The March equinox or Northward equinox is the equinox on the Earth when the subsolar point appears to leave the Southern Hemisphere and cross the celestial equator, heading northward as seen from Earth. The March equinox is known as the vernal equinox in the Northern Hemisphere and as the autumnal equinox in the Southern. On the Gregorian calendar, the Northward equinox can occur as early as 19 March or as late as 21 March at Greenwich. For a common year the computed time slippage is about 5 hours 49 minutes than the previous year, for a leap year about 18 hours 11 minutes earlier than the previous year. Balancing the increases of the common years against the losses of the leap years keeps the calendar date of the March equinox from drifting more than one day from 20 March each year; the March equinox may be taken to mark the beginning of spring and the end of winter in the Northern Hemisphere but marks the beginning of autumn and the end of summer in the Southern Hemisphere. In astronomy, the March equinox is the zero point of sidereal time and right ascension.
It serves as a reference for calendars and celebrations in many human cultures and religions. The point where the Sun crosses the celestial equator northwards is called the First Point of Aries. However, due to the precession of the equinoxes, this point is no longer in the constellation Aries, but rather in Pisces. By the year 2600 it will be in Aquarius; the Earth's axis causes the First Point of Aries to travel westwards across the sky at a rate of one degree every 72 years. Based on the modern constellation boundaries, the northward equinox passed from Taurus into Aries in the year −1865, passed into Pisces in the year −67, will pass into Aquarius in the year 2597, will pass into Capricornus in the year 4312, it passed by a'corner' of Cetus at 0°10′ distance in the year 1489. In its apparent motion on the day of an equinox, the Sun's disk crosses the Earth's horizon directly to the east at dawn—rising; the March equinox, like all equinoxes, is characterized by having an exactly equal amount of daylight and night across most latitudes on Earth.
Due to refraction of light rays in the Earth's atmosphere the Sun will be visible above the horizon when its disc is below the limb of the Earth. Additionally, when seen from the Earth, the Sun is a bright disc in the sky and not just a point of light, thus sunrise and sunset can be said to start several minutes before the sun's geometric center crosses the horizon, extends long after; these conditions produce differentials of actual durations of light and darkness at various locations on Earth during an equinox. This is most notable at the more extreme latitudes, where the Sun may be seen to travel sideways during the dawn and evening, drawing out the transition from day to night. At the north and south poles, the Sun appears to move around the horizon, just above the horizon, neither rising nor setting apart from a slight change in declination of about 0.39° per day as the equinox passes. The Babylonian calendar began with the first full moon after the vernal equinox, the day after the Sumerian goddess Inanna's return from the underworld, in the Akitu ceremony, with parades through the Ishtar Gate to the Eanna temple, the ritual re-enactment of the marriage to Tammuz, or Sumerian Dummuzi.
The Persian calendar begins each year at the northward equinox, observationally determined at Tehran. The Indian national calendar starts the year on the day next to the vernal equinox on 22 March with a 30-day month has 5 months of 31 days followed by 6 months of 30 days; the Julian calendar reform lengthened seven months and replaced the intercalary month with an intercalary day to be added every four years to February. It was based on a length for the year of 365 days and 6 hours, while the mean tropical year is about 11 minutes and 15 seconds less than that; this had the effect of adding about three quarters of an hour every four years. The effect accumulated from inception in 45 BC until the 16th century, when the northern vernal equinox fell on 10 or 11 March; the date in 1452 was 11 March, 11:52 In 2547 it will be 20 March, 21:18 and 3 March, 21:18. The Jewish Passover falls on the first full moon after the northern hemisphere vernal equinox, although it will occur on the second full moon.
The Christian Churches calculate Easter as the first Sunday after the first full moon on or after the March equinox. The official church definition for the equinox is 21 March; the Eastern Orthodox Churches use the older Julian calendar, while the western churches use the Gregorian calendar, the western full moons fall four, five or 34 days before the eastern ones. The result is that the two Easters fall on different days but they sometimes coincide; the earliest possible Easter date in any year is 22 March on each calendar. The latest possible Easter date in any year is 25 April; the northward equinox marks the first day of various calendars including the Iranian calendar. The ancient Iranian peoples new year's festival of Nowruz can be celebrated 21 March. According to the ancient Persian mythology Jamshid, the mythological king of Persia, ascended to the throne on this day and each year this is commemorated with festivities for two weeks. Along with Iranian peoples, it is a holiday celebrated by Turkic people, the North Caucasus and in Albania.
