movement of the earth is violent, then the movement of the stars must be very much more so. He acknowledged the contribution of the Pythagoreans and pointed to examples of relative motion, for Copernicus this was the first step in establishing the simpler pattern of planets circling a central sun. Tycho Brahe, who produced accurate observations on which Kepler based his laws, in 1600, William Gilbert strongly supported the earths rotation in his treatise on the earths magnetism and thereby influenced many of his contemporaries. Those like Gilbert who did not openly support or reject the motion of the earth about the sun are often called semi-Copernicans, however, the contributions of Kepler, Galileo and Newton gathered support for the theory of the rotation of the Earth. The earths rotation implies that the bulges and the poles are flattened
9.
Sunrise
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Sunrise or sun up is the instant at which the upper edge of the Sun appears over the horizon in the morning. The term can refer to the entire process of the Sun crossing the horizon. Although the Sun appears to rise from the horizon, it is actually the Earths motion that causes the Sun to appear, architect Buckminster Fuller proposed the terms sunsight and sunclipse to better represent the heliocentric model, though the terms have not entered into common language. Astronomically, sunrise occurs for only an instant, the moment at which the limb of the Sun appears tangent to the horizon. However, the term commonly refers to periods of time both before and after this point, Twilight, the period in the morning during which the sky is light. The beginning of morning twilight is called dawn, the period after the Sun rises during which striking colors and atmospheric effects are still seen. Sunrise occurs before the Sun actually reaches the horizon because the Suns image is refracted by the Earths atmosphere, at the horizon, the average amount of refraction is 34 arcminutes, though this amount varies based on atmospheric conditions. Also, unlike most other measurements, sunrise occurs when the Suns upper limb, rather than its center. The apparent radius of the Sun at the horizon is 16 arcminutes and these two angles combine to define sunrise to occur when the Suns center is 50 arcminutes below the horizon, or 90. 83° from the zenith. The timing of sunrise varies throughout the year and is affected by the viewers longitude and latitude, altitude. The analemma can be used to make predictions of the time of sunrise. In late winter and spring, sunrise as seen from temperate latitudes occurs earlier each day, reaching its earliest time near the summer solstice, after this point, the time of sunrise gets later each day, reaching its latest sometime around the winter solstice. Variations in atmospheric refraction can alter the time of sunrise by changing its apparent position, near the poles, the time-of-day variation is exaggerated, since the Sun crosses the horizon at a very shallow angle and thus rises more slowly. Accounting for atmospheric refraction and measuring from the leading edge slightly increases the duration of day relative to night. Sunrises occur approximately due east on the March and September equinoxes for all viewers on Earth, exact calculations of the azimuths of sunrise on other dates are complex, but they can be estimated with reasonable accuracy by using the analemma. Air molecules and airborne particles scatter white sunlight as it passes through the Earths atmosphere and this is done by a combination of Rayleigh scattering and Mie scattering. Because the shorter wavelength components, such as blue and green, scatter more strongly, the remaining reddened sunlight can then be scattered by cloud droplets and other relatively large particles to light up the horizon red and orange. The removal of the wavelengths of light is due to Rayleigh scattering by air molecules and particles much smaller than the wavelength of visible light
10.
Sunset
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Sunset or sundown, is the daily disappearance of the Sun below the horizon as a result of Earths rotation. The Sun will set exactly due west at the equator on the spring and fall equinoxes, the time of sunset is defined in astronomy as the moment when the trailing edge of the Suns disk disappears below the horizon. Dusk is at the end of astronomical twilight, and is the darkest moment of twilight just before night. Sunset creates unique atmospheric conditions such as the intense orange and red colors of the Sun. The time of sunset varies throughout the year, and is determined by the position on Earth, specified by longitude and latitude. During winter and spring, the days get longer and sunsets occur later every day until the day of the latest sunset, in the Northern Hemisphere, the latest sunset occurs late in June or in early July, but not on the summer solstice of June 21. This date depends on the viewers latitude, likewise, the earliest sunset does not occur on the winter solstice, but rather about two weeks earlier, again depending on the viewers latitude. In the Northern Hemisphere, it occurs in early December or late November, for a few weeks surrounding both solstices, both sunrise and sunset get slightly later each day. Even on the equator, sunrise and sunset shift several minutes back and forth through the year and these effects are plotted by an analemma. Sunsets occur almost exactly due west on the equinoxes for all viewers on Earth, exact calculations of the azimuths of sunset on other dates are complex, but they can be estimated with reasonable accuracy by using the analemma. As sunrise and sunset are calculated from the leading and trailing edges of the Sun, respectively, and not the center, the duration of a daytime is slightly longer than nighttime. Further, because the light from the Sun is refracted as it passes through the Earths atmosphere, refraction also affects the apparent shape of the Sun when it is very close to the horizon. It makes things appear higher in the sky than they really are, light from the bottom edge of the Suns disk is refracted more than light from the top, since refraction increases as the angle of elevation decreases. This raises the apparent position of the edge more than the top. Its width is unaltered, so the disk appears wider than it is high, the Sun also appears larger on the horizon, an optical illusion, similar to the moon illusion. Because the shorter wavelength components, such as blue and green, scatter more strongly, the remaining reddened sunlight can then be scattered by cloud droplets and other relatively large particles to light up the horizon red and orange. The removal of the wavelengths of light is due to Rayleigh scattering by air molecules and particles much smaller than the wavelength of visible light. The scattering by cloud droplets and other particles with diameters comparable to or larger than the sunlights wavelengths is due to Mie scattering and is not strongly wavelength-dependent
11.
Center of mass
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The distribution of mass is balanced around the center of mass and the average of the weighted position coordinates of the distributed mass defines its coordinates. Calculations in mechanics are simplified when formulated with respect to the center of mass. It is a point where entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the equivalent of a given object for application of Newtons laws of motion. In the case of a rigid body, the center of mass is fixed in relation to the body. The center of mass may be located outside the body, as is sometimes the case for hollow or open-shaped objects. In the case of a distribution of separate bodies, such as the planets of the Solar System, in orbital mechanics, the equations of motion of planets are formulated as point masses located at the centers of mass. The center of mass frame is a frame in which the center of mass of a system is at rest with respect to the origin of the coordinate system. The concept of center of mass in the form of the center of gravity was first introduced by the ancient Greek physicist, mathematician, and engineer Archimedes of Syracuse. He worked with simplified assumptions about gravity that amount to a uniform field, in work on floating bodies he demonstrated that the orientation of a floating object is the one that makes its center of mass as low as possible. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes, Newtons second law is reformulated with respect to the center of mass in Eulers first law. The center of mass is the point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero. In analogy to statistics, the center of mass is the location of a distribution of mass in space. Solving this equation for R yields the formula R =1 M ∑ i =1 n m i r i, solve this equation for the coordinates R to obtain R =1 M ∭ Q ρ r d V, where M is the total mass in the volume. If a continuous mass distribution has density, which means ρ is constant. The center of mass is not generally the point at which a plane separates the distribution of mass into two equal halves, in analogy with statistics, the median is not the same as the mean. The coordinates R of the center of mass of a system, P1 and P2, with masses m1. The percentages of mass at each point can be viewed as projective coordinates of the point R on this line, another way of interpreting the process here is the mechanical balancing of moments about an arbitrary point
12.
