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]