Question

Satellite AA orbits a planet at a distance dd from the planet's center with a centripetal acceleration a0a0. A second identical satellite BB orbits the same planet at a distance 2d2d from the planet's center with centripetal acceleration abab. What is the centripetal acceleration abab in terms of a0a0 ?

Answer 1

The centripetal acceleration of an identical satellite orbiting at twice the distance is a quarter of the original satellite's centripetal acceleration.

Step-by-step explanation:

The question revolves around the concept of centripetal acceleration for satellites orbiting a planet. Given that satellite AA orbits at distance dd from the planet's center with a centripetal acceleration a0a0, and satellite BB orbits at a distance 2d from the planet's center with centripetal acceleration abab, we need to find the relation between abab and a0a0.

In the case of satellite AA, the centripetal acceleration can be written as a0 = GM/dd², where G is the gravitational constant and M is the mass of the planet. For satellite BB, which is at a distance 2d, the centripetal acceleration is ab = GM/(2d)². Rearranging this, we get ab = GM/4d², which simplifies to ab = a0/4. Thus, the centripetal acceleration abab is a quarter of a0a0.