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

F_1 / F_2 = 4 / 3

Explanation:

Given:

- Planet 1:-

mass = m

orbit = R

- Planet 2:-

mass = 3m

orbit = 2R

- Mass of star = M

Find:

- The ratio of gravitational forces F_1 / F_2?

Solution:

- The force of attraction between star and planet 1 is given by:

F_1 = G * (m) * (M) / R^2

- The force of attraction between star and planet 2 is given by:

F_2 = G * (3m) * (M) / (2R) ^2

- the ratio of the two forces is:

F_1 / F_2 = [G * (m) * (M) / R^2] / [G * (3m) * (M) / (2R) ^2 ]

F_1 / F_2 = 4 / 3