Planetary coordinate system

Source: Wikipedia, the free encyclopedia.
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)

coordinate systems for planets
other than Earth. Similar coordinate systems are defined for other solid
selenographic coordinates for the Moon
. The coordinate systems for almost all of the solid bodies in 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]

Longitude

See also:
Prime meridian (planets)

The longitude systems of most of those bodies with observable rigid surfaces have been defined by references to a surface feature such as a

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,

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

See also: Equatorial bulge § Other celestial bodies

Planetographic latitude and planetocentric latitude may be similarly defined. The zero

axis of rotation (poles of astronomical bodies
). The reference surfaces for some planets (such as Earth and
oblate spheroids
.

Altitude

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

Further information: 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)

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,

centrifugal force
.

Equatorial bulge

Further information: Equatorial bulge
Equatorial bulge of the Solar Systems major celestial bodies
Body Diameter (km) Equatorial
bulge (km) 		Flattening
ratio 		Rotation
period (h) 		Density
(kg/m3) 		Deviation
from
Equatorial Polar
Earth 012,756.2 012,713.6 00 042.6 1 : 299.4 23.936 5515 1 : 232 −23%
Mars 006,792.4 006,752.4 00 040 1 : 170 24.632 3933 1 : 175 0+3%
Ceres 000 964.3 000 891.8 00072.5 1 : 13.3 09.074 2162 1 : 13.1 0−2%
Jupiter 142,984 133,708 09,276 1 : 15.41 09.925 1326 1 : 9.59 −38%
Saturn 120,536 108,728 11,808 1 : 10.21 10.56 0687 1 : 5.62 −45%
Uranus 051,118 049,946 01,172 1 : 43.62 17.24 1270 1 : 27.71 −36%
Neptune 049,528 048,682 00 846 1 : 58.54 16.11 1638 1 : 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

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

See also:
Triaxial ellipsoidal longitude and 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, 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 (

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

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. 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. ISBN 9780444527486
    .
  16. S2CID 119952798
    .
  17. ISBN 9789401123068
    .
  18. 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
Retrieved from "https://en.wikipedia.org/w/index.php?title=Planetary_coordinate_system&oldid=1209859168"