Orbit of the Moon
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Not to be confused with Lunar orbit. The Moon orbits Earth in the direction and completes one revolution relative to the stars in approximately 27.323 days. Earth and the Moon orbit about their barycentre, which lies about 4,600 km from Earths center, on average, the Moon is at a distance of about 385,000 km from Earths centre, which corresponds to about 60 Earth radii. With a mean velocity of 1.022 km/s, the Moon appears to move relative to the stars each hour by an amount roughly equal to its angular diameter. The Moon differs from most satellites of planets in that its orbit is close to the plane of the ecliptic. The plane of the orbit is inclined to the ecliptic by about 5°. The properties of the orbit described in this section are approximations, the Moons orbit around Earth has many irregularities, whose study has a long history. The orbit of the Moon is distinctly elliptical, with an eccentricity of 0.0549. The non-circular form of the lunar orbit causes variations in the Moons angular speed and apparent size as it moves towards, the mean angular movement relative to an imaginary observer at the barycentre is 13. 176° per day to the east. The Moons elongation is its angular distance east of the Sun at any time, at new moon, it is zero and the Moon is said to be in conjunction. At full moon, the elongation is 180° and it is said to be in opposition, in both cases, the Moon is in syzygy, that is, the Sun, Moon and Earth are nearly aligned. When elongation is either 90° or 270°, the Moon is said to be in quadrature, the orientation of the orbit is not fixed in space, but rotates over time. This orbital precession is also called apsidal precession and is the rotation of the Moons orbit within the orbital plane, the Moons apsidal precession is distinct from, and should not be confused with its axial precession. The mean inclination of the orbit to the ecliptic plane is 5. 145°. The rotational axis of the Moon is also not perpendicular to its plane, so the lunar equator is not in the plane of its orbit. Therefore, the angle between the ecliptic and the equator is always 1. 543°, even though the rotational axis of the Moon is not fixed with respect to the stars. The period from moonrise to moonrise at the poles is quite close to the sidereal period, when the sun is the furthest below the horizon, the moon will be full when it is at its highest point. The nodes are points at which the Moons orbit crosses the ecliptic, the Moon crosses the same node every 27.2122 days, an interval called the draconic or draconitic month
13.
Perturbation (astronomy)
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In astronomy, perturbation is the complex motion of a massive body subject to forces other than the gravitational attraction of a single other massive body. The other forces can include a body, resistance, as from an atmosphere. The study of perturbations began with the first attempts to predict planetary motions in the sky, in ancient times the causes were a mystery. Newton, at the time he formulated his laws of motion and of gravitation, applied them to the first analysis of perturbations, the complex motions of gravitational perturbations can be broken down. The hypothetical motion that the body follows under the effect of one other body only is typically a conic section. This is called a problem, or an unperturbed Keplerian orbit. The differences between that and the motion of the body are perturbations due to the additional gravitational effects of the remaining body or bodies. If there is one other significant body then the perturbed motion is a three-body problem. A general analytical solution exists for the problem, when more than two bodies are considered analytic solutions exist only for special cases. Even the two-body problem becomes insoluble if one of the bodies is irregular in shape, most systems that involve multiple gravitational attractions present one primary body which is dominant in its effects. The gravitational effects of the bodies can be treated as perturbations of the hypothetical unperturbed motion of the planet or satellite around its primary body. In methods of general perturbations, general differential equations, either of motion or of change in the elements, are solved analytically, usually by series expansions. The result is expressed in terms of algebraic and trigonometric functions of the orbital elements of the body in question. This can be applied generally to many different sets of conditions, historically, general perturbations were investigated first. The classical methods are known as variation of the elements, variation of parameters or variation of the constants of integration, in these methods, it is considered that the body is always moving in a conic section, however the conic section is constantly changing due to the perturbations. General perturbations is applicable if the perturbing forces are about one order of magnitude smaller, or less. In the Solar System, this is usually the case, Jupiter, general perturbation methods are preferred for some types of problems, as the source of certain observed motions are readily found. In effect, the positions and velocities are perturbed directly, special perturbations can be applied to any problem in celestial mechanics, as it is not limited to cases where the perturbing forces are small
14.
Planet
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The term planet is ancient, with ties to history, astrology, science, mythology, and religion. Several planets in the Solar System can be seen with the naked eye and these were regarded by many early cultures as divine, or as emissaries of deities. As scientific knowledge advanced, human perception of the planets changed, in 2006, the International Astronomical Union officially adopted a resolution defining planets within the Solar System. This definition is controversial because it excludes many objects of mass based on where or what they orbit. The planets were thought by Ptolemy to orbit Earth in deferent, at about the same time, by careful analysis of pre-telescopic observation data collected by Tycho Brahe, Johannes Kepler found the planets orbits were not circular but elliptical. As observational tools improved, astronomers saw that, like Earth, the planets rotated around tilted axes, and some shared such features as ice caps and seasons. Since the dawn of the Space Age, close observation by space probes has found that Earth and the planets share characteristics such as volcanism, hurricanes, tectonics. Planets are generally divided into two types, large low-density giant planets, and smaller rocky terrestrials. Under IAU definitions, there are eight planets in the Solar System, in order of increasing distance from the Sun, they are the four terrestrials, Mercury, Venus, Earth, and Mars, then the four giant planets, Jupiter, Saturn, Uranus, and Neptune. Six of the planets are orbited by one or more natural satellites, several thousands of planets around other stars have been discovered in the Milky Way. e. in the habitable zone. On December 20,2011, the Kepler Space Telescope team reported the discovery of the first Earth-sized extrasolar planets, Kepler-20e and Kepler-20f, orbiting a Sun-like star, Kepler-20. A2012 study, analyzing gravitational microlensing data, estimates an average of at least 1.6 bound planets for every star in the Milky Way, around one in five Sun-like stars is thought to have an Earth-sized planet in its habitable zone. The idea of planets has evolved over its history, from the lights of antiquity to the earthly objects of the scientific age. The concept has expanded to include not only in the Solar System. The ambiguities inherent in defining planets have led to much scientific controversy, the five classical planets, being visible to the naked eye, have been known since ancient times and have had a significant impact on mythology, religious cosmology, and ancient astronomy. In ancient times, astronomers noted how certain lights moved across the sky, as opposed to the fixed stars, ancient Greeks called these lights πλάνητες ἀστέρες or simply πλανῆται, from which todays word planet was derived. In ancient Greece, China, Babylon, and indeed all pre-modern civilizations, it was almost universally believed that Earth was the center of the Universe and that all the planets circled Earth. The first civilization known to have a theory of the planets were the Babylonians
15.
