Question

suppose a planet with three times the mass of earth is orbiting a star that has three times the mass of the sun at an average orbital radius that is three times larger than earths orbital radius. how big is the gravitational force that the star exerts on the planet compared to the gravitational force that the sun exerts on the earth?

Answer 1

Solution :

Let the mass of earth is .

Mass of planet is .

Let the mass of sun is .

Mass of star is .

Let the earth's orbital radius is .

So, the average orbital radius of the planet is

The magnitude of gravitational force is given by,

  , where is a universal constant.

and are the masses of two bodies.

is the distance between them.

Gravitational force exerted by the sun on the earth is

  

Gravitational force exerted by the star on the planet is

  

  

From equations and ,

Therefore, the gravitational force that the star exerts on the planet is equal in magnitude to the gravitational force that the sun exerts on the earth.