Planetary coordinate system

Last updated
Chart of lunar maria with lines of longitude and latitude. The prime meridian is the centre of the near side of the Moon. Astronomy for the use of schools and academies (1882) (14577550018).jpg
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) [1] [2] is a generalization of the geographic, geodetic, and the geocentric coordinate systems for planets 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, [3] [4] Venus, [5] Mars, [6] the four Galilean moons of Jupiter, [7] and Triton, the largest moon of Neptune. [8]

Contents

Longitude

The longitude systems of most of those bodies with observable rigid surfaces have been defined by references to a surface feature such as a 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 prograde) rotation; otherwise the rotation is said to be retrograde.

In the absence of other information, the axis of rotation is assumed to be normal to the mean orbital plane; 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 planets, since their surface features are constantly changing and moving at various rates, the rotation of their magnetic fields 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. [9] [10] For 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 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. [11] [12] [13]

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. [14] 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

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 ellipsoids of revolution for which the equatorial radius is larger than the polar radius, such that they are oblate spheroids.

Altitude

Vertical position can be expressed with respect to a given vertical datum, by means of physical quantities analogous to the 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). [15]

The areoid (the geoid of Mars) [16] has been measured using flight paths of satellite missions such as Mariner 9 and 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. [17]

The selenoid (the geoid of the Moon) has been measured gravimetrically by the GRAIL twin satellites. [18]

Ellipsoid of revolution (spheroid)

Reference ellipsoids 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 egg shaped, where its north and south polar radii differ by approximately 6 km (4 miles), 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. Since they have no permanent observable features, the choices of prime meridians are made according to mathematical rules.

Flattening

Comparison of the rotation period (sped up 10 000 times, negative values denoting retrograde), flattening and axial tilt of the planets and the Moon (SVG animation) Solar system bodies rotation animation.svg
Comparison of the rotation period (sped up 10 000 times, negative values denoting retrograde), flattening and axial tilt of the planets and the Moon (SVG animation)

For the WGS84 ellipsoid to model Earth, the defining values are [19]

a (equatorial radius): 6 378 137.0 m
(inverse flattening): 298.257 223 563

from which one derives

b (polar radius): 6 356 752.3142 m,

so that the difference of the major and minor semi-axes is 21.385 km (13 mi). 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 pix by 300 pix. Thus illustrations typically greatly exaggerate the flattening to highlight the concept of any planet's oblateness.

Other f values in the Solar System are 1⁄16 for Jupiter, 1⁄10 for Saturn, and 1⁄900 for the Moon. The flattening of the Sun is about 9×10−6.

Origin of flattening

In 1687, Isaac Newton published the 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). [20] The amount of flattening depends on the density and the balance of gravitational force and centrifugal force.

Equatorial bulge

Equatorial bulge of the Solar Systems major celestial bodies
BodyDiameter (km)Equatorial
bulge (km)		 Flattening
ratio		Rotation
period (h)		Density
(kg/m3)		Deviation
from
EquatorialPolar
Earth 12,756.212,713.642.61 : 299.423.93655151 : 232−23%
Mars 6,792.46,752.4401 : 17024.63239331 : 175+3%
Ceres 964.3891.872.51 : 13.39.07421621 : 13.1−2%
Jupiter 142,984133,7089,2761 : 15.419.92513261 : 9.59−38%
Saturn 120,536108,72811,8081 : 10.2110.566871 : 5.62−45%
Uranus 51,11849,9461,1721 : 43.6217.2412701 : 27.71−36%
Neptune 49,52848,6828461 : 58.5416.1116381 : 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 11808 km Saturn is the planet with the largest equatorial bulge in our Solar System.

Equatorial ridges

Equatorial bulges should not be confused with equatorial ridges . Equatorial ridges are a feature of at least four of Saturn's moons: the large moon Iapetus and the tiny moons Atlas, Pan, and 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 probe in 2005; the Daphnean ridge was discovered in 2017. The ridge on Iapetus is nearly 20 km wide, 13 km high and 1300 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

Small moons, asteroids, and comet nuclei frequently have irregular shapes. For some of these, such as Jupiter's 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 non-convex bodies, such as Eros, in that latitude and longitude don't always uniquely identify a single surface location.

Smaller bodies (Io, Mimas, etc.) tend to be better approximated by triaxial ellipsoids; however, triaxial ellipsoids would render many computations more complicated, especially those related to map projections. Many projections would lose their elegant and popular properties. For this reason spherical reference surfaces are frequently used in mapping programs.

See also

Related Research Articles

<span class="mw-page-title-main">Ecliptic</span> Apparent path of the Sun on the celestial sphere

The ecliptic or ecliptic plane is the orbital plane of Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic against the background of stars. The ecliptic is an important reference plane and is the basis of the ecliptic coordinate system.

<span class="mw-page-title-main">Geodesy</span> Science of measuring the shape, orientation, and gravity of the Earth and other astronomical bodies

Geodesy is the science of measuring and representing the geometry, gravity, and spatial orientation of the Earth in temporally varying 3D. It is called planetary geodesy when studying other astronomical bodies, such as planets or circumplanetary systems.

