Question

The gravitational force of a star on orbiting planet 1 is F_1. Planet 2, which is twice as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force F_2. What is the ratio F_1/F_2?

Answer 1

The ratio is
`(F_1)/(F_2) =1`

Step-by-step explanation:

From the question we are told that

The mass of planet 1 is
`m_1`

The first gravitational force is
`F_1`

The mass of planet two is
`m_2 = 2 m_1`

The distance of planet 1 from the star is
`d_1`

The distance of planet 2 from the star is
`d_2 = 2 d_1`

The second planet gravitational force is
`F_2`

The mass of the sun is
`m_s`

Generally the gravitational force for first planet is mathematically represented as

`F_1 = (Gm_s m_2 )/(d_1^2)`

The gravitational force for second planet is mathematically represented as

`F_2 = (Gm_s m_2)/(d_2^2)`

`F_2 = (Gm_s 2(m_1))/( 2d_1^2)`

`F_2 = (2Gm_s m_1)/( 2d_1^2)`

So
`(F_1)/(F_2) = ( (Gm_s m_2 )/(d_1^2))/( (2Gm_s m_1)/( 2d_1^2))`

`(F_1)/(F_2) =1`