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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, Rp. Size of the planet
determines its gravitational acceleration, as can be seen by the
correlation between radius and go 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:
--> Ve = (2gRp)1/2
Where m is the mass of a molecule, Rp is the radius of the planet,
and Ve 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.