It is a holiday for Zoroastrians, adherents of the Bahá'í Faith and Nizari Ismaili Muslims irrespective of ethnicity. The Bahá'í
In astronomy, the geocentric model is a superseded description of the Universe with Earth at the center. Under the geocentric model, the Sun, Moon and planets all orbited Earth; the geocentric model served as the predominant description of the cosmos in many ancient civilizations, such as those of Aristotle and Ptolemy. Two observations supported the idea. First, from anywhere on Earth, the Sun appears to revolve around Earth once per day. While the Moon and the planets have their own motions, they appear to revolve around Earth about once per day; the stars appeared to be fixed on a celestial sphere rotating once each day about an axis through the geographic poles of Earth. Second, Earth seems to be unmoving from the perspective of an earthbound observer. Ancient Greek, ancient Roman, medieval philosophers combined the geocentric model with a spherical Earth, in contrast to the older flat Earth model implied in some mythology; the ancient Jewish Babylonian uranography pictured a flat Earth with a dome-shaped, rigid canopy called the firmament placed over it.
However, the ancient Greeks believed that the motions of the planets were circular and not elliptical, a view, not challenged in Western culture until the 17th century, when Johannes Kepler postulated that orbits were heliocentric and elliptical. In 1687, Newton showed; the astronomical predictions of Ptolemy's geocentric model were used to prepare astrological and astronomical charts for over 1500 years. The geocentric model held sway into the early modern age, but from the late 16th century onward, it was superseded by the heliocentric model of Copernicus and Kepler. There was much resistance to the transition between these two theories; some Christian theologians were reluctant to reject a theory. Others felt a unknown theory could not subvert an accepted consensus for geocentrism; the geocentric model entered Greek philosophy at an early point. In the 6th century BC, Anaximander proposed a cosmology with Earth shaped like a section of a pillar, held aloft at the center of everything; the Sun and planets were holes in invisible wheels surrounding Earth.
About the same time, Pythagoras thought that the Earth was a sphere, but not at the center. These views were combined, so most educated Greeks from the 4th century BC on thought that the Earth was a sphere at the center of the universe. In the 4th century BC, two influential Greek philosophers and his student Aristotle, wrote works based on the geocentric model. According to Plato, the Earth was a sphere; the stars and planets were carried around the Earth on spheres or circles, arranged in the order: Moon, Venus, Mars, Saturn, fixed stars, with the fixed stars located on the celestial sphere. In his "Myth of Er", a section of the Republic, Plato describes the cosmos as the Spindle of Necessity, attended by the Sirens and turned by the three Fates. Eudoxus of Cnidus, who worked with Plato, developed a less mythical, more mathematical explanation of the planets' motion based on Plato's dictum stating that all phenomena in the heavens can be explained with uniform circular motion. Aristotle elaborated on Eudoxus' system.
In the developed Aristotelian system, the spherical Earth is at the center of the universe, all other heavenly bodies are attached to 47–55 transparent, rotating spheres surrounding the Earth, all concentric with it. These spheres, known as crystalline spheres, all moved at different uniform speeds to create the revolution of bodies around the Earth, they were composed of an incorruptible substance called aether. Aristotle believed that the Moon was in the innermost sphere and therefore touches the realm of Earth, causing the dark spots and the ability to go through lunar phases, he further described his system by explaining the natural tendencies of the terrestrial elements: Earth, fire, air, as well as celestial aether. His system held that Earth was the heaviest element, with the strongest movement towards the center, thus water formed a layer surrounding the sphere of Earth; the tendency of air and fire, on the other hand, was to move upwards, away from the center, with fire being lighter than air.
