A degree, usually denoted by °, is a measurement of a plane angle, defined so that a full rotation is 360 degrees. It is not an SI unit, as the SI unit of measure is the radian. Because a full rotation equals 2π radians, one degree is equivalent to π/180 radians, the original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. Ancient astronomers noticed that the sun, which follows through the path over the course of the year. Some ancient calendars, such as the Persian calendar, used 360 days for a year, the use of a calendar with 360 days may be related to the use of sexagesimal numbers. The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle, a chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree, Aristarchus of Samos and Hipparchus seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically.
Timocharis, Aristillus and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes, eratosthenes used a simpler sexagesimal system dividing a circle into 60 parts. Furthermore, it is divisible by every number from 1 to 10 except 7 and this property has many useful applications, such as dividing the world into 24 time zones, each of which is nominally 15° of longitude, to correlate with the established 24-hour day convention. Finally, it may be the case more than one of these factors has come into play. For many practical purposes, a degree is a small enough angle that whole degrees provide sufficient precision. When this is not the case, as in astronomy or for geographic coordinates, degree measurements may be written using decimal degrees, with the symbol behind the decimals. Alternatively, the sexagesimal unit subdivisions can be used. One degree is divided into 60 minutes, and one minute into 60 seconds, use of degrees-minutes-seconds is called DMS notation.
These subdivisions, called the arcminute and arcsecond, are represented by a single and double prime. For example,40. 1875° = 40° 11′ 15″, or, using quotation mark characters, additional precision can be provided using decimals for the arcseconds component. The older system of thirds, etc. which continues the sexagesimal unit subdivision, was used by al-Kashi and other ancient astronomers, but is rarely used today
Anton M. J. Tom Gehrels was a Dutch–American astronomer, Professor of Planetary Sciences, and Astronomer at the University of Arizona, Tucson. Gehrels was born at Haarlemmermeer, the Netherlands on February 21,1925, during World War II he was, as a teenager, active in the Dutch Resistance. After he escaped to England, he was sent back by parachute as an organizer for Special Operations Executive SOE committing sabotage against the German forces, after the war, he attended the University of Leiden where he graduated with a degree in physics and astronomy in 1951. He continued his education at the University of Chicago where he obtained his doctorate in astronomy, in 1960, he moved to the University of Arizona along with Gerard Kuiper where he would remain for the next 50 years. The trio are jointly credited with several thousand discoveries, Gehrels discovered a number of comets. He was Principal Investigator for the Imaging Photopolarimeter experiment on the Pioneer 10 and Pioneer 11 first flybys of Jupiter and he initiated the Spacewatch program in 1980 and was its Principal Investigator for electronic surveying to obtain statistics of asteroids and comets, including near-Earth asteroids.
Bob McMillan was co-investigator and manager, and became the PI in 1997, Gehrels taught an undergraduate course for non-science majors in Tucson in the Fall, and lectured a brief version of that in the Spring at the Physical Research Laboratory in Ahmedabad, India. His recent research was on universal evolution, which was woven in as the thread through these courses. He was the winner of the 2007 Harold Masursky Award for his outstanding service to planetary science. Gehrels was requested by the Journal Nature to write a review on a book regarding Wernher von Braun and he has therefore charged that von Braun was there regularly and much in charge, and that von Braun bears greater responsibility and guilt than his official biography would imply. Towards the end of the review it reads, Von Braun needs no phony defense. What is needed is a more sophisticated historical perspective, Tom Gehrels was the husband of Aleida J. Gehrels and father of Neil Gehrels, George Gehrels and Jo-Ann Gehrels. The minor planet 1777 Gehrels was named in his honour, the professional and personal papers of Tom Gehrels are held at the University of Arizona.