<span class="mw-page-title-main">Latitude</span> Geographic coordinate specifying north–south position

In geography, latitude is a coordinate that specifies the north–south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at the south pole to 90° at the north pole, with 0° at the Equator. Lines of constant latitude, or parallels, run east–west as circles parallel to the equator. Latitude and longitude are used together as a coordinate pair to specify a location on the surface of the Earth.

<span class="mw-page-title-main">Geographic coordinate system</span> System to specify locations on Earth

The geographic coordinate system (GCS) is a spherical or geodetic coordinate system for measuring and communicating positions directly on the Earth as latitude and longitude. It is the simplest, oldest and most widely used of the various spatial reference systems that are in use, and forms the basis for most others. Although latitude and longitude form a coordinate tuple like a cartesian coordinate system, the geographic coordinate system is not cartesian because the measurements are angles and are not on a planar surface.

<span class="mw-page-title-main">Equatorial coordinate system</span> Celestial coordinate system used to specify the positions of celestial objects

The equatorial coordinate system is a celestial coordinate system widely used to specify the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the centre of Earth, a fundamental plane consisting of the projection of Earth's equator onto the celestial sphere, a primary direction towards the vernal equinox, and a right-handed convention.

<span class="mw-page-title-main">Prime meridian</span> Line of longitude, at which longitude is defined to be 0°

A prime meridian is an arbitrarily-chosen meridian in a geographic coordinate system at which longitude is defined to be 0°. Together, a prime meridian and its anti-meridian form a great circle. This great circle divides a spheroid, like Earth, into two hemispheres: the Eastern Hemisphere and the Western Hemisphere. For Earth's prime meridian, various conventions have been used or advocated in different regions throughout history. Earth's current international standard prime meridian is the IERS Reference Meridian. It is derived, but differs slightly, from the Greenwich Meridian, the previous standard.

<span class="mw-page-title-main">Spheroid</span> Surface formed by rotating an ellipse

A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circular symmetry.

<span class="mw-page-title-main">Equatorial bulge</span> Outward bulge around a planets equator due to its rotation

An equatorial bulge is a difference between the equatorial and polar diameters of a planet, due to the centrifugal force exerted by the rotation about the body's axis. A rotating body tends to form an oblate spheroid rather than a sphere.

<span class="mw-page-title-main">Earth radius</span> Distance from the Earth surface to a point near its center

Earth radius is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly 6,378 km (3,963 mi) to a minimum of nearly 6,357 km (3,950 mi).

<span class="mw-page-title-main">Figure of the Earth</span> Size and shape used to model the Earth for geodesy

In geodesy, the figure of the Earth is the size and shape used to model planet Earth. The kind of figure depends on application, including the precision needed for the model. A spherical Earth is a well-known historical approximation that is satisfactory for geography, astronomy and many other purposes. Several models with greater accuracy have been developed so that coordinate systems can serve the precise needs of navigation, surveying, cadastre, land use, and various other concerns.

<span class="mw-page-title-main">Areography</span> Delineation and characterization of Martian regions

Areography, also known as the geography of Mars, is a subfield of planetary science that entails the delineation and characterization of regions on Mars. Areography is mainly focused on what is called physical geography on Earth; that is the distribution of physical features across Mars and their cartographic representations. In April 2023, The New York Times reported an updated global map of Mars based on images from the Hope spacecraft. A related, but much more detailed, global Mars map was released by NASA on 16 April 2023.

<span class="mw-page-title-main">Selenographic coordinate system</span> Coordinate system used on the Moon

The selenographic coordinate system is used to refer to locations on the surface of Earth's moon. Any position on the lunar surface can be referenced by specifying two numerical values, which are comparable to the latitude and longitude of Earth. The longitude gives the position east or west of the Moon's prime meridian, which is the line passing from the lunar north pole through the point on the lunar surface directly facing Earth to the lunar south pole. This can be thought of as the midpoint of the visible Moon as seen from the Earth. The latitude gives the position north or south of the lunar equator. Both of these coordinates are given in degrees.

The navigational triangle or PZX triangle is a spherical triangle used in astronavigation to determine the observer's position on the globe. It is composed of three reference points on the celestial sphere:

<span class="mw-page-title-main">Earth-centered, Earth-fixed coordinate system</span> 3-D coordinate system centered on the Earth

The Earth-centered, Earth-fixed coordinate system, also known as the geocentric coordinate system, is a cartesian spatial reference system that represents locations in the vicinity of the Earth as X, Y, and Z measurements from its center of mass. Its most common use is in tracking the orbits of satellites and in satellite navigation systems for measuring locations on the surface of the Earth, but it is also used in applications such as tracking crustal motion.

The poles of astronomical bodies are determined based on their axis of rotation in relation to the celestial poles of the celestial sphere. Astronomical bodies include stars, planets, dwarf planets and small Solar System bodies such as comets and minor planets, as well as natural satellites and minor-planet moons.

<span class="mw-page-title-main">Earth ellipsoid</span> Geometric figure which approximates the Earths shape

An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations.

