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

Answer:

ratio = 1 : 4.5

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:

$F_1=\frac{Gm_1m_2}{r^2}$

The force F₂:

$F_2=\frac{Gm_1(2m_2)}{(3r)^2}$

The ratio:

$\frac{F_2}{F_1}=\frac{2}{9}$