Beyond the layer of fire, were the solid spheres of aether in which the celestial bodies were embedded. They, were entirely composed of aether. Adherence to the geocentric model stemmed from several important observations. First of all, if the Earth did move one ought to be able to observe the shifting of the fixed stars due to stellar parallax. In short, if the Earth was moving, the shapes of the constellations should change over the course of a year. If they did not appear to move, the stars are either much farther away than the Sun and the planets than conceived, making their motion undetectable, or in reality they are not moving at all; because the stars were much further away than Greek astronomers postulated, stellar parallax was not detected until the 19th century. Therefore, the Greeks chose the simpler of the two explanations. Another observ
A planet is an astronomical body orbiting a star or stellar remnant, massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, has cleared its neighbouring region of planetesimals. The term planet is ancient, with ties to history, science and religion. Five planets in the Solar System are visible to the naked eye; these were regarded by many early cultures as emissaries of deities. As scientific knowledge advanced, human perception of the planets changed, incorporating a number of disparate objects. In 2006, the International Astronomical Union adopted a resolution defining planets within the Solar System; this definition is controversial because it excludes many objects of planetary mass based on where or what they orbit. Although eight of the planetary bodies discovered before 1950 remain "planets" under the modern definition, some celestial bodies, such as Ceres, Pallas and Vesta, Pluto, that were once considered planets by the scientific community, are no longer viewed as such.
The planets were thought by Ptolemy to orbit Earth in epicycle motions. Although the idea that the planets orbited the Sun had been suggested many times, it was not until the 17th century that this view was supported by evidence from the first telescopic astronomical observations, performed by Galileo Galilei. About the same time, by careful analysis of pre-telescopic observational data collected by Tycho Brahe, Johannes Kepler found the planets' orbits were elliptical rather than circular; as observational tools improved, astronomers saw that, like Earth, each of the planets rotated around an axis tilted with respect to its orbital pole, 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 other planets share characteristics such as volcanism, hurricanes and hydrology. Planets are divided into two main types: large low-density giant planets, smaller rocky terrestrials. There are eight planets in the Solar System.
In order of increasing distance from the Sun, they are the four terrestrials, Venus and Mars the four giant planets, Saturn 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; as of 1 April 2019, 4,023 known extrasolar planets in 3,005 planetary systems, ranging in size from just above the size of the Moon to gas giants about twice as large as Jupiter have been discovered, out of which more than 100 planets are the same size as Earth, nine of which are at the same relative distance from their star as Earth from the Sun, i.e. in the circumstellar 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. A 2012 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 divine lights of antiquity to the earthly objects of the scientific age; the concept has expanded to include worlds not only in the Solar System, but in hundreds of other extrasolar systems. 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, ancient astronomy. In ancient times, astronomers noted how certain lights moved across the sky, as opposed to the "fixed stars", which maintained a constant relative position in the sky. Ancient Greeks called these lights πλάνητες ἀστέρες or πλανῆται, from which today's word "planet" was derived. In ancient Greece, China and indeed all pre-modern civilizations, it was universally believed that Earth was the center of the Universe and that all the "planets" circled Earth.
The reasons for this perception were that stars and planets appeared to revolve around Earth each day and the common-sense perceptions that Earth was solid and stable and that it was not moving but at rest. The first civilization known to have a functional theory of the planets were the Babylonians, who lived in Mesopotamia in the first and second millennia BC; the oldest surviving planetary astronomical text is the Babylonian Venus tablet of Ammisaduqa, a 7th-century BC copy of a list of observations of the motions of the planet Venus, that dates as early as the second millennium BC. The MUL. APIN is a pair of cuneiform tablets dating from the 7th century BC that lays out the motions of the Sun and planets over the course of the year; the Babylonian astrologers laid the foundations of what would become Western astrology. The Enuma anu enlil, written during the Neo-Assyrian period in the 7th century BC, comprises a list of omens and their relationships with various celestial phenomena including the motions of the planets.
Venus and the outer planets Mars and Saturn were all identified by Babylonian astronomers. These would remain the only known planets until the invention of the telescope in early modern times; the ancient Greeks did not attach as much significance to the planets as the Babylonians. The Pythagoreans, in the 6th and 5t
Polar regions of Earth
The polar regions called the frigid zones, of Earth are the regions of the planet that surround its geographical poles, lying within the polar circles. These high latitudes are dominated by Earth's polar ice caps: the northern resting on the Arctic Ocean and the southern on the continent of Antarctica; the Arctic has various definitions, including the region north of the Arctic Circle, or the region north of 60° north latitude, or the region from the North Pole south to the timberline. The Antarctic is defined as south of 60° south latitude, or the continent of Antarctica; the 1959 Antarctic Treaty uses the former definition. The two polar regions are distinguished from the other two climatic and biomatic belts of Earth, a tropics belt near the equator, two middle latitude regions located between the tropics and polar regions. Polar regions receive less intense solar radiation than the other parts of Earth because the sun's energy arrives at an oblique angle, spreading over a larger area, travels a longer distance through the Earth's atmosphere in which it may be absorbed, scattered or reflected, the same thing that causes winters to be colder than the rest of the year in temperate areas.