<span class="mw-page-title-main">Earth-centered inertial</span> Coordinate frames

Earth-centered inertial (ECI) coordinate frames have their origins at the center of mass of Earth and are fixed with respect to the stars. "I" in "ECI" stands for inertial, in contrast to the "Earth-centered – Earth-fixed" (ECEF) frames, which remains fixed with respect to Earth's surface in its rotation, and then rotates with respect to stars.

<span class="mw-page-title-main">Vertical datum</span> Reference surface for vertical positions

In geodesy, surveying, hydrography and navigation, vertical datum or altimetric datum, is a reference coordinate surface used for vertical positions, such as the elevations of Earth-bound features and altitudes of satellite orbits and in aviation. In planetary science, vertical datums are also known as zero-elevation surface or zero-level reference.

<span class="mw-page-title-main">Equator</span> Imaginary line halfway between Earths North and South poles

The equator is a circle of latitude that divides a spheroid, such as Earth, into the Northern and Southern hemispheres. On Earth, the Equator is an imaginary line located at 0 degrees latitude, about 40,075 km (24,901 mi) in circumference, halfway between the North and South poles. The term can also be used for any other celestial body that is roughly spherical.

<span class="mw-page-title-main">Geodetic coordinates</span> Geographic coordinate system

Geodetic coordinates are a type of curvilinear orthogonal coordinate system used in geodesy based on a reference ellipsoid. They include geodetic latitude (north/south) ϕ, longitude (east/west) λ, and ellipsoidal heighth. The triad is also known as Earth ellipsoidal coordinates.

References

  1. ↑ https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/Tutorials/pdf/individual_docs/17_frames_and_coordinate_systems.pdf
  2. ↑ "Planetocentric and planetographic coordinates".
  3. ↑ Davies, M. E., "Surface Coordinates and Cartography of Mercury," Journal of Geophysical Research, Vol. 80, No. 17, June 10, 1975.
  4. ↑ Davies, M. E., S. E. Dwornik, D. E. Gault, and R. G. Strom, NASA Atlas of Mercury, NASA Scientific and Technical Information Office, 1978.
  5. ↑ 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.
  6. ↑ 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.
  7. ↑ Merton E. Davies, Thomas A. Hauge, et al.: Control Networks for the Galilean Satellites: November 1979 R-2532-JPL/NASA
  8. ↑ 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.
  9. ↑ Where is zero degrees longitude on Mars? – Copyright 2000 – 2010 European Space Agency. All rights reserved.
  10. ↑ 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.
  11. ↑ Davies, M. E., "Surface Coordinates and Cartography of Mercury," Journal of Geophysical Research, Vol. 80, No. 17, June 10, 1975.
  12. ↑ Archinal, Brent A.; A'Hearn, Michael F.; Bowell, Edward L.; Conrad, Albert R.; et al. (2010). "Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2009". Celestial Mechanics and Dynamical Astronomy. 109 (2): 101–135. Bibcode:2011CeMDA.109..101A. doi:10.1007/s10569-010-9320-4. ISSN   0923-2958. S2CID   189842666.
  13. ↑ "USGS Astrogeology: Rotation and pole position for the Sun and planets (IAU WGCCRE)". Archived from the original on October 24, 2011. Retrieved October 22, 2009.
  14. ↑ First map of extraterrestrial planet – Center of Astrophysics.
  15. ↑ Wieczorek, M. A. (2007). "Gravity and Topography of the Terrestrial Planets". Treatise on Geophysics. pp. 165–206. doi:10.1016/B978-044452748-6.00156-5. ISBN   9780444527486.
  16. ↑ Ardalan, A. A.; Karimi, R.; Grafarend, E. W. (2009). "A New Reference Equipotential Surface, and Reference Ellipsoid for the Planet Mars". Earth, Moon, and Planets. 106 (1): 1–13. doi:10.1007/s11038-009-9342-7. ISSN   0167-9295. S2CID   119952798.
  17. ↑ Cattermole, Peter (1992). Mars The story of the Red Planet. Dordrecht: Springer Netherlands. p. 185. ISBN   9789401123068.
  18. ↑ Lemoine, Frank G.; Goossens, Sander; Sabaka, Terence J.; Nicholas, Joseph B.; Mazarico, Erwan; Rowlands, David D.; Loomis, Bryant D.; Chinn, Douglas S.; Caprette, Douglas S.; Neumann, Gregory A.; Smith, David E.; Zuber, Maria T. (2013). "High‒degree gravity models from GRAIL primary mission data". Journal of Geophysical Research: Planets. American Geophysical Union (AGU). 118 (8): 1676–1698. Bibcode:2013JGRE..118.1676L. doi: 10.1002/jgre.20118 . hdl: 2060/20140010292 . ISSN   2169-9097.
  19. ↑ The WGS84 parameters are listed in the National Geospatial-Intelligence Agency publication TR8350.2 page 3-1.
  20. ↑ Isaac Newton:Principia Book III Proposition XIX Problem III, p. 407 in Andrew Motte translation
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.