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{{Short description|Coordinate system for planets}}
[[File:Astronomy for the use of schools and academies (1882) (14577550018).jpg|thumb|Chart of lunar maria with lines of longitude and latitude. The [[prime meridian]] is the centre of the [[near side of the Moon]].]]

A '''planetary coordinate system''' (also referred to as '''''planetographic''''', '''''planetodetic''''', or '''''planetocentric''''')<ref>https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/Tutorials/pdf/individual_docs/17_frames_and_coordinate_systems.pdf {{Bare URL PDF|date=August 2024}}</ref><ref>{{cite web | url=https://www.daviddarling.info/encyclopedia/P/planetocentric_coordinates.html | title=Planetocentric and planetographic coordinates }}</ref> is a generalization of the [[geographic coordinate system|geographic]], [[geodetic coordinate system|geodetic]], and the [[geocentric coordinate system|geocentric]] [[coordinate systems]] for [[planet]]s other than Earth.
Similar coordinate systems are defined for other solid [[celestial bodies]], such as in 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>
A '''planetary datum''' is a generalization of [[geodetic datum]]s for other planetary bodies, such as the [[Mars datum]]; it requires the specification of physical reference points or surfaces with fixed coordinates, such as a specific crater for the reference meridian or the best-fitting [[equigeopotential]] as zero-level surface.<ref>{{Cite web |title=lorem ipsum |url=https://planetarynames.wr.usgs.gov/Page/Website |access-date=2024-10-02 |website=planetarynames.wr.usgs.gov|language=en-GB}}</ref>

==Longitude==
{{see also|Prime meridian (planets)}}
{{More citations needed section|date=January 2020}}

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 [[giant planet]]s, 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>[http://www.esa.int/SPECIALS/Mars_Express/SEM0VQV4QWD_0.html 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 sunlight). 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">{{cite journal |last1=Archinal |first1=Brent A. |display-authors=4 |last2=A'Hearn |first2=Michael F. |last3=Bowell |first3=Edward L. |last4=Conrad |first4=Albert R. |last5=Consolmagno |first5=Guy J. |last6=Courtin |first6=Régis |last7=Fukushima |first7=Toshio |last8=Hestroffer |first8=Daniel |last9=Hilton |first9=James L. |last10=Krasinsky |first10=George A. |last11=Neumann |first11=Gregory A. |last12=Oberst |first12=Jürgen |last13=Seidelmann |first13=P. Kenneth |last14=Stooke |first14=Philip J. |last15=Tholen |first15=David J. |last16=Thomas |first16=Peter C. |last17=Williams |first17=Iwan P. |title=Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2009 |journal=Celestial Mechanics and Dynamical Astronomy |volume=109 |issue=2 |date=2010 |pages=101–135 |issn=0923-2958 |doi=10.1007/s10569-010-9320-4 |bibcode=2011CeMDA.109..101A|s2cid=189842666 }}</ref><ref name="usgs">{{cite web |url=https://astrogeology.usgs.gov/Projects/WGCCRE/constants/iau2000_table1.html |access-date=October 22, 2009 |title=USGS Astrogeology: Rotation and pole position for the Sun and planets (IAU WGCCRE) |archive-url=https://web.archive.org/web/20111024101856/http://astrogeology.usgs.gov/Projects/WGCCRE/constants/iau2000_table1.html |archive-date=October 24, 2011 |url-status=dead}}</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>[http://www.cfa.harvard.edu/image_archive/2007/31/lores.jpg 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]].

==Latitude==
{{see also|Equatorial bulge}}
{{stub section|date=May 2021}}

'''Planetographic latitude''' and '''planetocentric latitude''' may be similarly defined.
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.

==Altitude==
[[Vertical position]] can be expressed with respect to a given [[vertical datum]], by means of physical quantities analogous to the [[topography|topographical]] [[geocentric distance]] (compared to a constant [[nominal Earth radius]] or the varying [[geocentric radius]] of the reference ellipsoid surface) or [[altitude]]/[[elevation]] (above and below the [[geoid]]).<ref>{{Cite book | doi = 10.1016/B978-044452748-6.00156-5| chapter = Gravity and Topography of the Terrestrial Planets| title = Treatise on Geophysics| pages = 165–206| year = 2007| last1 = Wieczorek | first1 = M. A. | isbn = 9780444527486}}</ref>