The axial tilt of the Earth has a major effect on climate of the polar regions. Since the polar regions are the farthest from the equator, they receive the least amount of sunlight and are therefore frigid; the large amount of ice and snow reflects a large part of what little sunlight the Polar regions receive, contributing to the cold. Polar regions are characterized by the polar climate cold temperatures, heavy glaciation wherever there is sufficient precipitation to form permanent ice, extreme variations in daylight hours, with twenty-four hours of daylight in summer, complete darkness at mid-winter. There are many settlements in Earth's north polar region. Countries with claims to Arctic regions are: the United States, Denmark, Finland, Sweden and Russia. Arctic circumpolar populations share more in common with each other than with other populations within their national boundaries; as such, the northern polar region is diverse in human cultures. The southern polar region has no permanent human habitation.
McMurdo Station is the largest research station in Antarctica, run by the United States. Other notable stations include Palmer Station and Amundsen–Scott South Pole Station, Esperanza Base and Marambio Base, Scott Base, Vostok Station. While there are no indigenous human cultures, there is a complex ecosystem along Antarctica's coastal zones. Coastal upwelling provides abundant nutrients which feeds krill, a type of marine crustacea, which in turn feeds a complex of living creatures from penguins to blue whales. Polar regions at Curlie The Polar Regions International Polar Foundation Arctic Environmental Atlas Earth's Polar Regions on Windows to the Universe Arctic Studies Center, Smithsonian Institution Scott Polar Research Institute, University of Cambridge WWF:The Polar Regions World Environment Day 2007 "Melting Ice" image gallery at The Guardian Polar Discovery Victor, Paul-Émile. Man and the Conquest of the Poles, trans. by Scott Sullivan. New York: Simon & Schuster, 1963
In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, which may be centered on Earth or the observer. If centered on the observer, half of the sphere would resemble a hemispherical screen over the observing location; the celestial sphere is a practical tool for spherical astronomy, allowing astronomers to specify the apparent positions of objects in the sky if their distances are unknown or irrelevant. In the equatorial coordinate system, the celestial equator divides the celestial sphere into two halves: the northern and southern celestial hemispheres; because astronomical objects are at such remote distances, casual observation of the sky offers no information on their actual distances. All celestial objects seem far away, as if fixed onto the inside of a sphere with a large but unknown radius, which appears to rotate westward overhead.
For purposes of spherical astronomy, concerned only with the directions to celestial objects, it makes no difference if this is the case or if it is Earth, rotating while the celestial sphere is stationary. The celestial sphere can be considered to be infinite in radius; this means any point within it, including that occupied by the observer, can be considered the center. It means that all parallel lines, be they millimetres apart or across the Solar System from each other, will seem to intersect the sphere at a single point, analogous to the vanishing point of graphical perspective. All parallel planes will seem to intersect the sphere in a coincident great circle. Conversely, observers looking toward the same point on an infinite-radius celestial sphere will be looking along parallel lines, observers looking toward the same great circle, along parallel planes. On an infinite-radius celestial sphere, all observers see the same things in the same direction. For some objects, this is over-simplified.
Objects which are near to the observer will seem to change position against the distant celestial sphere if the observer moves far enough, from one side of planet Earth to the other. This effect, known as parallax, can be represented as a small offset from a mean position; the celestial sphere can be considered to be centered at the Earth's center, the Sun's center, or any other convenient location, offsets from positions referred to these centers can be calculated. In this way, astronomers can predict geocentric or heliocentric positions of objects on the celestial sphere, without the need to calculate the individual geometry of any particular observer, the utility of the celestial sphere is maintained. 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, is applied frequently by astronomers. For instance, the Astronomical Almanac for 2010 lists the apparent geocentric position of the Moon on January 1 at 00:00:00.00 Terrestrial Time, in equatorial coordinates, as right ascension 6h 57m 48.86s, declination +23° 30' 05.5".
