Asked Dec 13, 2019

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. 


Expert Answer

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,


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Gmm' F = F = m'a Gmm' = m'a d? Gm d? ad? G ||

Step 2

therefore, the mass of th...

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