Satellite A A orbits a planet at a distance d d from the planet’s center with a centripetal acceleration a0 a 0 . A second identical satellite B B orbits the same planet at a distance 2d 2 d from the planet’s center with centripetal acceleration ab a b . What is the centripetal acceleration ab a b in terms of a0 a 0 ?

Explanation:

Since the centripetal force F_C is, in this case, the gravitational force F_G exerted by the planet, we can say that:

In the case of the satellite A we have:

And in the case of the satellite B:

Finally, using these two expressions, we obtain :

In words, the centripetal acceleration a_b is equal to one fourth of a_0.

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