Question

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

What is the ratio F2F1? You can ignore the gravitational force between the two planets.

Answer 1

ratio = 1 : 4.5

Step-by-step explanation:

If m₁ is the mass of the star and m₂ the mass of the planet, the force of gravity F₁ for planet 1 is given by:

`F_1=(Gm_1m_2)/(r^2)`

The force F₂:

`F_2=(Gm_1(2m_2))/((3r)^2)`

The ratio:

`(F_2)/(F_1)=(2)/(9)`