Ellipsoidal coordinates
Ellipsoidal coordinates are spherical coordinates (i.e. coordinates on an ellipsoid of revolution ) that are defined analogously to the geographic coordinates on the earth's surface. You can refer to two types of ellipsoids:
- on a flattened ellipsoid, the shape of which most larger celestial bodies have, or
- to an elongated ellipsoid , which has more of a theoretical meaning, but can also be a model for equilibrium figures.
The definition of precise ellipsoidal coordinates is especially important for the earth , where they can already be measured to the nearest centimeter, and (less precisely) for the observation of the nearby planets .
The sun and moon, on the other hand, are almost spherical , which makes complicated ellipsoidal calculations for these two celestial bodies unnecessary.
Ellipsoidal coordinates in geodesy
- The ellipsoidal width of a point on the surface of an ellipsoid of revolution is the angle which its normal ellipsoid forms with the equatorial plane of the solid of revolution .
- The ellipsoidal length is the angle counted in the axis of rotation of the ellipsoid between the meridian plane of the point and the meridian plane of a reference point. It therefore requires the definition of a prime meridian .
In geodesy - d. H. In relation to a reference - or mean earth ellipsoid - the two ellipsoidal coordinates are also called geodetic latitude and geodetic longitude . They can also be understood as the components of the direction vector of the ellipsoidal normal and are an important calculation variable in earth measurement , land surveying and cartography .
The purely geometrically defined ellipsoidal coordinates must not be confused with the vector components of the perpendicular direction . This is determined by the mass distribution of the body and is therefore of a physical nature. On earth, their components at a measuring point are called astronomical latitude and astronomical longitude . The difference between them and the ellipsoidal coordinates of the measuring point is the deviation from the perpendicular .
Ellipsoidal coordinates on planets
Even on the planets of the solar system , positions are sometimes given in ellipsoidal coordinates if the deviation from the spherical shape is more than a few per thousand . In this case, an ellipsoid of revolution (or in a few cases also a three-axis ellipsoid ) is adapted to the shape of the celestial body, to which the latitudes and longitudes are then related.
The large gas planets Jupiter and Saturn (1:16 and 1:10 respectively) have the strongest flattening in the solar system , followed by the ice giants Uranus and Neptune (2–3%) and Mars (3-axis). For the Saturn coordinates and those of its outer neighbors Uranus and Jupiter, no special term is used because the surfaces show only few details, but for the two closer planets:
- areographic coordinates on Mars
- iovigraphic coordinates on Jupiter.
While the latitude is defined by the rotation of the planet (or its equatorial plane), the respective prime meridian is to be chosen arbitrarily for the ellipsoidal length . On Mars, it was laid by a striking dark line structure in the north of the Meridiani Sinus plain . At Jupiter there was even a need for two length systems I and II, because the cloudy equatorial strips rotate differently by about 5.2 minutes .
On the sun and on the earth's moon, however, spherical coordinates are sufficient because flattening is hardly detectable by measurement:
- heliographic coordinates on the sun
- selenographic coordinates on the moon.
The extent to which the eccentricity of the moon's center of gravity (by almost 2 km towards the earth) is included in the coordinates is not handled uniformly.
See also
literature
- Karl Ledersteger : Astronomical and physical geodesy (earth measurement). Volume V of the series of reference books Jordan-Eggert-Kneissl, Handbuch der Vermessungskunde, Verlag JB Metzler, Stuttgart 1969
- Wolfgang Torge : Geodesy , 3rd edition. Verlag de Gruyter, Berlin 2001.