Fgnievinski: moving section from geographic coordinate system
A '''planetary coordinate system''' is a generalization of the [[geographic coordinate system]] and the [[geocentric coordinate system]] for [[planet]]s other than Earth.
Similar coordinate systems are defined for other solid [[celestial bodies]], such as the ''[[selenographic coordinates]]'' for the [[Moon]].
The coordinate systems for almost all of the solid bodies in the [[Solar System]] were established by [[Merton E. Davies]] of the [[Rand Corporation]], including [[Mercury (planet)|Mercury]],<ref>Davies, M. E., "Surface Coordinates and Cartography of Mercury," Journal of Geophysical Research, Vol. 80, No. 17, June 10, 1975.</ref><ref>Davies, M. E., S. E. Dwornik, D. E. Gault, and R. G. Strom, NASA Atlas of Mercury, NASA Scientific and Technical Information Office, 1978.</ref> [[Venus]],<ref>Davies, M. E., T. R. Colvin, P. G. Rogers, P. G. Chodas, W. L. Sjogren, W. L. Akim, E. L. Stepanyantz, Z. P. Vlasova, and A. I. Zakharov, "The Rotation Period, Direction of the North Pole, and Geodetic Control Network of Venus," Journal of Geophysical Research, Vol. 97, £8, pp. 13,14 1-13,151, 1992.</ref> [[Mars]],<ref>Davies, M. E., and R. A. Berg, "Preliminary Control Net of Mars,"Journal of Geophysical Research, Vol. 76, No. 2, pps. 373-393, January 10, 1971.</ref> the four [[Galilean moons]] of [[Jupiter]],<ref>[[Merton E. Davies]], Thomas A. Hauge, et al.: Control Networks for the Galilean Satellites: November 1979 R-2532-JPL/NASA</ref> and [[Triton (moon)|Triton]], the largest [[Natural satellite|moon]] of [[Neptune]].<ref>Davies, M. E., P. G. Rogers, and T. R. Colvin, "A Control Network of Triton," Journal of Geophysical Research, Vol. 96, E l, pp. 15, 675-15, 681, 1991.</ref>
==Latitude==
The zero [[latitude]] plane ([[Equator]]) can be defined as orthogonal to the mean [[axis of rotation]] ([[poles of astronomical bodies]]).
The reference surfaces for some planets (such as Earth and [[Mars]]) are [[ellipsoid]]s of revolution for which the equatorial radius is larger than the polar radius, such that they are [[oblate spheroid]]s.
==Longitude==
Liquid error: wrong number of arguments (given 1, expected 2)
The longitude systems of most of those bodies with observable rigid surfaces have been defined by references to a surface feature such as a [[Impact crater|crater]]. The [[north pole]] is that pole of rotation that lies on the north side of the [[invariable plane]] of the solar system (near the [[ecliptic]]). The location of the prime meridian as well as the position of the body's north pole on the celestial sphere may vary with time due to precession of the axis of rotation of the planet (or satellite). If the position angle of the body's prime meridian increases with time, the body has a direct (or [[direct motion|prograde]]) rotation; otherwise the rotation is said to be [[retrograde motion|retrograde]].
In the absence of other information, the axis of rotation is assumed to be normal to the mean [[Orbital plane (astronomy)|orbital plane]]; [[Mercury (planet)|Mercury]] and most of the satellites are in this category. For many of the satellites, it is assumed that the rotation rate is equal to the mean [[orbital period]]. In the case of the [[gas giant|giant planets]], since their surface features are constantly changing and moving at various rates, the rotation of their [[magnetic field]]s is used as a reference instead. In the case of the [[Sun]], even this criterion fails (because its magnetosphere is very complex and does not really rotate in a steady fashion), and an agreed-upon value for the rotation of its equator is used instead.
For '''planetographic longitude''', west longitudes (i.e., longitudes measured positively to the west) are used when the rotation is prograde, and east longitudes (i.e., longitudes measured positively to the east) when the rotation is retrograde. In simpler terms, imagine a distant, non-orbiting observer viewing a planet as it rotates. Also suppose that this observer is within the plane of the planet's equator. A point on the Equator that passes directly in front of this observer later in time has a higher planetographic longitude than a point that did so earlier in time.