The ''[[areoid]]'' (the geoid of [[Mars]])<ref name="ArdalanKarimi2009">{{cite journal|last1=Ardalan|first1=A. A.|last2=Karimi|first2=R.|last3=Grafarend|first3=E. W.|title=A New Reference Equipotential Surface, and Reference Ellipsoid for the Planet Mars|journal=Earth, Moon, and Planets|volume=106|issue=1|year=2009|pages=1–13|issn=0167-9295|doi=10.1007/s11038-009-9342-7|s2cid=119952798}}</ref> has been measured using flight paths of satellite missions such as [[Mariner 9]] and [[Viking program|Viking]]. The main departures from the ellipsoid expected of an ideal fluid are from the [[Tharsis]] volcanic plateau, a continent-size region of elevated terrain, and its antipodes.<ref name=Cattermole>{{cite book|last1=Cattermole|first1=Peter|title=Mars The story of the Red Planet|date=1992|publisher=[[Springer Netherlands]]|location=Dordrecht|isbn=9789401123068|page=185}}</ref>

The ''[[selenoid]]'' (the geoid of the [[Moon]]) has been measured [[gravimetry|gravimetrically]] by the [[GRAIL]] twin satellites.<ref>{{cite journal | last1=Lemoine | first1=Frank G. | last2=Goossens | first2=Sander | last3=Sabaka | first3=Terence J. | last4=Nicholas | first4=Joseph B. | last5=Mazarico | first5=Erwan | last6=Rowlands | first6=David D. | last7=Loomis | first7=Bryant D. | last8=Chinn | first8=Douglas S. | last9=Caprette | first9=Douglas S. | last10=Neumann | first10=Gregory A. | last11=Smith | first11=David E. | last12=Zuber | first12=Maria T. | title=High‒degree gravity models from GRAIL primary mission data | journal=Journal of Geophysical Research: Planets | publisher=American Geophysical Union (AGU) | volume=118 | issue=8 | year=2013 | issn=2169-9097 | doi=10.1002/jgre.20118 | pages=1676–1698| bibcode=2013JGRE..118.1676L | doi-access=free | hdl=2060/20140010292 | hdl-access=free }}</ref>

== Ellipsoid of revolution (spheroid) {{anchor|Ellipsoid|Spheroid}} ==
[[Reference ellipsoid]]s are also useful for defining [[geodetic coordinates]] and mapping 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 {{convert|6|km|0|abbr=in}}, 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.

===Flattening===
{{further|Flattening}}
{{solar_system_bodies_rotation_animation.svg}}
For the [[WGS84]] ellipsoid to model [[Earth]], the ''defining'' values are<ref>[http://earth-info.nga.mil/GandG/publications/tr8350.2/tr8350_2.html The WGS84 parameters are listed in the National Geospatial-Intelligence Agency publication TR8350.2] page 3-1.</ref> 
: {{mvar|a}} (equatorial radius): 6 378 137.0&nbsp;m
: <math>\frac{1}{f}\,\!</math> (inverse flattening): 298.257 223 563
from which one derives
: {{mvar|b}} (polar radius): 6 356 752.3142&nbsp;m,
so that the difference of the major and minor semi-axes is {{convert|21.385|km|0|abbr=on}}. This is only 0.335% of the major axis, so a representation of Earth on a computer screen would be sized as 300 pixels by 299 pixels. This is rather indistinguishable from a sphere shown as 300{{nbsp}}pix by 300{{nbsp}}pix. Thus illustrations [[artistic license|typically greatly exaggerate]] the flattening to highlight the concept of any planet's oblateness.

Other {{mvar|f}} values in the Solar System are {{frac|1|16}} for [[Jupiter]], {{frac|1|10}} for [[Saturn]], and {{frac|1|900}} for the [[Moon]]. The flattening of the [[Sun]] is about {{val|9|e=-6}}.

====Origin of flattening====
In 1687, [[Isaac Newton]] published the ''[[Philosophiæ Naturalis Principia Mathematica|Principia]]'' in which he included a proof that a rotating self-gravitating fluid body in equilibrium takes the form of an oblate [[ellipsoid]] of revolution (a [[spheroid]]).<ref name=newton>Isaac Newton:''Principia'' Book III Proposition XIX Problem III, p. 407 in [https://archive.org/stream/ost-physics-newtonspmathema00newtrich/newtonspmathema00newtrich#page/n411/mode/2up Andrew Motte translation]</ref> The amount of flattening depends on the [[density]] and  the balance of [[gravitational force]] and [[centrifugal force (rotating reference frame)|centrifugal force]].