Special airborne services in Europe and Far East, 1944–1948, Astronomy and physics, Leiden University 1951. Ph. D. astronomy and astrophysics, Univ. of Chicago,1956, Professor of Planetary Sciences and Astronomy, Univ. of Arizona, 1961–2011. Binzel, Tom Gehrels, and Mildred Shapely Matthews Tucson, University of Arizona Press ISBN 0-8165-1123-3 Hazards Due to Comets and Asteroids, edited by Tom Gehrels, Mildred Shapley Matthews, and A
Orbital inclination measures the tilt of an objects orbit around a celestial body. It is expressed as the angle between a plane and the orbital plane or axis of direction of the orbiting object. For a satellite orbiting the Earth directly above the equator, the plane of the orbit is the same as the Earths equatorial plane. The general case is that the orbit is tilted, it spends half an orbit over the northern hemisphere. If the orbit swung between 20° north latitude and 20° south latitude, its orbital inclination would be 20°, the inclination is one of the six orbital elements describing the shape and orientation of a celestial orbit. It is the angle between the plane and the plane of reference, normally stated in degrees. For a satellite orbiting a planet, the plane of reference is usually the plane containing the planets equator, for planets in the Solar System, the plane of reference is usually the ecliptic, the plane in which the Earth orbits the Sun. This reference plane is most practical for Earth-based observers, Earths inclination is, by definition, zero.
Inclination could instead be measured with respect to another plane, such as the Suns equator or the invariable plane, the inclination of orbits of natural or artificial satellites is measured relative to the equatorial plane of the body they orbit, if they orbit sufficiently closely. The equatorial plane is the perpendicular to the axis of rotation of the central body. An inclination of 30° could be described using an angle of 150°, the convention is that the normal orbit is prograde, an orbit in the same direction as the planet rotates. Inclinations greater than 90° describe retrograde orbits, thus, An inclination of 0° means the orbiting body has a prograde orbit in the planets equatorial plane. An inclination greater than 0° and less than 90° describe prograde orbits, an inclination of 63. 4° is often called a critical inclination, when describing artificial satellites orbiting the Earth, because they have zero apogee drift. An inclination of exactly 90° is an orbit, in which the spacecraft passes over the north and south poles of the planet.
An inclination greater than 90° and less than 180° is a retrograde orbit, an inclination of exactly 180° is a retrograde equatorial orbit. For gas giants, the orbits of moons tend to be aligned with the giant planets equator, the inclination of exoplanets or members of multiple stars is the angle of the plane of the orbit relative to the plane perpendicular to the line-of-sight from Earth to the object. An inclination of 0° is an orbit, meaning the plane of its orbit is parallel to the sky. An inclination of 90° is an orbit, meaning the plane of its orbit is perpendicular to the sky
A minor planet is an astronomical object in direct orbit around the Sun that is neither a planet nor exclusively classified as a comet. Minor planets can be dwarf planets, trojans, Kuiper belt objects, as of 2016, the orbits of 709,706 minor planets were archived at the Minor Planet Center,469,275 of which had received permanent numbers. The first minor planet to be discovered was Ceres in 1801, the term minor planet has been used since the 19th century to describe these objects. The term planetoid has used, especially for larger objects such as those the International Astronomical Union has called dwarf planets since 2006. Historically, the asteroid, minor planet, and planetoid have been more or less synonymous. This terminology has become complicated by the discovery of numerous minor planets beyond the orbit of Jupiter. A Minor planet seen releasing gas may be classified as a comet. Before 2006, the IAU had officially used the term minor planet, during its 2006 meeting, the IAU reclassified minor planets and comets into dwarf planets and small Solar System bodies.
Objects are called dwarf planets if their self-gravity is sufficient to achieve hydrostatic equilibrium, all other minor planets and comets are called small Solar System bodies. The IAU stated that the minor planet may still be used. However, for purposes of numbering and naming, the distinction between minor planet and comet is still used. Hundreds of thousands of planets have been discovered within the Solar System. The Minor Planet Center has documented over 167 million observations and 729,626 minor planets, of these,20,570 have official names. As of March 2017, the lowest-numbered unnamed minor planet is 1974 FV1, as of March 2017, the highest-numbered named minor planet is 458063 Gustavomuler. There are various broad minor-planet populations, traditionally, most have been bodies in the inner Solar System. Near-Earth asteroids, those whose orbits take them inside the orbit of Mars. Further subclassification of these, based on distance, is used, Apohele asteroids orbit inside of Earths perihelion distance.
