Satellite a orbits a planet at a distance d from the planet’s center with a centripetal acceleration a0. a second identical satellite b orbits the same planet at a distance 2d from the planet’s center with centripetal acceleration ab. what is the centripetal acceleration ab in terms of a0?

To solve this problem it is necessary to use the concepts related to the Gravitational Force and Newton's Second Law, as far as we know:

Where,

G = Gravitational constant

M = Mass of earth (in this case)

m = mass of satellite

r = radius

In the other hand we have the second's newton law:

Where,

m = mass

a = acceleration

Equation both equations we have,

For the problem we have that,

Satellite A:

Satellite B:

The ratio between the two satellites would be,

Solving for a_B,

Therefore the centripetal acceleration of   is a quarter of

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