The Escape velocity from a planet is defined to be the speed of an object would

Question

The Escape velocity from a planet is defined to be the speed of an object would need in order to be "just barely" able to reach outer space. In other words, it's the speed an object must have at the surface of a planet so that as the object's distance from the planet approached infinity, its speed approached zero.

Determining escape velocity is easy with the true potenital energy formula for gravity.

U(r)= -G ((mM)/r)

m is mass of object

M mass of planet

a) Derive a formula for escape velocity (you will also need to refer to the radius of the planet R)

b) Calculate the escape velocity for earth by looking up its mass and radius. (Convert to miles/second)

C) If a rocket began at rest on Earth's surface and could somehow very quickly burn all of its fuel so that it attained its final velocity while still being near surface, what percent of its inital mass would have to be fuel in order for it to reach escape velocity? Assume exhaust speed is ve = 1.3 miles/second

Explanation / Answer

a ) (2GM/R)^(1/2)

b) 11200 m/s

c) 84.3%

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