Reference frames supply the base to define positions and velocities by means of coordinates. In 3dimensional space, for example, you need 3 coordinates to determine a position. The collection of coordinates is called a vector. Only vectors referring to the same reference frame may be combined in a meaningful manner. You may characterize reference frames by three quantities:
 reference point (a center body or a virtual center point, the origin)
 reference plane (ecliptic, equator, horizon, ..., the xyplane)
 reference direction (vernal equinox, Greenwich, South, ..., xaxis)
We mostly use (righthanded) rectangular coordinate systems (euclidean systems), The following reference frames are common in celestial mechanics and astronomy:
Name 
Origin 
XYPlane 
XAxis 
Heliocentric ecliptical system 
Sun 
Ecliptic 
Vernal Equinox 
Geocentric ecliptical system 
Earth 
Ecliptic 
Vernal Equinox 
Spacefixed equatorial system 
Earth 
Equator 
Vernal Equinox 
Earthfixed equatorial system 
Earth 
Equator 
Greenwich/Eq. 
Topocentric equatorial system 
Observer 
 Equator 
 Greenwich/Eq. 
Topocentric horizon system 
Observer 
Horizon 
South 
Further distinctions concerning equatorial systems are required for high precision transformations. Due to the gravitational pull of mainly the Sun and the Moon, the Earth's rotation axis is tumbling in space. Therefore, the Earthfixed reference frames are moving disorderly in space as well. Well known are the main effects like nutation (period of approx. 18 years) and precession (period of approx. 26000 years). Less known are the short term variations which displace the rotation axis with respect to the Earth's surface and increase or decrease the speed of rotation.
If the reference frames are in mutual motion, small "corrections" have to be added to the transformed vectors due to the finite speed of light (aberration and light time correction, in the solar system these may amount to some tens of arcseconds). To further increase the precision of transformations, even more tiny "corrections" have to be added, which take into account the presence of gravitational fields (some milliarcseconds to less than two arcseconds in the solar system). Concerning accuracy, remember: One arcsecond is the angle enclosing a dollar coin in a distance of about 4 kilometers (!). The Transform applet uses today's noon as the actual epoch and assumes an observer at the north pole for the sake of simplicity. The aforementioned "corrections" are being neglected. When choosing polar coordinates instead of rectangular ones, be sure of entering decimal degrees (dd.dddd) for the angles. In the case of polar coordinates, r represents the distance according to the chosen unit, ph shows the angle between the xaxis and the projection of the vector onto the xyplane and th is the angle enclosed by the zaxis and the vector.
Transformations are performed by leaving the cursor in one of the textfields which are going to represent the input and hitting RETURN, or, by selecting a reference frame. Relationships between reference frames:
Frame1 
Frame2 
relationship 
Heliocentric ecliptical system 
Geocentric ecliptical system 
Heliocentric position of the Earth 
Geocentric ecliptical system 
Spacefixed equatorial system 
Mean obliquity of ecliptic 
Spacefixed equatorial system 
Earthfixed equatorial system 
Sidereal time 
Earthfixed equatorial system 
Topocentric equatorial system 
Geocentric position of observer 
Topocentric equatorial system 
Topocentric horizon system 
Longitude and latitude of observer 
Mutual motions are taking place between
Frame1 
Frame2 
Motion 
Heliocentric ecliptical system 
Geocentric ecliptical system 
Earth orbiting the Sun 
Earthfixed equatorial system 
Topocentric equatorial system 
Observer rotating about the Earth's rotation axis 
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Dieter Egger, last update 20020226