Aten asteroids, those that have semi-major axes of less than Earths, Apollo asteroids are those asteroids with a semimajor axis greater than Earths, while having a perihelion distance of 1.017 AU or less. Like Aten asteroids, Apollo asteroids are Earth-crossers, amor asteroids are those near-Earth asteroids that approach the orbit of Earth from beyond, but do not cross it
The ecliptic is the apparent path of the Sun on the celestial sphere, and is the basis for the ecliptic coordinate system. It refers to the plane of this path, which is coplanar with the orbit of Earth around the Sun, the motions as described above are simplifications. Due to the movement of Earth around the Earth–Moon center of mass, due to further perturbations by the other planets of the Solar System, the Earth–Moon barycenter wobbles slightly around a mean position in a complex fashion. The ecliptic is actually the apparent path of the Sun throughout the course of a year, because Earth takes one year to orbit the Sun, the apparent position of the Sun takes the same length of time to make a complete circuit of the ecliptic. With slightly more than 365 days in one year, the Sun moves a little less than 1° eastward every day, this is a simplification, based on a hypothetical Earth that orbits at uniform speed around the Sun. The actual speed with which Earth orbits the Sun varies slightly during the year, for example, the Sun is north of the celestial equator for about 185 days of each year, and south of it for about 180 days.
The variation of orbital speed accounts for part of the equation of time, if the equator is projected outward to the celestial sphere, forming the celestial equator, it crosses the ecliptic at two points known as the equinoxes. The Sun, in its apparent motion along the ecliptic, crosses the equator at these points, one from south to north. The crossing from south to north is known as the equinox, known as the first point of Aries. The crossing from north to south is the equinox or descending node. Likewise, the ecliptic itself is not fixed, the gravitational perturbations of the other bodies of the Solar System cause a much smaller motion of the plane of Earths orbit, and hence of the ecliptic, known as planetary precession. The combined action of two motions is called general precession, and changes the position of the equinoxes by about 50 arc seconds per year. Once again, this is a simplification, periodic motions of the Moon and apparent periodic motions of the Sun cause short-term small-amplitude periodic oscillations of Earths axis, and hence the celestial equator, known as nutation.
Obliquity of the ecliptic is the used by astronomers for the inclination of Earths equator with respect to the ecliptic. It is about 23. 4° and is currently decreasing 0.013 degrees per hundred years due to planetary perturbations, the angular value of the obliquity is found by observation of the motions of Earth and other planets over many years. From 1984, the Jet Propulsion Laboratorys DE series of computer-generated ephemerides took over as the ephemeris of the Astronomical Almanac. Obliquity based on DE200, which analyzed observations from 1911 to 1979, was calculated, jPLs fundamental ephemerides have been continually updated. J. Laskar computed an expression to order T10 good to 0″. 04/1000 years over 10,000 years, all of these expressions are for the mean obliquity, that is, without the nutation of the equator included
In celestial mechanics, the mean anomaly is an angle used in calculating the position of a body in an elliptical orbit in the classical two-body problem. Define T as the time required for a body to complete one orbit. In time T, the radius vector sweeps out 2π radians or 360°. The average rate of sweep, n, is n =2 π T or n =360 ∘ T, define τ as the time at which the body is at the pericenter. From the above definitions, a new quantity, M, the mean anomaly can be defined M = n, because the rate of increase, n, is a constant average, the mean anomaly increases uniformly from 0 to 2π radians or 0° to 360° during each orbit. It is equal to 0 when the body is at the pericenter, π radians at the apocenter, if the mean anomaly is known at any given instant, it can be calculated at any instant by simply adding n δt where δt represents the time difference. Mean anomaly does not measure an angle between any physical objects and it is simply a convenient uniform measure of how far around its orbit a body has progressed since pericenter.
The mean anomaly is one of three parameters that define a position along an orbit, the other two being the eccentric anomaly and the true anomaly. Define l as the longitude, the angular distance of the body from the same reference direction. Thus mean anomaly is M = l − ϖ, mean angular motion can be expressed, n = μ a 3, where μ is a gravitational parameter which varies with the masses of the objects, and a is the semi-major axis of the orbit. Mean anomaly can be expanded, M = μ a 3, and here mean anomaly represents uniform angular motion on a circle of radius a
Ingrid van Houten-Groeneveld
Ingrid van Houten-Groeneveld was a Dutch astronomer. In a jointly-credited trio with Tom Gehrels and her husband Cornelis Johannes van Houten, the trio are jointly credited with several thousand asteroid discoveries. Van Houten-Groeneveld died on 30 March 2015, at the age of 93, in Oegstgeest, the Themistian main-belt asteroid 1674 Groeneveld – discovered by Karl Reinmuth at Heidelberg and independently discovered by Finnish astronomer Yrjö Väisälä in 1938, was named in her honor. Veröffentlichungen der Badischen Landessternwarte zu Heidelberg, Ingrid, Gerard P. Photometric studies of asteroids. Kent, J. van Biesbroeck, G. van Houten, Van Houten-Groeneveld, van Houten, C. J. Photometrics Studies of Asteroids. Bilo, E. H. Van Houten-Groeneveld, I, the original values of 1/a for 17 cometary orbits. Bulletin of the Astronomical Institutes of the Netherlands, the original values of 1/a for seven comets. Bulletin of the Astronomical Institutes of the Netherlands, definitive elements for comets 1951 I and 1955 IV.
