3.6 105

1.7 10"5 0.8 10 5 0.9 10 11 1.1 10"9 0.5 10"10 1.2 10"10 4.2 10~12 0.6 10~13 1.7 10~14 1.0 10~16 4.0 1022

Source: Cornelisse, Schöyer, and Wakker. [11]

approximation, often sufficient for the preliminary planning of space missions, is then obtained by assuming that the two volumes corresponding to cases 1 and 2 are separated by a spherical boundary of radius rpi centered on the planet. The resulting sphere is referred to as the sphere of influence of the planet.

A numerical estimate for this radius can be obtained by equating at the boundary, where rpi,s = rpi, the relative magnitudes of the disturbances to each other, therefore

An approximation that can often be made is to assume that when the spacecraft is within the sphere of influence of the planet, the spacecraft is subject only to the attraction by the planet and outside it is subject only to the attraction by the sun. Use of this approximation is therefore referred to as the patched conics method.

Although case 2 has been discussed in terms of the combined action of the sun and a planet, it is often also applicable to the combination of a planet and one of its moons. In the case, for instance, of the earth and the moon, it is important, however, to note, as indicated in Table 3.4, that the disturbances of an earth-orbiting spacecraft by the sun and by the moon are of similar magnitude. In this case, it is no longer sufficient to consider only from which follows

Table 3.5 Radii of the spheres of influence of the planets


rpi in 106 km

rpi as a multiple of the planet's mean radius


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