## Ideal and Real Orbits

THE orbits that we have discussed in the preceding two chapters are often called Keplerian orbits, named after Johannes Kepler, and sometimes referred to as ideal orbits. If we imagine a satellite in orbit around the Earth, and the only force acting upon it is that of a perfect inverse square law gravity field (see Chapter 1), then the resulting orbital motion is described as ideal. The main distinguishing feature of an ideal orbit is that the attributes defining the orbit—its shape, size, and orbital inclination (see Chapter 2)— all remain fixed; that is to say, they do not change with time.

In contrast to an ideal orbit, the defining attributes of real orbits do change, and this is due to the effects of orbital perturbations. This is just a fancy phrase to describe forces that act on the satellite, in addition to the inverse square law of gravity, that cause its path to differ from an ideal circular or elliptical orbit. When the mission analysis team designs the orbital aspects of an Earth orbiting mission, it has to take these aspects into account. There are a number of different sources of perturbations, and this chapter discusses the most common ones.

The gravity field of the Earth is very close to being described by Isaac Newton's inverse square law, although there are small departures from this. The dominant part of Earth's gravity field, described by the inverse square law, is sometimes referred to as the central gravity field. The small departures are sometimes called gravity anomalies and are a form of perturbation that causes the satellite to deviate from ideal orbital motion. Speaking more generally, the effects of orbit perturbations from all sources are small compared to the central gravity field. As a consequence, real orbits are basically the same shape as ideal orbits—circles and ellipses—but their shape, size, and orbital inclination change slowly over time.

G. Swinerd, How Spacecraft Fly: Spaceflight Without Formulae, DOI: 10.1007/978-0-387-76572-3_3, © Praxis Publishing, Ltd. 2008