Implied in this position is. For many rough uses, this position, as seen from the Earth's center, is adequate. For applications requiring precision, the Almanac gives formulae and methods for calculating the topocentric coordinates, that is, as seen from a particular place on the Earth's surface, based on the geocentric position; this abbreviates the amount of detail necessary in such almanacs, as each observer can handle their own specific circumstances. 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, form the bases of the reference systems; these include the Earth's equator and orbit. At their intersections with the celestial sphere, these form the celestial equator, the north and south celestial poles, the ecliptic, respectively; as the celestial sphere is considered arbitrary or infinite in radius, all observers see the celestial equator, celestial poles, ecliptic at the same place against the background stars.
From these bases, directions toward objects in the sky can be quantified by constructing celestial coordinate systems. Similar to geographic longitude and latitude, the equatorial coordinate system specifies positions relative to the celestial equator and celestial poles, using right ascension and declination; the ecliptic coordinate system specifies positions relative to the ecliptic, using ecliptic longitude and latitude. Besides the equatorial and ecliptic systems, some other celestial coordinate systems, like the galactic coordinate system, are more appropriate for particular purposes; the ancients assumed the literal truth of stars attached to a celestial sphere, revolving about the Earth in one day, a fixed Earth. The Eudoxan planetary model, on which the Aristotelian and Ptolemaic models were based, was the first geometric explanation for the "wandering" of the classical planets; the outer most of these "crystal spheres" was thought to carry the fixed stars. Eudoxus used 27 concentric spherical solids to answer Plato's challenge: "By the assumption of what uniform and orderly motions can the appa
Right ascension is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the point above the earth in question. When paired with declination, these astronomical coordinates specify the direction of a point on the celestial sphere in the equatorial coordinate system. An old term, right ascension refers to the ascension, or the point on the celestial equator that rises with any celestial object as seen from Earth's equator, where the celestial equator intersects the horizon at a right angle, it contrasts with oblique ascension, the point on the celestial equator that rises with any celestial object as seen from most latitudes on Earth, where the celestial equator intersects the horizon at an oblique angle. Right ascension is the celestial equivalent of terrestrial longitude. Both right ascension and longitude measure an angle from a primary direction on an equator. Right ascension is measured from the Sun at the March equinox i.e. the First Point of Aries, the place on the celestial sphere where the Sun crosses the celestial equator from south to north at the March equinox and is located in the constellation Pisces.
Right ascension is measured continuously in a full circle from that alignment of Earth and Sun in space, that equinox, the measurement increasing towards the east. As seen from Earth, objects noted to have 12h RA are longest visible at the March equinox. On those dates at midnight, such objects will reach their highest point. How high depends on their declination. Any units of angular measure could have been chosen for right ascension, but it is customarily measured in hours and seconds, with 24h being equivalent to a full circle. Astronomers have chosen this unit to measure right ascension because they measure a star's location by timing its passage through the highest point in the sky as the Earth rotates; the line which passes through the highest point in the sky, called the meridian, is the projection of a longitude line onto the celestial sphere. Since a complete circle contains 24h of right ascension or 360°, 1/24 of a circle is measured as 1h of right ascension, or 15°. A full circle, measured in right-ascension units, contains 24 × 60 × 60 = 86400s, or 24 × 60 = 1440m, or 24h.
Because right ascensions are measured in hours, they can be used to time the positions of objects in the sky. For example, if a star with RA = 1h 30m 00s is at its meridian a star with RA = 20h 00m 00s will be on the/at its meridian 18.5 sidereal hours later. Sidereal hour angle, used in celestial navigation, is similar to right ascension, but increases westward rather than eastward. Measured in degrees, it is the complement of right ascension with respect to 24h, it is important not to confuse sidereal hour angle with the astronomical concept of hour angle, which measures angular distance of an object westward from the local meridian. The Earth's axis rotates westward about the poles of the ecliptic, completing one cycle in about 26,000 years; this movement, known as precession, causes the coordinates of stationary celestial objects to change continuously, if rather slowly. Therefore, equatorial coordinates are inherently relative to the year of their observation, astronomers specify them with reference to a particular year, known as an epoch.
