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=(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=(m_1M)/(R^2)`

The gravitational force of the star on planet 2,

`\begin{gathered} F_2=(4m_1M)/((4R)^2) \\ F_2=(m_1M)/(4R^2) \end{gathered}`

Ratio:

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