Question

The gravitational force of a star on orbiting planet 1 is F1. Planet 2, which is twice as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force F2. What is the ratio F1/F2?

Short answer

The ratio F1/F2 =2

Step-by-step solution

Given Information

The gravitational force of a star on orbiting planet 1 is F1.

Planet 2, is twice as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force F2.

Explanation

The Gravitation force is given as

$F=G\frac{m_1{m}_2}{r^2}$

First find the gravitational force on each planet and get the ratio.

Gravitational force on planet 1

$F_1=\frac{G\times M_1\times M_1}{{R_1}^2}....................\left(1\right)$

Gravitational force on planet 2. Substitute M₂= 2 M₁ and R₂=2R₁

role="math" localid="1649250783330" $F_2=\frac{G\times M_1\times \left(2M_1\right)}{(2{R_1)}^2}....................\left(2\right)$

Now divide equation (1) by (2), we get

$\frac{F_1}{F_2}=2$