Solar System
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The Solar System is the gravitationally bound system comprising the Sun and the objects that orbit it, either directly or indirectly. Of those objects that orbit the Sun directly, the largest eight are the planets, with the remainder being significantly smaller objects, such as dwarf planets, of the objects that orbit the Sun indirectly, the moons, two are larger than the smallest planet, Mercury. The Solar System formed 4.6 billion years ago from the collapse of a giant interstellar molecular cloud. The vast majority of the mass is in the Sun. The four smaller inner planets, Mercury, Venus, Earth and Mars, are terrestrial planets, being composed of rock. The four outer planets are giant planets, being more massive than the terrestrials. All planets have almost circular orbits that lie within a flat disc called the ecliptic. The Solar System also contains smaller objects, the asteroid belt, which lies between the orbits of Mars and Jupiter, mostly contains objects composed, like the terrestrial planets, of rock and metal. Beyond Neptunes orbit lie the Kuiper belt and scattered disc, which are populations of trans-Neptunian objects composed mostly of ices, within these populations are several dozen to possibly tens of thousands of objects large enough that they have been rounded by their own gravity. Such objects are categorized as dwarf planets, identified dwarf planets include the asteroid Ceres and the trans-Neptunian objects Pluto and Eris. In addition to two regions, various other small-body populations, including comets, centaurs and interplanetary dust clouds. Six of the planets, at least four of the dwarf planets, each of the outer planets is encircled by planetary rings of dust and other small objects. The solar wind, a stream of charged particles flowing outwards from the Sun, the heliopause is the point at which pressure from the solar wind is equal to the opposing pressure of the interstellar medium, it extends out to the edge of the scattered disc. The Oort cloud, which is thought to be the source for long-period comets, the Solar System is located in the Orion Arm,26,000 light-years from the center of the Milky Way. For most of history, humanity did not recognize or understand the concept of the Solar System, the invention of the telescope led to the discovery of further planets and moons. The principal component of the Solar System is the Sun, a G2 main-sequence star that contains 99. 86% of the known mass. The Suns four largest orbiting bodies, the giant planets, account for 99% of the mass, with Jupiter. The remaining objects of the Solar System together comprise less than 0. 002% of the Solar Systems total mass, most large objects in orbit around the Sun lie near the plane of Earths orbit, known as the ecliptic
16.
Barycenter
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The barycenter is the center of mass of two or more bodies that are orbiting each other, or the point around which they both orbit. It is an important concept in such as astronomy and astrophysics. The distance from a center of mass to the barycenter can be calculated as a simple two-body problem. In cases where one of the two objects is more massive than the other, the barycenter will typically be located within the more massive object. Rather than appearing to orbit a center of mass with the smaller body. This is the case for the Earth–Moon system, where the barycenter is located on average 4,671 km from the Earths center, when the two bodies are of similar masses, the barycenter will generally be located between them and both bodies will follow an orbit around it. This is the case for Pluto and Charon, as well as for many binary asteroids and it is also the case for Jupiter and the Sun, despite the thousandfold difference in mass, due to the relatively large distance between them. In astronomy, barycentric coordinates are non-rotating coordinates with the origin at the center of mass of two or more bodies, the International Celestial Reference System is a barycentric one, based on the barycenter of the Solar System. In geometry, the barycenter is synonymous with centroid, the geometric center of a two-dimensional shape. The barycenter is one of the foci of the orbit of each body. This is an important concept in the fields of astronomy and astrophysics. If a is the distance between the centers of the two bodies, r1 is the axis of the primarys orbit around the barycenter. When the barycenter is located within the massive body, that body will appear to wobble rather than to follow a discernible orbit. The following table sets out some examples from the Solar System, figures are given rounded to three significant figures. If Jupiter had Mercurys orbit, the Sun–Jupiter barycenter would be approximately 55,000 km from the center of the Sun, but even if the Earth had Eris orbit, the Sun–Earth barycenter would still be within the Sun. To calculate the motion of the Sun, you would need to sum all the influences from all the planets, comets, asteroids. If all the planets were aligned on the side of the Sun. The calculations above are based on the distance between the bodies and yield the mean value r1
17.
Sidereal time
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Sidereal time /saɪˈdɪəriəl/ is a time-keeping system that astronomers use to locate celestial objects. Using sidereal time it is possible to point a telescope to the proper coordinates in the night sky. Briefly, sidereal time is a scale that is based on Earths rate of rotation measured relative to the fixed stars rather than the Sun. From a given point, a star found at one location in the sky will be found at the same location on another night at the same sidereal time. This is similar to how the time kept by a sundial can be used to find the location of the Sun, just as the Sun and Moon appear to rise in the east and set in the west due to the rotation of Earth, so do the stars. Both solar time and sidereal time make use of the regularity of Earths rotation about its polar axis, a mean sidereal day is 23 hours,56 minutes,4.0916 seconds, the time it takes Earth to make one rotation relative to the vernal equinox. The longer true sidereal period is called a day by the International Earth Rotation. It is also referred to as the period of rotation. Maps of the stars in the night sky use declination and right ascension as coordinates and these correspond to latitude and longitude respectively. In the sky, the meridian is the north to south line that goes through the point directly overhead. Solar time is measured by the apparent diurnal motion of the Sun, a mean solar day is the average time between local solar noons. Earth makes one rotation around its axis in a sidereal day, so after a sidereal day has passed, Earth still needs to rotate slightly more before the Sun reaches local noon according to solar time. A mean solar day is, therefore, nearly 4 minutes longer than a sidereal day, the stars are so far away that Earths movement along its orbit makes nearly no difference to their apparent direction, and so they return to their highest point in a sidereal day. Another way to see this difference is to notice that, relative to the stars, therefore, there is one fewer solar day per year than there are sidereal days. This makes a sidereal day approximately 365. 24/366.24 times the length of the 24-hour solar day, Earths rotation is not a simple rotation around an axis that would always remain parallel to itself. Earths rotational axis itself rotates about an axis, orthogonal to Earths orbit. This phenomenon is called the precession of the equinoxes, because of this precession, the stars appear to move around Earth in a manner more complicated than a simple constant rotation. In this reference frame, Earths rotation is close to constant and it is also in this reference frame that the tropical year, the year related to Earths seasons, represents one orbit of Earth around the Sun
18.
Equation of time
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The equation of time describes the discrepancy between two kinds of solar time. The word equation is used in the sense of reconcile a difference. The two times that differ are the apparent solar time, which tracks the motion of the sun, and mean solar time. Apparent solar time can be obtained by measurement of the current position of the Sun, Mean solar time, for the same place, would be the time indicated by a steady clock set so that over the year its differences from apparent solar time would resolve to zero. The equation of time is the east or west component of the analemma, the equation of time values for each day of the year, compiled by astronomical observatories, were widely listed in almanacs and ephemerides. During a year the equation of time varies as shown on the graph, apparent time, and the sundial, can be ahead by as much as 16 min 33 s, or behind by as much as 14 min 6 s. The equation of time has zeros near 15 April,13 June,1 September and 25 December, ignoring very slow changes in the Earths orbit and rotation, these events are repeated at the same times every tropical year. However, due to the number of days in a year. The equation of time is constant only for a planet with zero axial tilt, on Mars the difference between sundial time and clock time can be as much as 50 minutes, due to the considerably greater eccentricity of its orbit. The planet Uranus, which has a large axial tilt, has an equation of time that makes its days start. There is no accepted definition of the sign of the equation of time. Some publications show it as positive when a sundial is ahead of a clock, as shown in the graph above, others when the clock is ahead of the sundial. In the English-speaking world, the usage is the more common. Anyone who makes use of a table or graph should first check its sign usage. Often, there is a note or caption which explains it, otherwise, the sign can be determined by knowing that, during the first three months of each year, the clock is ahead of the sundial. The mnemonic NYSS, for new year, sundial slow, can be useful, some published tables avoid the ambiguity by not using signs, but by showing phrases such as sundial fast or sundial slow instead. In this article, and others in English Wikipedia, a value of the equation of time implies that a sundial is ahead of a clock. The phrase equation of time is derived from the medieval Latin, the word aequātiō was widely used in early astronomy to tabulate the difference between an observed value and the expected value
19.
