1.2.5 System Ingredients

SATELLITE EPHEMERIDES

A satellite ephemeris may take a number of forms (in order of decreasing convenience for a user):

• a list of coordinates as a function of time,
• a polynomial representation of the trajectory in a suitable reference system (for example alongtrack, crosstrack, or radial components), or
• satellite position and velocity at some reference time, requiring these parameters to be derived for subsequent times through a solution of the Equations of Motion.
  
  

Satellite ephemerides must be computed, and fundamental to this task are the issues of reference systems (see earlier sections) and the forces acting on a satellite in orbit. After a satellite has separated from its carrier rocket it begins orbiting about the earth. The satellite's orbit is determined by its initial position and velocity, and the force fields which are in effect (SEEBER, 1993). In the case of the gravitational field of a spherically symmetric body (a reasonable approximation of the earth to the level of about 1 part in 10³) this produces an elliptical orbit which is fixed in space -- the Keplerian ellipse (Figure 1).

Figure 1. The Keplerian Ellipse and Keplerian Orbital Elements.

Due to the effects of other gravitational and non-gravitational forces which perturb the orbit, the actual trajectory of the satellite departs from the ideal Keplerian ellipse. In general, the forces that influence satellite motion are (Figure 2):

• the non-spherical gravitational attraction of the earth,
• the gravitational attractions of the sun, moon, and planets (the so-called "third body" effects),
• atmospheric drag effects,
• solar radiation pressure (both direct and albedo components), and
• the variable part of the earth's gravitational field arising from the solid earth and ocean tides.
  
  

Figure 2. Perturbing forces acting on a near-earth satellite.

In order to determine the motion of a satellite to a high precision these perturbing forces must be accurately modelled. If these forces were known perfectly, and the initial position and velocity of the satellite were given, then the integration of the Equations of Motion would give the satellite's position and velocity at any time in the future:

(1.2-16)

where  is the acceleration vector, r is the satellite position vector, GM_e is the product of the gravitational constant and the mass of the earth, and _t are the total perturbing accelerations acting on the satellite, all expressed in the CCRS system.

However, the models for the perturbing forces are not error-free. Hence an "orbit computation" is performed in which satellite observations obtained at tracking sites of known position are analysed in order to produce an orbit (by adjusting the initial parameters of the orbit, possibly together with several additional force model parameters) that is a "best fit" to the available observations. Determining this orbit is the task of the satellite geodesist.

The final orbit may need to be transformed so that the "orbiting control stations" can be used as "targets" by the average user. In particular the "natural" reference system for satellite computations is a non-rotating (CCRS) system, but the reference system required by users is an earth-fixed one (the CTRS). The transformations were described in an earlier section.

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© Chris Rizos, SNAP-UNSW, 1999