Bulletin of the Astronomical Institutes of the Netherlands, Van Houten, C. J. Van Houten-Groeneveld, I. A new periodic comet observed in 1960, Van Houten, C. J. Van Houten-Groeneveld, I. The Palomar-Leiden survey of faint minor planets, Van Houten, C. J. van Houten-Groeneveld, I. The density of Trojans near the preceding Lagrangian Point, pole coordinates of the asteroids 9 Metis,22 Kalliope, and 44 NYSA. Van Houten, C. J. Zappala, V. Photoelectric photometry of seven asteroids, Van Houten, C. J. Rotation period and phase curve of the asteroids 349 Dembowska and 354 Eleonora. Van Houten, C. J. Wisse-Schouten, M. Bardwell, Van Houten, C. J. van Houten-Groeneveld, I. Gehrels, T. Van Houten, C. J. Wisse, Hicks, M. D. Helin, E. F. Shoemaker, C. S. Van Houten-Groeneveld, I. Bowell, E. Trujillo, C. A. Kavelaars, mcNaught, R. H. Gehrels, T. Van Houten, C. J. Van Houten-Groeneveld, I. Gehrels, T. Van Houten, C. J. Wisse, Helin, E. F. Shoemaker, C. S. Van Houten-Groeneveld, I. Bowell, E. Kavelaars, J. Bus, S. J. Hicks, M. Lawrence, Helin, E. F.
Shoemaker, C. S. Van Houten-Groeneveld, I
The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is an orbit, values between 0 and 1 form an elliptical orbit,1 is a parabolic escape orbit. The term derives its name from the parameters of conic sections and it is normally used for the isolated two-body problem, but extensions exist for objects following a rosette orbit through the galaxy. In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit, the eccentricity of this Kepler orbit is a non-negative number that defines its shape. The limit case between an ellipse and a hyperbola, when e equals 1, is parabola, radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of the orbit, not the eccentricity. Radial orbits have zero angular momentum and hence eccentricity equal to one, keeping the energy constant and reducing the angular momentum, elliptic and hyperbolic orbits each tend to the corresponding type of radial trajectory while e tends to 1.
For a repulsive force only the trajectory, including the radial version, is applicable. For elliptical orbits, a simple proof shows that arcsin yields the projection angle of a circle to an ellipse of eccentricity e. For example, to view the eccentricity of the planet Mercury, tilt any circular object by that angle and the apparent ellipse projected to your eye will be of that same eccentricity. From Medieval Latin eccentricus, derived from Greek ἔκκεντρος ekkentros out of the center, from ἐκ- ek-, eccentric first appeared in English in 1551, with the definition a circle in which the earth, sun. Five years later, in 1556, a form of the word was added. The eccentricity of an orbit can be calculated from the state vectors as the magnitude of the eccentricity vector, e = | e | where. For elliptical orbits it can be calculated from the periapsis and apoapsis since rp = a and ra = a, where a is the semimajor axis. E = r a − r p r a + r p =1 −2 r a r p +1 where, rp is the radius at periapsis. For Earths annual orbit path, ra/rp ratio = longest_radius / shortest_radius ≈1.034 relative to center point of path, the eccentricity of the Earths orbit is currently about 0.0167, the Earths orbit is nearly circular.
Venus and Neptune have even lower eccentricity, over hundreds of thousands of years, the eccentricity of the Earths orbit varies from nearly 0.0034 to almost 0.058 as a result of gravitational attractions among the planets. The table lists the values for all planets and dwarf planets, Mercury has the greatest orbital eccentricity of any planet in the Solar System. Such eccentricity is sufficient for Mercury to receive twice as much solar irradiation at perihelion compared to aphelion, before its demotion from planet status in 2006, Pluto was considered to be the planet with the most eccentric orbit