Axial tilt
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In astronomy, axial tilt, also known as obliquity, is the angle between an objects rotational axis and its orbital axis, or, equivalently, the angle between its equatorial plane and orbital plane. At an obliquity of zero, the two axes point in the direction, i. e. the rotational axis is perpendicular to the orbital plane. Over the course of an orbit, the obliquity usually does not change considerably, and this causes one pole to be directed more toward the Sun on one side of the orbit, and the other pole on the other side — the cause of the seasons on the Earth. Earths obliquity oscillates between 22.1 and 24.5 degrees on a 41, 000-year cycle, the mean obliquity is currently 23°26′13. 4″. There are two methods of specifying tilt. The IAU also uses the rule to define a positive pole for the purpose of determining orientation. Using this convention, Venus is tilted 177° and it is denoted by the Greek letter ε. Earth currently has a tilt of about 23. 4°. This value remains about the relative to a stationary orbital plane throughout the cycles of axial precession. But the ecliptic due to planetary perturbations, and the obliquity of the ecliptic is not a fixed quantity. At present, it is decreasing at a rate of about 47″ per century, Earths obliquity may have been reasonably accurately measured as early as 1100 BC in India and China. The ancient Greeks had good measurements of the obliquity since about 350 BC, about 830 AD, the Caliph Al-Mamun of Baghdad directed his astronomers to measure the obliquity, and the result was used in the Arab world for many years. It was widely believed, during the Middle Ages, that both precession and Earths obliquity oscillated around a value, with a period of 672 years. Earths axis remains tilted in the direction with reference to the background stars throughout a year. This means that one pole will be directed away from the Sun at one side of the orbit and this is the cause of Earths seasons. Summer occurs in the Northern hemisphere when the pole is directed toward the Sun. Variations in Earths axial tilt can influence the seasons and is likely a factor in climate change. The exact angular value of the obliquity is found by observation of the motions of Earth, from 1984, the Jet Propulsion Laboratorys DE series of computer-generated ephemerides took over as the fundamental ephemeris of the Astronomical Almanac
20.
Plane (geometry)
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In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far. A plane is the analogue of a point, a line. When working exclusively in two-dimensional Euclidean space, the article is used, so. Many fundamental tasks in mathematics, geometry, trigonometry, graph theory and graphing are performed in a space, or in other words. Euclid set forth the first great landmark of mathematical thought, a treatment of geometry. He selected a small core of undefined terms and postulates which he used to prove various geometrical statements. Although the plane in its sense is not directly given a definition anywhere in the Elements. In his work Euclid never makes use of numbers to measure length, angle, in this way the Euclidean plane is not quite the same as the Cartesian plane. This section is concerned with planes embedded in three dimensions, specifically, in R3. In a Euclidean space of any number of dimensions, a plane is determined by any of the following. A line and a point not on that line, a line is either parallel to a plane, intersects it at a single point, or is contained in the plane. Two distinct lines perpendicular to the plane must be parallel to each other. Two distinct planes perpendicular to the line must be parallel to each other. Specifically, let r0 be the vector of some point P0 =. The plane determined by the point P0 and the vector n consists of those points P, with position vector r, such that the vector drawn from P0 to P is perpendicular to n. Recalling that two vectors are perpendicular if and only if their dot product is zero, it follows that the plane can be described as the set of all points r such that n ⋅ =0. Expanded this becomes a + b + c =0, which is the form of the equation of a plane. This is just a linear equation a x + b y + c z + d =0 and this familiar equation for a plane is called the general form of the equation of the plane
21.
Orbit
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In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet about a star or a natural satellite around a planet. Normally, orbit refers to a regularly repeating path around a body, to a close approximation, planets and satellites follow elliptical orbits, with the central mass being orbited at a focal point of the ellipse, as described by Keplers laws of planetary motion. For ease of calculation, in most situations orbital motion is adequately approximated by Newtonian Mechanics, historically, the apparent motions of the planets were described by European and Arabic philosophers using the idea of celestial spheres. This model posited the existence of perfect moving spheres or rings to which the stars and it assumed the heavens were fixed apart from the motion of the spheres, and was developed without any understanding of gravity. After the planets motions were accurately measured, theoretical mechanisms such as deferent. Originally geocentric it was modified by Copernicus to place the sun at the centre to help simplify the model, the model was further challenged during the 16th century, as comets were observed traversing the spheres. The basis for the understanding of orbits was first formulated by Johannes Kepler whose results are summarised in his three laws of planetary motion. Second, he found that the speed of each planet is not constant, as had previously been thought. Third, Kepler found a relationship between the orbital properties of all the planets orbiting the Sun. For the planets, the cubes of their distances from the Sun are proportional to the squares of their orbital periods. Jupiter and Venus, for example, are respectively about 5.2 and 0.723 AU distant from the Sun, their orbital periods respectively about 11.86 and 0.615 years. The proportionality is seen by the fact that the ratio for Jupiter,5. 23/11.862, is equal to that for Venus,0. 7233/0.6152. Idealised orbits meeting these rules are known as Kepler orbits, isaac Newton demonstrated that Keplers laws were derivable from his theory of gravitation and that, in general, the orbits of bodies subject to gravity were conic sections. Newton showed that, for a pair of bodies, the sizes are in inverse proportion to their masses. Where one body is more massive than the other, it is a convenient approximation to take the center of mass as coinciding with the center of the more massive body. Lagrange developed a new approach to Newtonian mechanics emphasizing energy more than force, in a dramatic vindication of classical mechanics, in 1846 le Verrier was able to predict the position of Neptune based on unexplained perturbations in the orbit of Uranus. This led astronomers to recognize that Newtonian mechanics did not provide the highest accuracy in understanding orbits, in relativity theory, orbits follow geodesic trajectories which are usually approximated very well by the Newtonian predictions but the differences are measurable. Essentially all the evidence that can distinguish between the theories agrees with relativity theory to within experimental measurement accuracy
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Equator
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The Equator usually refers to an imaginary line on the Earths surface equidistant from the North Pole and South Pole, dividing the Earth into the Northern Hemisphere and Southern Hemisphere. The Equator is about 40,075 kilometres long, some 78. 7% lies across water and 21. 3% over land, other planets and astronomical bodies have equators similarly defined. Generally, an equator is the intersection of the surface of a sphere with the plane that is perpendicular to the spheres axis of rotation. The latitude of the Earths equator is by definition 0° of arc, the equator is the only line of latitude which is also a great circle — that is, one whose plane passes through the center of the globe. The plane of Earths equator when projected outwards to the celestial sphere defines the celestial equator, in the cycle of Earths seasons, the plane of the equator passes through the Sun twice per year, at the March and September equinoxes. To an observer on the Earth, the Sun appears to travel North or South over the equator at these times, light rays from the center of the Sun are perpendicular to the surface of the Earth at the point of solar noon on the Equator. Locations on the Equator experience the quickest sunrises and sunsets because the sun moves nearly perpendicular to the horizon for most of the year. The Earth bulges slightly at the Equator, the diameter of the Earth is 12,750 kilometres. Because the Earth spins to the east, spacecraft must also launch to the east to take advantage of this Earth-boost of speed, seasons result from the yearly revolution of the Earth around the Sun and the tilt of the Earths axis relative to the plane of revolution. During the year the northern and southern hemispheres are inclined toward or away from the sun according to Earths position in its orbit, the hemisphere inclined toward the sun receives more sunlight and is in summer, while the other hemisphere receives less sun and is in winter. At the equinoxes, the Earths axis is not tilted toward the sun, instead it is perpendicular to the sun meaning that the day is about 12 hours long, as is the night, across the whole of the Earth. Near the Equator there is distinction between summer, winter, autumn, or spring. The temperatures are usually high year-round—with the exception of high mountains in South America, the temperature at the Equator can plummet during rainstorms. In many tropical regions people identify two seasons, the wet season and the dry season, but many places close to the Equator are on the oceans or rainy throughout the year, the seasons can vary depending on elevation and proximity to an ocean. The Equator lies mostly on the three largest oceans, the Pacific Ocean, the Atlantic Ocean, and the Indian Ocean. The highest point on the Equator is at the elevation of 4,690 metres, at 0°0′0″N 77°59′31″W and this is slightly above the snow line, and is the only place on the Equator where snow lies on the ground. At the Equator the snow line is around 1,000 metres lower than on Mount Everest, the Equator traverses the land of 11 countries, it also passes through two island nations, though without making a landfall in either. Starting at the Prime Meridian and heading eastwards, the Equator passes through, Despite its name, however, its island of Annobón is 155 km south of the Equator, and the rest of the country lies to the north
