Teaching Physics with the Physics Suite Edward F. Redish

Escape velocity

According to Newton's Universal theory of gravitation, the gravitational potential energy of an object due to the Earth is given by

PEGrav = -GmME/r

where m is the mass of the object, ME is the mass of the Earth, r is the distance the object is from the center of the earth, and G is Newton's universal gravitational constant, 2/3 x 10-10 N-m2/kg2.

a) Using this result and energy conservation, calculate what velocity a rocket would have to have leaving the space station 400 km up above the Earth's surface in order to "escape" from the Earth's gravitational pull; that is to get far enough away from the Earth so that its gravitational PE is essentially zero. (This is the so-called "escape velocity.")

b) The formula stated above doesn't look like the "mgh" formula we know and love (?) from our previous work. Why don't these look the same? Which is right? If Newton is right, how can we use mgh and get away with it?

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