Question

The gravitational force of a star on an orbiting planet 1 is F1. Planet 2, which is four times as massive as planet 1 and orbits at four times larger distance from the star, experiences gravitational force F2.Part AWhat is the ratio F2F1? You can ignore the gravitational force between the two planets.

Answer 1

Given

Gravitational force is given by,

$F=\frac{GmM}{R^2}$

Where m and M are the masses of the objects, R is the distance between them and G is the gravitational constant.

The gravitational force of the star on planet 1,

$F_1=\frac{m_1M}{R^2}$

The gravitational force of the star on planet 2,

$\begin{gathered} F_2=\frac{4m_1M}{(4R)^2} \\ F_2=\frac{m_1M}{4R^2} \end{gathered}$

Ratio:

The ratio of gravitational forces F₂ : F₁ = 1 : 4