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Great circle
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A great circle, also known as an orthodrome or Riemannian circle, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere. This partial case of a circle of a sphere is opposed to a circle, the intersection of the sphere. Any diameter of any great circle coincides with a diameter of the sphere, and therefore all great circles have the same circumference as each other, a great circle is the largest circle that can be drawn on any given sphere. Every circle in Euclidean 3-space is a circle of exactly one sphere. For most pairs of points on the surface of a sphere, there is a great circle through the two points. The exception is a pair of points, for which there are infinitely many great circles. The minor arc of a circle between two points is the shortest surface-path between them. In this sense, the arc is analogous to “straight lines” in Euclidean geometry. The length of the arc of a great circle is taken as the distance between two points on a surface of a sphere in Riemannian geometry. The great circles are the geodesics of the sphere, in higher dimensions, the great circles on the n-sphere are the intersection of the n-sphere with 2-planes that pass through the origin in the Euclidean space Rn+1. To prove that the arc of a great circle is the shortest path connecting two points on the surface of a sphere, one can apply calculus of variations to it. Consider the class of all paths from a point p to another point q. Introduce spherical coordinates so that p coincides with the north pole. Any curve on the sphere that does not intersect either pole, except possibly at the endpoints, can be parametrized by θ = θ, ϕ = ϕ, a ≤ t ≤ b provided we allow φ to take on arbitrary real values. The infinitesimal arc length in these coordinates is d s = r θ ′2 + ϕ ′2 sin 2 θ d t. So the length of a curve γ from p to q is a functional of the curve given by S = r ∫ a b θ ′2 + ϕ ′2 sin 2 θ d t. Note that S is at least the length of the meridian from p to q, S ≥ r ∫ a b | θ ′ | d t ≥ r | θ − θ |. Since the starting point and ending point are fixed, S is minimized if and only if φ =0, so the curve must lie on a meridian of the sphere φ = φ0 = constant
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Equinox
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An equinox is the moment in which the plane of Earths equator passes through the center of the Sun, which occurs twice each year, around 20 March and 23 September. On an equinox, day and night are of equal duration all over the planet. They are not exactly equal, however, due to the size of the sun. To avoid this ambiguity, the word equilux is sometimes used to mean a day in which the durations of light, see Length of equinoctial day and night for further discussion. The word is derived from the Latin aequinoctium, aequus and nox, the equinoxes are the only times when the solar terminator is perpendicular to the equator. As a result, the northern and southern hemispheres are equally illuminated, the word comes from Latin equi or equal and nox meaning night. In other words, the equinoxes are the times when the subsolar point is on the equator. The subsolar point crosses the equator moving northward at the March equinox, the equinoxes, along with solstices, are directly related to the seasons of the year. In the southern hemisphere, the equinox occurs in September. When Julius Caesar established the Julian calendar in 45 BC, he set 25 March as the date of the spring equinox. Because the Julian year is longer than the tropical year. By 1500 AD, it had drifted backwards to 11 March and this drift induced Pope Gregory XIII to create a modern Gregorian calendar. However, the leap year intervals in his calendar were not smooth and this causes the equinox to oscillate by about 53 hours around its mean position. This in turn raised the possibility that it could fall on 22 March, the astronomers chose the appropriate number of days to omit so that the equinox would swing from 19 to 21 March but never fall on the 22nd. Vernal equinox and Autumnal equinox, these names are direct derivatives of Latin. The equivalent common language English terms spring equinox and autumn equinox are even more ambiguous, March equinox and September equinox, names referring to the months of the year they occur, with no ambiguity as to which hemisphere is the context. They are still not universal, however, as not all use a solar-based calendar where the equinoxes occur every year in the same month. Northward equinox and southward equinox, names referring to the apparent direction of motion of the Sun
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Perpendicular
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In elementary geometry, the property of being perpendicular is the relationship between two lines which meet at a right angle. The property extends to other related geometric objects, a line is said to be perpendicular to another line if the two lines intersect at a right angle. Perpendicularity can be shown to be symmetric, meaning if a first line is perpendicular to a second line, for this reason, we may speak of two lines as being perpendicular without specifying an order. Perpendicularity easily extends to segments and rays, in symbols, A B ¯ ⊥ C D ¯ means line segment AB is perpendicular to line segment CD. A line is said to be perpendicular to an if it is perpendicular to every line in the plane that it intersects. This definition depends on the definition of perpendicularity between lines, two planes in space are said to be perpendicular if the dihedral angle at which they meet is a right angle. Perpendicularity is one instance of the more general mathematical concept of orthogonality, perpendicularity is the orthogonality of classical geometric objects. Thus, in advanced mathematics, the perpendicular is sometimes used to describe much more complicated geometric orthogonality conditions. The word foot is used in connection with perpendiculars. This usage is exemplified in the top diagram, above, the diagram can be in any orientation. The foot is not necessarily at the bottom, step 2, construct circles centered at A and B having equal radius. Let Q and R be the points of intersection of two circles. Step 3, connect Q and R to construct the desired perpendicular PQ, to prove that the PQ is perpendicular to AB, use the SSS congruence theorem for and QPB to conclude that angles OPA and OPB are equal. Then use the SAS congruence theorem for triangles OPA and OPB to conclude that angles POA, to make the perpendicular to the line g at or through the point P using Thales theorem, see the animation at right. The Pythagorean Theorem can be used as the basis of methods of constructing right angles, for example, by counting links, three pieces of chain can be made with lengths in the ratio 3,4,5. These can be out to form a triangle, which will have a right angle opposite its longest side. This method is useful for laying out gardens and fields, where the dimensions are large, the chains can be used repeatedly whenever required. If two lines are perpendicular to a third line, all of the angles formed along the third line are right angles
26.
Celestial equator
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The celestial equator is a great circle on the imaginary celestial sphere, in the same plane as the Earths equator. In other words, it is a projection of the terrestrial equator out into space, as a result of the Earths axial tilt, the celestial equator is inclined by 23. 4° with respect to the ecliptic plane. An observer standing on the Earths equator visualizes the celestial equator as a semicircle passing directly overhead through the zenith, as the observer moves north, the celestial equator tilts towards the opposite horizon. Celestial objects near the equator are visible worldwide, but they culminate the highest in the sky in the tropics. The celestial equator currently passes through these constellations, Celestial bodies other than Earth also have similarly defined celestial equators, Celestial pole Celestial sphere Declination Equatorial coordinate system
27.
