# You are a scientist exploring a mysterious planet. You have performed measurements and know the following things:The planet has radius d. It is orbiting his star in a circular orbit of radius b. it takes time T to complete one orbit around the star. the free-fall acceleration on the surface of the planet is a. Derive an expression for the mass and of the star in terms of b,T, and G the universal gravitational constant.

Question
Asked Dec 13, 2019
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You are a scientist exploring a mysterious planet. You have performed measurements and know the following things:

The planet has radius d.
It is orbiting his star in a circular orbit of radius b.
it takes time T to complete one orbit around the star.
the free-fall acceleration on the surface of the planet is a.

Derive an expression for the mass and of the star in terms of b,T, and G the universal gravitational constant.

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Step 1

let the mass of the planet be m and that of the star is M,

the weight of an object at the surface of the  planet is equal to the gravitational force acting on it.that is,

Step 2

therefore, the mass of th...

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