However, '''planetocentric longitude''' is always measured positively to the east, regardless of which way the planet rotates. ''East'' is defined as the counter-clockwise direction around the planet, as seen from above its north pole, and the north pole is whichever pole more closely aligns with the Earth's north pole. Longitudes traditionally have been written using "E" or "W" instead of "+" or "−" to indicate this polarity. For example, −91°, 91°W, +269° and 269°E all mean the same thing.
The modern standard for maps of Mars (since about 2002) is to use planetocentric coordinates. Guided by the works of historical astronomers, [[Merton E. Davies]] established the meridian of Mars at [[Airy-0]] crater.<ref>[https://ift.tt/3gXe6Bp Where is zero degrees longitude on Mars?] – Copyright 2000 – 2010 © European Space Agency. All rights reserved.</ref><ref>Davies, M. E., and R. A. Berg, "Preliminary Control Net of Mars,"Journal of Geophysical Research, Vol. 76, No. 2, pps. 373-393, January 10, 1971.</ref> For [[Mercury (planet)|Mercury]], the only other planet with a solid surface visible from Earth, a thermocentric coordinate is used: the prime meridian runs through the point on the equator where the planet is hottest (due to the planet's rotation and orbit, the sun briefly [[Apparent retrograde motion|retrogrades]] at noon at this point during [[perihelion]], giving it more sun). By convention, this meridian is defined as exactly twenty degrees of longitude east of [[Hun Kal (crater)|Hun Kal]].<ref>Davies, M. E., "Surface Coordinates and Cartography of Mercury," Journal of Geophysical Research, Vol. 80, No. 17, June 10, 1975.</ref><ref name="ArchinalA’Hearn2010">Liquid error: wrong number of arguments (given 1, expected 2)</ref><ref name="usgs"></ref>
[[Tidal lock|Tidally-locked]] bodies have a natural reference longitude passing through the point nearest to their parent body: 0° the center of the primary-facing hemisphere, 90° the center of the leading hemisphere, 180° the center of the anti-primary hemisphere, and 270° the center of the trailing hemisphere.<ref>[https://ift.tt/2RdZrXH First map of extraterrestrial planet] – Center of Astrophysics.</ref> However, [[libration]] due to non-circular orbits or axial tilts causes this point to move around any fixed point on the celestial body like an [[analemma]].
== Ellipsoid of revolution ==
[[Reference ellipsoid]]s are also useful for geodetic mapping of other planetary bodies including planets, their satellites, asteroids and comet nuclei. Some well observed bodies such as the [[Moon]] and [[Mars]] now have quite precise reference ellipsoids.
For rigid-surface nearly-spherical bodies, which includes all the rocky planets and many moons, ellipsoids are defined in terms of the axis of rotation and the mean surface height excluding any atmosphere. Mars is actually [[Oval (geometry)|egg shaped]], where its north and south polar radii differ by approximately , however this difference is small enough that the average polar radius is used to define its ellipsoid. The Earth's Moon is effectively spherical, having almost no bulge at its equator. Where possible, a fixed observable surface feature is used when defining a reference meridian.
For gaseous planets like [[Jupiter]], an effective surface for an ellipsoid is chosen as the equal-pressure boundary of one [[Bar (unit)|bar]]. Since they have no permanent observable features, the choices of prime meridians are made according to mathematical rules.
== Triaxial ellipsoid (spheroid) ==
Small moons, asteroids, and comet nuclei frequently have irregular shapes. For some of these, such as Jupiter's [[Io (moon)|Io]], a scalene (triaxial) ellipsoid is a better fit than the oblate spheroid. For highly irregular bodies, the concept of a reference ellipsoid may have no useful value, so sometimes a spherical reference is used instead and points identified by planetocentric latitude and longitude. Even that can be problematic for [[convex set|non-convex]] bodies, such as [[433 Eros|Eros]], in that latitude and longitude don't always uniquely identify a single surface location.
Smaller bodies ([[Io (moon)|Io]], [[Mimas (moon)|Mimas]], etc.) tend to be better approximated by [[triaxial ellipsoid]]s; however, triaxial ellipsoids would render many computations more complicated, especially those related to [[map projection]]s. Many projections would lose their elegant and popular properties. For this reason spherical reference surfaces are frequently used in mapping programs.
==See also==
*[[Geoid#Other celestial bodies]]
*[[Planetary cartography]]
==References==
[[Category:Planetary science|C]]
[[Category:Celestial coordinate system]]
[[Category:Coordinate system]]
[[Category:Astronomy]]
[[Category:Astrometry]]
[[Category:Geodesy]]
[[Category:Cartography]]
[[Category:Navigation]]
Similar coordinate systems are defined for other solid [[celestial bodies]], such as the ''[[selenographic coordinates]]'' for the [[Moon]].