Coordinates from different epochs must be mathematically rotated to match each other, or to match a standard epoch. Right ascension for "fixed stars" near the ecliptic and equator increases by about 3.05 seconds per year on average, or 5.1 minutes per century, but for fixed stars further from the ecliptic the rate of change can be anything from negative infinity to positive infinity. The right ascension of Polaris is increasing quickly; the North Ecliptic Pole in Draco and the South Ecliptic Pole in Dorado are always at right ascension 18h and 6h respectively. The used standard epoch is J2000.0, January 1, 2000 at 12:00 TT. The prefix "J" indicates. Prior to J2000.0, astronomers used the successive Besselian epochs B1875.0, B1900.0, B1950.0. The concept of right ascension has been known at least as far back as Hipparchus who measured stars in equatorial coordinates in the 2nd century BC, but Hipparchus and his successors made their star catalogs in ecliptic coordinates, the use of RA was limited to special cases.
With the invention of the telescope, it became possible for astronomers to observe celestial objects in greater detail, provided that the telescope could be kept pointed at the object for a period of time. The easiest way to do, to use an equatorial mount, which allows the telescope to be aligned with one of its two pivots parallel to the Earth's axis. A motorized clock drive is used with an equatorial mount to cancel out the Earth's rotation; as the equatorial mount became adopted for observation, the equatorial coordinate system, which includes right ascension, was adopted at the same time for simplicity. Equatorial mounts could be pointed at objects with known right ascension and declination by the use of setting circles; the first star catalog to use right ascen
In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet. Orbit refers to a repeating trajectory, although it may refer to a non-repeating trajectory. To a close approximation and satellites follow elliptic orbits, with the central mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion. For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital motion; 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 planets were attached.
It assumed the heavens were fixed apart from the motion of the spheres, was developed without any understanding of gravity. After the planets' motions were more measured, theoretical mechanisms such as deferent and epicycles were added. Although the model was capable of reasonably predicting the planets' positions in the sky and more epicycles were required as the measurements became more accurate, hence the model became unwieldy. 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 modern understanding of orbits was first formulated by Johannes Kepler whose results are summarised in his three laws of planetary motion. First, he found that the orbits of the planets in our Solar System are elliptical, not circular, as had been believed, that the Sun is not located at the center of the orbits, but rather at one focus. Second, he found that the orbital speed of each planet is not constant, as had been thought, but rather that the speed depends on the planet's distance from the Sun.
Third, Kepler found a universal 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 about 5.2 and 0.723 AU distant from the Sun, their orbital periods 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, in accord with the relationship. Idealised orbits meeting these rules are known as Kepler orbits. Isaac Newton demonstrated that Kepler's 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 orbits' sizes are in inverse proportion to their masses, that those bodies orbit their common center of mass. Where one body is much 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.
Advances in Newtonian mechanics were used to explore variations from the simple assumptions behind Kepler orbits, such as the perturbations due to other bodies, or the impact of spheroidal rather than spherical bodies. Lagrange developed a new approach to Newtonian mechanics emphasizing energy more than force, made progress on the three body problem, discovering the Lagrangian points. In a dramatic vindication of classical mechanics, in 1846 Urbain Le Verrier was able to predict the position of Neptune based on unexplained perturbations in the orbit of Uranus. Albert Einstein in his 1916 paper The Foundation of the General Theory of Relativity explained that gravity was due to curvature of space-time and removed Newton's assumption that changes propagate instantaneously; 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 approximated well by the Newtonian predictions but the differences are measurable.
All the experimental evidence that can distinguish between the theories agrees with relativity theory to within experimental measurement accuracy. The original vindication of general relativity is that it was able to account for the remaining unexplained amount in precession of Mercury's perihelion first noted by Le Verrier. However, Newton's solution is still used for most short term purposes since it is easier to use and sufficiently accurate. Within a planetary system, dwarf planets and other minor planets and space debris orbit the system's barycenter in elliptical orbits. A comet in a parabolic or hyperbolic orbit about a barycenter is not gravitationally bound to the star and therefore is not considered part of the star's planetary system. Bodies which are gravitationally bound to one of the planets in a planetary system, either natural or artificial satellites, follow orbits about a barycenter near or within that planet. Owing to mutual gravitational perturbations, the eccentricities of the planetary orbits vary over time.
Mercury, the smallest planet in the Solar System, has the most eccentric orbit