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

Answer:

The ratio is  $\frac{F_1}{F_2} =1$

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

        $F_1 = \frac{Gm_s m_2 }{d_1^2}$

The  gravitational force for second planet is mathematically represented as  

       $F_2 = \frac{Gm_s m_2}{d_2^2}$

           $F_2 = \frac{Gm_s 2(m_1)}{ 2d_1^2}$

           $F_2 = \frac{2Gm_s m_1}{ 2d_1^2}$

So     $\frac{F_1}{F_2} = \frac{ \frac{Gm_s m_2 }{d_1^2}}{ \frac{2Gm_s m_1}{ 2d_1^2}}$

         $\frac{F_1}{F_2} =1$