Orbital node
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An orbital node is one of the two points where an orbit crosses a plane of reference to which it is inclined. An orbit that is contained in the plane of reference has no nodes, common planes of reference include, For a geocentric orbit, the Earths equatorial plane. In this case, non-inclined orbits are called equatorial, for a heliocentric orbit, the ecliptic. In this case, non-inclined orbits are called ecliptic, for an orbit outside the Solar System, the plane through the primary perpendicular to a line through the observer and the primary. If a reference direction from one side of the plane of reference to the other is defined, the two nodes can be distinguished. For geocentric and heliocentric orbits, the node is where the orbiting object moves north through the plane of reference. The position of the node may be used as one of a set of parameters, called orbital elements and this is done by specifying the longitude of the ascending node The line of nodes is the intersection of the objects orbital plane with the plane of reference. It passes through the two nodes, the symbol of the ascending node is, and the symbol of the descending node is. In medieval and early times the ascending and descending nodes were called the dragons head and dragons tail. These terms originally referred to the times when the Moon crossed the apparent path of the sun in the sky, also, corruptions of the Arabic term such as ganzaar, genzahar, geuzaar and zeuzahar were used in the medieval West to denote either of the nodes. Pp. 196–197, p.65, pp. 95–96, the Greek terms αναβιβάζων and καταβιβάζων were also used for the ascending and descending nodes, giving rise to the English words anabibazon and catabibazon. For the orbit of the Moon around the Earth, the plane is taken to be the ecliptic. The gravitational pull of the Sun upon the Moon causes its nodes, called the nodes, to precess gradually westward. Eclipse Euler angles Longitude of the ascending node
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Axial precession
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In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical bodys rotational axis. The term precession typically refers only to this largest part of the motion, other changes in the alignment of Earths axis—nutation and this term is still used in non-technical discussions, that is, when detailed mathematics are absent. Their combination was named general precession, instead of precession of the equinoxes, lunisolar precession is caused by the gravitational forces of the Moon and Sun on Earths equatorial bulge, causing Earths axis to move with respect to inertial space. Lunisolar precession is about 500 times greater than planetary precession, many references to the old terms exist in publications predating the change. Etymologically, precession and procession are both terms that relate to motion, Precession is derived from the Latin praecedere, to precede, to come before or earlier), while procession is derived from the Latin procedere, to march forward, to advance). Generally the term procession is used to describe a group of objects moving forward, the stars viewed from Earth are seen to proceed in a procession from east to west daily, due to the Earth’s diurnal motion, and yearly, due to the Earth’s revolution around the Sun. At the same time the stars can be observed to anticipate slightly such motion, at the rate of approximately 50 arc seconds per year, in describing this motion astronomers generally have shortened the term to simply precession. This issue is further obfuscated by the fact that many astronomers are physicists or astrophysicists, the precession of the Earths axis has a number of observable effects. First, the positions of the south and north celestial poles appear to move in circles against the backdrop of stars. Thus, while today the star Polaris lies approximately at the celestial pole, this will change over time. In approximately 3200 years, the star Gamma Cephei in the Cepheus constellation will succeed Polaris for this position, the south celestial pole currently lacks a bright star to mark its position, but over time precession also will cause bright stars to become south stars. As the celestial poles shift, there is a gradual shift in the apparent orientation of the whole star field. Secondly, the position of the Earth in its orbit around the Sun at the solstices, equinoxes, or other time defined relative to the seasons, slowly changes. For example, suppose that the Earths orbital position is marked at the summer solstice, in other words, the solstice occurred a little earlier in the orbit. Thus, the year, measuring the cycle of seasons, is about 20 minutes shorter than the sidereal year. For further details, see Changing pole stars and Polar shift and equinoxes shift, according to Ptolemys Almagest, Hipparchus measured the longitude of Spica and other bright stars. Comparing his measurements with data from his predecessors, Timocharis and Aristillus and he also compared the lengths of the tropical year and the sidereal year, and found a slight discrepancy. Virtually all of the writings of Hipparchus are lost, including his work on precession and they are mentioned by Ptolemy, who explains precession as the rotation of the celestial sphere around a motionless Earth
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Orbital pole
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An orbital pole is either end of an imaginary line running through the center of an orbit perpendicular to the orbital plane, projected onto the celestial sphere. It is similar in concept to a pole but based on the planets orbit instead of the planets rotation. The orbital pole of the earth is referred to as the Ecliptic pole, the ecliptic poles are the points on the celestial sphere where it meets the imaginary line perpendicular to the ecliptic plane, in which the Earth travels on its orbit around the Sun. There are two poles, Due to precession, the celestial pole moves in a circle around the ecliptic poles once every 25,800 years. It is not possible to have a pole at the zenith in a dark sky. By definition, the poles are located 90 degrees from the Suns position. Therefore, whenever either ecliptic pole is directly overhead, the Sun must be on the horizon, the ecliptic poles can be at the zenith on the Arctic and Antarctic Circles
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Precession
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Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, in other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called nutation, in physics, there are two types of precession, torque-free and torque-induced. In astronomy, precession refers to any of several changes in an astronomical bodys rotational or orbital parameters. An important example is the change in the orientation of the axis of rotation of the Earth. Torque-free precession implies that no moment is applied to the body. In torque-free precession, the momentum is a constant. What makes this possible is a moment of inertia, or more precisely. The inertia matrix is composed of the moments of inertia of a body calculated with respect to coordinate axes. If an object is asymmetric about its axis of rotation. The result is that the component of the velocities of the body about each axis will vary inversely with each axis moment of inertia. When an object is not perfectly solid, internal vortices will tend to damp torque-free precession, R new = exp R old for the skew-symmetric matrix ×. Torque-induced precession is the phenomenon in which the axis of a spinning object describes a cone in space when a torque is applied to it. The phenomenon is seen in a spinning toy top. If the speed of the rotation and the magnitude of the external torque are constant, the spin axis will move at right angles to the direction that would intuitively result from the external torque. In the case of a toy top, its weight is acting downwards from its center of mass and these two opposite forces produce a torque which causes the top to precess. The device depicted on the right is gimbal mounted, from inside to outside there are three axes of rotation, the hub of the wheel, the gimbal axis, and the vertical pivot. To distinguish between the two axes, rotation around the wheel hub will be called spinning, and rotation around the gimbal axis will be called pitching
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Moon
