## Third Body Forces

Third-body force perturbations are caused by the gravitational influence of a third body in addition to the spacecraft and the Earth. The Earth is not isolated in the universe; there are other celestial bodies out there, the gravitational fields of which can have a significant effect on the motion of an Earth-orbiting spacecraft. The Sun and the Moon have the greatest perturbing effect. If we think about these bodies, and look at Figure 3.7, then the total gravity force governing the motion of the spacecraft becomes a

Figure 3.7: The motion of the orbiting spacecraft is influenced not only by Earth's gravity but also by the gravity fields of third bodies, principally the Sun and the moon.

sum of the gravity forces due to the Earth, the Sun, and the Moon. In most applications, the analysis of third-body perturbations includes only the influence of the Sun and the Moon, and then the effects are often called luni-solar perturbations. Of course, if high positioning accuracy is required for a particular spacecraft mission, then other third bodies, such as Mars, Venus, and Jupiter, can be included in the analysis until the required degree of precision is achieved.

The effects of third-body forces on low-altitude circular orbits are small. In this case, the Earth's gravity field dominates the contributions from other celestial bodies due to the spacecraft's closeness to the Earth. However, if the spacecraft's orbit takes it to a significant distance from the Earth, for example, in geostationary Earth orbit or at the apogee of a highly eccentric orbit, then the gravitational influence of third bodies is more important. The Earth's gravity force on the spacecraft is reduced because of the greater distance from the Earth's center, whereas the gravitational force due to, say, the Sun has not changed significantly. The overall effect on the orbit remains small, but the ratio of the Sun's gravity force to that of Earth has increased. Therefore, the effects of third-body perturbations are greater in high-altitude orbits. The next obvious question is, What changes do third-body forces produce in the spacecraft's orbit?

In answering this question, an important thing to note is that the gravity field of third bodies generally produce perturbing forces that are out of the plane of the spacecraft's orbit. This is because bodies like the Sun and the

Moon are not often to be found within the plane of the spacecraft's orbit. As a consequence, the main effect of the third-body perturbations is to cause small changes in the plane of the orbit, that is, changes in the orbital inclination. In addition, small oscillations in the size and shape of the orbit are also produced, which can be important for a highly eccentric orbit with a low perigee altitude. In this case, the size and shape variations result in an oscillation in the perigee height, and this can cause the perigee to dip in and out of Earth's atmosphere (see next section on spacecraft aerodynamics). A reentry of the spacecraft into the atmosphere may then result, with the unpleasant prospect of a premature end to the spacecraft's mission life.

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