The coordinate systems for almost all of the solid bodies in the [[Solar System]] were established by [[Merton E. Davies]] of the [[Rand Corporation]], including [[Mercury (planet)|Mercury]],<ref>Davies, M. E., "Surface Coordinates and Cartography of Mercury," Journal of Geophysical Research, Vol. 80, No. 17, June 10, 1975.</ref><ref>Davies, M. E., S. E. Dwornik, D. E. Gault, and R. G. Strom, NASA Atlas of Mercury, NASA Scientific and Technical Information Office, 1978.</ref> [[Venus]],<ref>Davies, M. E., T. R. Colvin, P. G. Rogers, P. G. Chodas, W. L. Sjogren, W. L. Akim, E. L. Stepanyantz, Z. P. Vlasova, and A. I. Zakharov, "The Rotation Period, Direction of the North Pole, and Geodetic Control Network of Venus," Journal of Geophysical Research, Vol. 97, £8, pp. 13,14 1-13,151, 1992.</ref> [[Mars]],<ref>Davies, M. E., and R. A. Berg, "Preliminary Control Net of Mars,"Journal of Geophysical Research, Vol. 76, No. 2, pps. 373-393, January 10, 1971.</ref> the four [[Galilean moons]] of [[Jupiter]],<ref>[[Merton E. Davies]], Thomas A. Hauge, et al.: Control Networks for the Galilean Satellites: November 1979 R-2532-JPL/NASA</ref> and [[Triton (moon)|Triton]], the largest [[Natural satellite|moon]] of [[Neptune]].<ref>Davies, M. E., P. G. Rogers, and T. R. Colvin, "A Control Network of Triton," Journal of Geophysical Research, Vol. 96, E l, pp. 15, 675-15, 681, 1991.</ref>
==Latitude==
The zero [[latitude]] plane ([[Equator]]) can be defined as orthogonal to the mean [[axis of rotation]] ([[poles of astronomical bodies]]).
The reference surfaces for some planets (such as Earth and [[Mars]]) are [[ellipsoid]]s of revolution for which the equatorial radius is larger than the polar radius, such that they are [[oblate spheroid]]s.
==Longitude==
Liquid error: wrong number of arguments (given 1, expected 2)
The longitude systems of most of those bodies with observable rigid surfaces have been defined by references to a surface feature such as a [[Impact crater|crater]]. The [[north pole]] is that pole of rotation that lies on the north side of the [[invariable plane]] of the solar system (near the [[ecliptic]]). The location of the prime meridian as well as the position of the body's north pole on the celestial sphere may vary with time due to precession of the axis of rotation of the planet (or satellite). If the position angle of the body's prime meridian increases with time, the body has a direct (or [[direct motion|prograde]]) rotation; otherwise the rotation is said to be [[retrograde motion|retrograde]].
In the absence of other information, the axis of rotation is assumed to be normal to the mean [[Orbital plane (astronomy)|orbital plane]]; [[Mercury (planet)|Mercury]] and most of the satellites are in this category. For many of the satellites, it is assumed that the rotation rate is equal to the mean [[orbital period]]. In the case of the [[gas giant|giant planets]], since their surface features are constantly changing and moving at various rates, the rotation of their [[magnetic field]]s is used as a reference instead. In the case of the [[Sun]], even this criterion fails (because its magnetosphere is very complex and does not really rotate in a steady fashion), and an agreed-upon value for the rotation of its equator is used instead.
For '''planetographic longitude''', west longitudes (i.e., longitudes measured positively to the west) are used when the rotation is prograde, and east longitudes (i.e., longitudes measured positively to the east) when the rotation is retrograde. In simpler terms, imagine a distant, non-orbiting observer viewing a planet as it rotates. Also suppose that this observer is within the plane of the planet's equator. A point on the Equator that passes directly in front of this observer later in time has a higher planetographic longitude than a point that did so earlier in time.
However, '''planetocentric longitude''' is always measured positively to the east, regardless of which way the planet rotates. ''East'' is defined as the counter-clockwise direction around the planet, as seen from above its north pole, and the north pole is whichever pole more closely aligns with the Earth's north pole. Longitudes traditionally have been written using "E" or "W" instead of "+" or "−" to indicate this polarity. For example, −91°, 91°W, +269° and 269°E all mean the same thing.
