Escape Velocity

We begin by looking at the solar system, the physical properties of planets, and their relationship to the sun. Figure 1 gives various characteristics of bodies in our solar system that have atmospheres, listed in order of their distance from the sun (except for Titan, which is a satellite of Saturn). The first column gives the size of the body as indicated by its radius, R_p. Size of the planet determines its gravitational acceleration, as can be seen by the correlation between radius and g_o in the second column. Gravity, in turn, controls the escape velocity. Ve, given in column 3, which is the minimum speed that molecules must move if they are able to escape from the gravitational pull of the body. Earth, for example, being the fourth smallest planet on this list, has the fourth smallest escape velocity of 11.2 km/s or about 7 miles per second. If we wanted to launch a spacecraft to be completely free of the earth's gravitational field, it would have to have a speed of 7 miles per second. Just putting a spacecraft in orbit, of course, is a quite different problem, because the orbital parameters are determined by the balance of gravitational force and the motion of the spacecraft as will be shown in the unit on satellites.

The escape velocity can be calculated from a balance of gravitational energy at the planet surface and kinetic energy:

Where m is the mass of a molecule, R_p is the radius of the planet, and V_e is escape velocity.

This shows that the escape velocity does not depend on the mass of the particle trying to escape, so the escape velocity is the same for a space ship as for a hydrogen molecule.

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