=== Equatorial bulge ===
{{further|Equatorial bulge}}

{| class="wikitable float center"
|+ Equatorial bulge of the Solar Systems major celestial bodies
|-
! rowspan="2" | Body
! colspan="2" | Diameter (km)
! rowspan="2" | Equatorial<br>bulge (km)
! rowspan="2" | [[Flattening]]<br>ratio
! rowspan="2" | Rotation<br>period (h)
! rowspan="2" | Density<br>(kg/m<sup>3</sup>)
! rowspan="2" | <math>f</math>
! rowspan="2" | Deviation<br>from <math>f</math>
|-
! Equatorial 
! Polar
|-
| [[Earth]]                      || {{0}}12,756.2   || {{0}}12,713.6   || {{0|00&nbsp;0}}42.6 || 1&nbsp;:&nbsp;299.4 || 23.936     || 5515     || 1&nbsp;:&nbsp;232   || −23%
|-
| [[Mars]]                       || {{0|00}}6,792.4 || {{0|00}}6,752.4 || {{0|00&nbsp;0}}40   || 1&nbsp;:&nbsp;170   || 24.632     || 3933     || 1&nbsp;:&nbsp;175   || {{0}}+3%
|-
| [[Ceres (dwarf planet)|Ceres]] || {{0|000&nbsp;}}964.3 || {{0|000&nbsp;}}891.8 || {{0|000}}72.5        || 1&nbsp;:&nbsp;13.3  || {{0}}9.074 || 2162     || 1&nbsp;:&nbsp;13.1  || {{0}}−2%
|-
| [[Jupiter]]                    || 142,984         || 133,708         || {{0}}9,276     || 1&nbsp;:&nbsp;15.41 || {{0}}9.925 || 1326     || 1&nbsp;:&nbsp;9.59  || −38%
|-
| [[Saturn]]                     || 120,536         || 108,728         || 11,808         || 1&nbsp;:&nbsp;10.21 || 10.56      || {{0}}687 || 1&nbsp;:&nbsp;5.62  || −45%
|-
| [[Uranus]]                     || {{0}}51,118     || {{0}}49,946     || {{0}}1,172     || 1&nbsp;:&nbsp;43.62 || 17.24      || 1270     || 1&nbsp;:&nbsp;27.71 || −36%
|-
| [[Neptune]]                    || {{0}}49,528     || {{0}}48,682     || {{0|00&nbsp;}}846   || 1&nbsp;:&nbsp;58.54 || 16.11      || 1638     || 1&nbsp;:&nbsp;31.22 || −47%
|}

Generally any celestial body that is rotating (and that is sufficiently massive to draw itself into spherical or near spherical shape) will have an equatorial bulge matching its rotation rate. With {{val|11808|u=km}} [[Saturn]] is the planet with the largest equatorial bulge in our Solar System.

====Equatorial ridges====
Equatorial bulges should not be confused with ''[[equatorial ridge|equatorial ridges]]''. Equatorial ridges are a feature of at least four of Saturn's moons: the large moon [[Iapetus (moon)|Iapetus]] and the tiny moons [[Atlas (moon)|Atlas]], [[Pan (moon)|Pan]], and [[Daphnis (moon)|Daphnis]]. These ridges closely follow the moons' equators. The ridges appear to be unique to the Saturnian system, but it is uncertain whether the occurrences are related or a coincidence. The first three were discovered by the [[Cassini-Huygens|''Cassini'' probe]] in 2005; the Daphnean ridge was discovered in 2017. The ridge on Iapetus is nearly 20&nbsp;km wide, 13&nbsp;km high and 1300&nbsp;km long. The ridge on Atlas is proportionally even more remarkable given the moon's much smaller size, giving it a disk-like shape. Images of Pan show a structure similar to that of Atlas, while the one on Daphnis is less pronounced.

== Triaxial ellipsoid ==
{{see also|Triaxial ellipsoidal longitude|Map projection of the triaxial ellipsoid}}

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==
*[[Apparent longitude]]
*[[Areography]] (geography of Mars)
*[[Astronomical coordinate systems]]
*[[List of tallest mountains in the Solar System]]
*[[Planetary cartography]]
*[[Planetary surface]]
*[[Topography of Mars]]
*[[Selenography]] (Topography of the Moon)

==References==
{{reflist}}

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