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?

Respuesta :

Answer:

The ratio is  [tex]\frac{F_1}{F_2} =1[/tex]

Explanation:

From the question we are told that

    The mass of planet 1 is [tex]m_1[/tex]

    The first gravitational force is [tex]F_1[/tex]

     The mass of planet two is [tex]m_2 = 2 m_1[/tex]

       The distance of planet 1 from the star is [tex]d_1[/tex]

     The distance of planet 2 from the star is [tex]d_2 = 2 d_1[/tex]

      The second planet  gravitational force is [tex]F_2[/tex]

      The mass of the sun is  [tex]m_s[/tex]

Generally the  gravitational force for first planet is mathematically represented as

        [tex]F_1 = \frac{Gm_s m_2 }{d_1^2}[/tex]

The  gravitational force for second planet is mathematically represented as  

       [tex]F_2 = \frac{Gm_s m_2}{d_2^2}[/tex]

           [tex]F_2 = \frac{Gm_s 2(m_1)}{ 2d_1^2}[/tex]

           [tex]F_2 = \frac{2Gm_s m_1}{ 2d_1^2}[/tex]

So     [tex]\frac{F_1}{F_2} = \frac{ \frac{Gm_s m_2 }{d_1^2}}{ \frac{2Gm_s m_1}{ 2d_1^2}}[/tex]

         [tex]\frac{F_1}{F_2} =1[/tex]

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