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The Moon is an astronomical body that orbits planet Earth, being Earths only permanent natural satellite. It is the fifth-largest natural satellite in the Solar System, following Jupiters satellite Io, the Moon is second-densest satellite among those whose densities are known. The average distance of the Moon from the Earth is 384,400 km, the Moon is thought to have formed about 4.51 billion years ago, not long after Earth. It is the second-brightest regularly visible celestial object in Earths sky, after the Sun and its surface is actually dark, although compared to the night sky it appears very bright, with a reflectance just slightly higher than that of worn asphalt. Its prominence in the sky and its cycle of phases have made the Moon an important cultural influence since ancient times on language, calendars, art. The Moons gravitational influence produces the ocean tides, body tides, and this matching of apparent visual size will not continue in the far future. The Moons linear distance from Earth is currently increasing at a rate of 3.82 ±0.07 centimetres per year, since the Apollo 17 mission in 1972, the Moon has been visited only by uncrewed spacecraft. The usual English proper name for Earths natural satellite is the Moon, the noun moon is derived from moone, which developed from mone, which is derived from Old English mōna, which ultimately stems from Proto-Germanic *mǣnōn, like all Germanic language cognates. Occasionally, the name Luna is used, in literature, especially science fiction, Luna is used to distinguish it from other moons, while in poetry, the name has been used to denote personification of our moon. The principal modern English adjective pertaining to the Moon is lunar, a less common adjective is selenic, derived from the Ancient Greek Selene, from which is derived the prefix seleno-. Both the Greek Selene and the Roman goddess Diana were alternatively called Cynthia, the names Luna, Cynthia, and Selene are reflected in terminology for lunar orbits in words such as apolune, pericynthion, and selenocentric. The name Diana is connected to dies meaning day, several mechanisms have been proposed for the Moons formation 4.51 billion years ago, and some 60 million years after the origin of the Solar System. These hypotheses also cannot account for the angular momentum of the Earth–Moon system. This hypothesis, although not perfect, perhaps best explains the evidence, eighteen months prior to an October 1984 conference on lunar origins, Bill Hartmann, Roger Phillips, and Jeff Taylor challenged fellow lunar scientists, You have eighteen months. Go back to your Apollo data, go back to computer, do whatever you have to. Dont come to our conference unless you have something to say about the Moons birth, at the 1984 conference at Kona, Hawaii, the giant impact hypothesis emerged as the most popular. Afterward there were only two groups, the giant impact camp and the agnostics. Giant impacts are thought to have been common in the early Solar System, computer simulations of a giant impact have produced results that are consistent with the mass of the lunar core and the present angular momentum of the Earth–Moon system
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Figure of the Earth
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The expression figure of the Earth has various meanings in geodesy according to the way it is used and the precision with which the Earths size and shape is to be defined. The actual topographic surface is most apparent with its variety of land forms and this is, in fact, the surface on which actual Earth measurements are made. The topographic surface is generally the concern of topographers and hydrographers, the Pythagorean concept of a spherical Earth offers a simple surface that is mathematically easy to deal with. Many astronomical and navigational computations use it as a representing the Earth. The idea of a planar or flat surface for Earth, however, is sufficient for surveys of small areas, as the local topography is far more significant than the curvature. Plane-table surveys are made for small areas, and no account is taken of the curvature of the Earth. A survey of a city would likely be computed as though the Earth were a surface the size of the city. For such small areas, exact positions can be determined relative to each other without considering the size, in the mid- to late 20th century, research across the geosciences contributed to drastic improvements in the accuracy of the figure of the Earth. The primary utility of this improved accuracy was to provide geographical and gravitational data for the guidance systems of ballistic missiles. This funding also drove the expansion of geoscientific disciplines, fostering the creation, the models for the figure of the Earth vary in the way they are used, in their complexity, and in the accuracy with which they represent the size and shape of the Earth. The simplest model for the shape of the entire Earth is a sphere, the Earths radius is the distance from Earths center to its surface, about 6,371 kilometers. The concept of a spherical Earth dates back to around the 6th century BC, the first scientific estimation of the radius of the earth was given by Eratosthenes about 240 BC, with estimates of the accuracy of Eratosthenes’s measurement ranging from 2% to 15%. The Earth is only approximately spherical, so no single value serves as its natural radius, distances from points on the surface to the center range from 6,353 km to 6,384 km. Several different ways of modeling the Earth as a sphere each yield a mean radius of 6,371 kilometers, regardless of the model, any radius falls between the polar minimum of about 6,357 km and the equatorial maximum of about 6,378 km. The difference 21 kilometers correspond to the polar radius being approximately 0. 3% shorter than the equator radius, since the Earth is flattened at the poles and bulges at the equator, geodesy represents the shape of the earth with an oblate spheroid. The oblate spheroid, or oblate ellipsoid, is an ellipsoid of revolution obtained by rotating an ellipse about its shorter axis and it is the regular geometric shape that most nearly approximates the shape of the Earth. A spheroid describing the figure of the Earth or other body is called a reference ellipsoid. The reference ellipsoid for Earth is called an Earth ellipsoid, an ellipsoid of revolution is uniquely defined by two numbers, two dimensions, or one dimension and a number representing the difference between the two dimensions
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Minute and second of arc
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A minute of arc, arcminute, arc minute, or minute arc is a unit of angular measurement equal to 1/60 of one degree. Since one degree is 1/360 of a turn, one minute of arc is 1/21600 of a turn, a second of arc, arcsecond, or arc second is 1/60 of an arcminute, 1/3600 of a degree, 1/1296000 of a turn, and π/648000 of a radian. To express even smaller angles, standard SI prefixes can be employed, the number of square arcminutes in a complete sphere is 4 π2 =466560000 π ≈148510660 square arcminutes. The standard symbol for marking the arcminute is the prime, though a single quote is used where only ASCII characters are permitted. One arcminute is thus written 1′ and it is also abbreviated as arcmin or amin or, less commonly, the prime with a circumflex over it. The standard symbol for the arcsecond is the prime, though a double quote is commonly used where only ASCII characters are permitted. One arcsecond is thus written 1″ and it is also abbreviated as arcsec or asec. In celestial navigation, seconds of arc are used in calculations. This notation has been carried over into marine GPS receivers, which normally display latitude and longitude in the format by default. An arcsecond is approximately the angle subtended by a U. S. dime coin at a distance of 4 kilometres, a milliarcsecond is about the size of a dime atop the Eiffel Tower as seen from New York City. A microarcsecond is about the size of a period at the end of a sentence in the Apollo mission manuals left on the Moon as seen from Earth, since antiquity the arcminute and arcsecond have been used in astronomy. The principal exception is Right ascension in equatorial coordinates, which is measured in units of hours, minutes. These small angles may also be written in milliarcseconds, or thousandths of an arcsecond, the unit of distance, the parsec, named from the parallax of one arcsecond, was developed for such parallax measurements. It is the distance at which the radius of the Earths orbit would subtend an angle of one arcsecond. The ESA astrometric space probe Gaia is hoped to measure star positions to 20 microarcseconds when it begins producing catalog positions sometime after 2016, there are about 1.3 trillion µas in a turn. Currently the best catalog positions of stars actually measured are in terms of milliarcseconds, apart from the Sun, the star with the largest angular diameter from Earth is R Doradus, a red supergiant with a diameter of 0.05 arcsecond. The dwarf planet Pluto has proven difficult to resolve because its angular diameter is about 0.1 arcsecond, space telescopes are not affected by the Earths atmosphere but are diffraction limited. For example, the Hubble space telescope can reach a size of stars down to about 0. 1″
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Observational astronomy
