Question

An astronaut in space is in orbit 250 km above the surface of Earth. What is the gravitational acceleration on the astronaut at this altitude?

Answer 1

for acceleration due to gravity is given by a=GMr2where G is the gravitational constant and M is the mass of Earth. The value at this altitude is 9.08 ms−2.

Explanation:

Constants:

G=6.67408×10−11 m3kg−1s−2

M=5.972×1024 kg

The radius of Earth is r=6.371×106 m

In this case, we need to add another 2.5×105 m (250 km) to the radius, to give r=6.621×106 m

So:

a=GMr2=6.67×10−11×5.97×1024(6.621×106)2=9.08 ms−2

This makes sense, since the acceleration due to gravity is 9.81 ms−2. The radius has been increased by only about 4%, but the acceleration due to gravity is inversely proportional to the square of the radius.

Answer 2

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