The modern standard for maps of Mars (since about 2002) is to use planetocentric coordinates. Guided by the works of historical astronomers, [[Merton E. Davies]] established the meridian of Mars at [[Airy-0]] crater.<ref>[https://ift.tt/3gXe6Bp Where is zero degrees longitude on Mars?] – Copyright 2000 – 2010 © European Space Agency. All rights reserved.</ref><ref>Davies, M. E., and R. A. Berg, "Preliminary Control Net of Mars,"Journal of Geophysical Research, Vol. 76, No. 2, pps. 373-393, January 10, 1971.</ref> For [[Mercury (planet)|Mercury]], the only other planet with a solid surface visible from Earth, a thermocentric coordinate is used: the prime meridian runs through the point on the equator where the planet is hottest (due to the planet's rotation and orbit, the sun briefly [[Apparent retrograde motion|retrogrades]] at noon at this point during [[perihelion]], giving it more sun). By convention, this meridian is defined as exactly twenty degrees of longitude east of [[Hun Kal (crater)|Hun Kal]].<ref>Davies, M. E., "Surface Coordinates and Cartography of Mercury," Journal of Geophysical Research, Vol. 80, No. 17, June 10, 1975.</ref><ref name="ArchinalA’Hearn2010">Liquid error: wrong number of arguments (given 1, expected 2)</ref><ref name="usgs"></ref>
[[Tidal lock|Tidally-locked]] bodies have a natural reference longitude passing through the point nearest to their parent body: 0° the center of the primary-facing hemisphere, 90° the center of the leading hemisphere, 180° the center of the anti-primary hemisphere, and 270° the center of the trailing hemisphere.<ref>[https://ift.tt/2RdZrXH First map of extraterrestrial planet] – Center of Astrophysics.</ref> However, [[libration]] due to non-circular orbits or axial tilts causes this point to move around any fixed point on the celestial body like an [[analemma]].
== Ellipsoid of revolution ==
[[Reference ellipsoid]]s are also useful for geodetic mapping of other planetary bodies including planets, their satellites, asteroids and comet nuclei. Some well observed bodies such as the [[Moon]] and [[Mars]] now have quite precise reference ellipsoids.
For rigid-surface nearly-spherical bodies, which includes all the rocky planets and many moons, ellipsoids are defined in terms of the axis of rotation and the mean surface height excluding any atmosphere. Mars is actually [[Oval (geometry)|egg shaped]], where its north and south polar radii differ by approximately , however this difference is small enough that the average polar radius is used to define its ellipsoid. The Earth's Moon is effectively spherical, having almost no bulge at its equator. Where possible, a fixed observable surface feature is used when defining a reference meridian.
For gaseous planets like [[Jupiter]], an effective surface for an ellipsoid is chosen as the equal-pressure boundary of one [[Bar (unit)|bar]]. Since they have no permanent observable features, the choices of prime meridians are made according to mathematical rules.
== Triaxial ellipsoid (spheroid) ==
Small moons, asteroids, and comet nuclei frequently have irregular shapes. For some of these, such as Jupiter's [[Io (moon)|Io]], a scalene (triaxial) ellipsoid is a better fit than the oblate spheroid. For highly irregular bodies, the concept of a reference ellipsoid may have no useful value, so sometimes a spherical reference is used instead and points identified by planetocentric latitude and longitude. Even that can be problematic for [[convex set|non-convex]] bodies, such as [[433 Eros|Eros]], in that latitude and longitude don't always uniquely identify a single surface location.
Smaller bodies ([[Io (moon)|Io]], [[Mimas (moon)|Mimas]], etc.) tend to be better approximated by [[triaxial ellipsoid]]s; however, triaxial ellipsoids would render many computations more complicated, especially those related to [[map projection]]s. Many projections would lose their elegant and popular properties. For this reason spherical reference surfaces are frequently used in mapping programs.
==See also==
*[[Geoid#Other celestial bodies]]
*[[Planetary cartography]]
==References==
[[Category:Planetary science|C]]
[[Category:Celestial coordinate system]]
[[Category:Coordinate system]]
[[Category:Astronomy]]
[[Category:Astrometry]]
[[Category:Geodesy]]
[[Category:Cartography]]
[[Category:Navigation]]
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