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It is the practice of observing celestial objects by using telescopes and other astronomical apparatus. As a science, the study of astronomy is somewhat hindered in that direct experiments with the properties of the distant universe are not possible, however, this is partly compensated by the fact that astronomers have a vast number of visible examples of stellar phenomena that can be examined. This allows for data to be plotted on graphs. Nearby examples of phenomena, such as variable stars, can then be used to infer the behavior of more distant representatives. Those distant yardsticks can then be employed to measure other phenomena in that neighborhood, galileo Galilei turned a telescope to the heavens and recorded what he saw. Since that time, observational astronomy has made steady advances with each improvement in telescope technology, visible-light astronomy falls in the middle of this range. Infrared astronomy deals with the detection and analysis of infrared radiation, the most common tool is the reflecting telescope but with a detector sensitive to infrared wavelengths. Space telescopes are used at wavelengths where the atmosphere is opaque. Radio astronomy detects radiation of millimetre to decametre wavelength, the receivers are similar to those used in radio broadcast transmission but much more sensitive. High-energy astronomy includes X-ray astronomy, gamma-ray astronomy, and extreme UV astronomy, in addition to using electromagnetic radiation, modern astrophysicists can also make observations using neutrinos, cosmic rays or gravitational waves. Observing a source using multiple methods is known as multi-messenger astronomy, optical and radio astronomy can be performed with ground-based observatories, because the atmosphere is relatively transparent at the wavelengths being detected. Observatories are usually located at high altitudes so as to minimise the absorption and distortion caused by the Earths atmosphere, some wavelengths of infrared light are heavily absorbed by water vapor, so many infrared observatories are located in dry places at high altitude, or in space. Powerful gamma rays can, however be detected by the air showers they produce. For much of the history of astronomy, almost all observation was performed in the visual spectrum with optical telescopes. The seeing conditions depend on the turbulence and thermal variations in the air, locations that are frequently cloudy or suffer from atmospheric turbulence limit the resolution of observations. Likewise the presence of the full Moon can brighten up the sky with scattered light, for observation purposes, the optimal location for an optical telescope is undoubtedly in outer space. There the telescope can make observations without being affected by the atmosphere, however, at present it remains costly to lift telescopes into orbit. Thus the next best locations are certain mountain peaks that have a number of cloudless days
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Mercury (planet)
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Mercury is the smallest and innermost planet in the Solar System. Its orbital period around the Sun of 88 days is the shortest of all the planets in the Solar System and it is named after the Roman deity Mercury, the messenger to the gods. Like Venus, Mercury orbits the Sun within Earths orbit as a planet, so it can only be seen visually in the morning or the evening sky. Also, like Venus and the Moon, the displays the complete range of phases as it moves around its orbit relative to Earth. Seen from Earth, this cycle of phases reoccurs approximately every 116 days, although Mercury can appear as a bright star-like object when viewed from Earth, its proximity to the Sun often makes it more difficult to see than Venus. Mercury is tidally or gravitationally locked with the Sun in a 3,2 resonance, as seen relative to the fixed stars, it rotates on its axis exactly three times for every two revolutions it makes around the Sun. As seen from the Sun, in a frame of reference that rotates with the orbital motion, an observer on Mercury would therefore see only one day every two years. Mercurys axis has the smallest tilt of any of the Solar Systems planets, at aphelion, Mercury is about 1.5 times as far from the Sun as it is at perihelion. Mercurys surface appears heavily cratered and is similar in appearance to the Moons, the polar regions are constantly below 180 K. The planet has no natural satellites. Mercury is one of four planets in the Solar System. It is the smallest planet in the Solar System, with a radius of 2,439.7 kilometres. Mercury is also smaller—albeit more massive—than the largest natural satellites in the Solar System, Ganymede, Mercury consists of approximately 70% metallic and 30% silicate material. Mercurys density is the second highest in the Solar System at 5.427 g/cm3, Mercurys density can be used to infer details of its inner structure. Although Earths high density results appreciably from gravitational compression, particularly at the core, Mercury is much smaller, therefore, for it to have such a high density, its core must be large and rich in iron. Geologists estimate that Mercurys core occupies about 55% of its volume, Research published in 2007 suggests that Mercury has a molten core. Surrounding the core is a 500–700 km mantle consisting of silicates, based on data from the Mariner 10 mission and Earth-based observation, Mercurys crust is estimated to be 35 km thick. One distinctive feature of Mercurys surface is the presence of narrow ridges
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Venus
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Venus is the second planet from the Sun, orbiting it every 224.7 Earth days. It has the longest rotation period of any planet in the Solar System and it is named after the Roman goddess of love and beauty. It is the second-brightest natural object in the sky after the Moon, reaching an apparent magnitude of −4.6. Because Venus orbits within Earths orbit it is a planet and never appears to venture far from the Sun. Venus is a planet and is sometimes called Earths sister planet because of their similar size, mass, proximity to the Sun. It is radically different from Earth in other respects and it has the densest atmosphere of the four terrestrial planets, consisting of more than 96% carbon dioxide. The atmospheric pressure at the surface is 92 times that of Earth. Venus is by far the hottest planet in the Solar System, with a surface temperature of 735 K. Venus is shrouded by an layer of highly reflective clouds of sulfuric acid. It may have had water oceans in the past, but these would have vaporized as the temperature rose due to a greenhouse effect. The water has probably photodissociated, and the hydrogen has been swept into interplanetary space by the solar wind because of the lack of a planetary magnetic field. Venuss surface is a dry desertscape interspersed with rocks and is periodically resurfaced by volcanism. As one of the brightest objects in the sky, Venus has been a fixture in human culture for as long as records have existed. It has been sacred to gods of many cultures, and has been a prime inspiration for writers and poets as the morning star. Venus was the first planet to have its motions plotted across the sky, as the closest planet to Earth, Venus has been a prime target for early interplanetary exploration. It was the first planet beyond Earth visited by a spacecraft, Venuss thick clouds render observation of its surface impossible in visible light, and the first detailed maps did not emerge until the arrival of the Magellan orbiter in 1991. Plans have been proposed for rovers or more missions. Venus is one of the four planets in the Solar System
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Mars
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Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, after Mercury. Named after the Roman god of war, it is referred to as the Red Planet because the iron oxide prevalent on its surface gives it a reddish appearance. Mars is a planet with a thin atmosphere, having surface features reminiscent both of the impact craters of the Moon and the valleys, deserts, and polar ice caps of Earth. The rotational period and seasonal cycles of Mars are likewise similar to those of Earth, Mars is the site of Olympus Mons, the largest volcano and second-highest known mountain in the Solar System, and of Valles Marineris, one of the largest canyons in the Solar System. The smooth Borealis basin in the northern hemisphere covers 40% of the planet, Mars has two moons, Phobos and Deimos, which are small and irregularly shaped. These may be captured asteroids, similar to 5261 Eureka, a Mars trojan, there are ongoing investigations assessing the past habitability potential of Mars, as well as the possibility of extant life. Future astrobiology missions are planned, including the Mars 2020 and ExoMars rovers, liquid water cannot exist on the surface of Mars due to low atmospheric pressure, which is about 6⁄1000 that of the Earths, except at the lowest elevations for short periods. The two polar ice caps appear to be largely of water. The volume of ice in the south polar ice cap, if melted. On November 22,2016, NASA reported finding a large amount of ice in the Utopia Planitia region of Mars. The volume of water detected has been estimated to be equivalent to the volume of water in Lake Superior, Mars can easily be seen from Earth with the naked eye, as can its reddish coloring. Its apparent magnitude reaches −2.91, which is surpassed only by Jupiter, Venus, the Moon, optical ground-based telescopes are typically limited to resolving features about 300 kilometers across when Earth and Mars are closest because of Earths atmosphere. Mars is approximately half the diameter of Earth with an area only slightly less than the total area of Earths dry land. Mars is less dense than Earth, having about 15% of Earths volume and 11% of Earths mass, the red-orange appearance of the Martian surface is caused by iron oxide, or rust. It can look like butterscotch, other common colors include golden, brown, tan. Like Earth, Mars has differentiated into a metallic core overlaid by less dense materials. Current models of its interior imply a core with a radius of about 1,794 ±65 kilometers, consisting primarily of iron and this iron sulfide core is thought to be twice as rich in lighter elements than Earths. The core is surrounded by a mantle that formed many of the tectonic and volcanic features on the planet
