|(Refer to simplifying assumptions from section 1)
The stationary point is the centre of mass, not the centre of the Earth - but the satellite
is so small as to make this negligible in virtually all cases.
The earth cannot be treated as a point mass since it is not a sphere:
- Polar flattening is 1/298th of the equatorial radius (i.e. approximately elliptical
polar cross section)
- "Gravity field" is not smooth - i.e. gravity is stronger or weaker in some
areas than a smooth, homogeneous Earth would indicate.
Other forces will act on the satellite to perturb the orbit:
- Gravitational force of Sun and Moon
- Atmospheric drag (in lower orbits)
- Minor perturbations (planetary gravity, solar pressure, magnetic interaction with
Earth's magnetic field)
The effects of the "real world" forces are to cause movements of the satellites
orbit relative to the Earth which would not be predicted by Kepler:
- Precession of the orbit plane around the Earth's N-S axis
- Precession of the orbit perigee n the plane of the orbit
This means that not all orbits are useful!
Approximate magnitudes of relative forces acting on a satellite at specific heights above
the Earth's surface:
||7 * 10-4
||3 * 10-2
||4 * 10-6
||1 * 10-4
||1 * 10-3
||4 * 10-6
[Relative force = (Average force exerted by perturbation) / (Force exerted by a symmetrical
Major perturbations of a general satellite orbit:
Relatively complex equations govern rate of precession of argument of perigee and plane of
Stable or near stable conditions exist which lead to useful orbits:
- "Molniya" orbit
- Sun-synchronous orbits
Perturbations mean that real orbits cannot be predicted over extended period, however
prediction is reliable over short periods of a few days for most orbits.
So predictions are used based on regularly updated orbital element sets to determine the
real world satellite path and position.