Question

if the distance between a planet and the sun is doubled, how does the gravitational force between them change?
a it becomes one - fourth as strong
b it becomes half as strong
c it remains the same
d it doubles

Explanation:

Step1: Recall gravitational - force formula

The gravitational force formula is $F = G\frac{Mm}{r^{2}}$, where $G$ is the gravitational constant, $M$ and $m$ are the masses of the two objects (Sun and planet), and $r$ is the distance between them.

Step2: Consider the new - distance case

Let the initial distance be $r_1$ and the initial force be $F_1=G\frac{Mm}{r_1^{2}}$. When the distance is doubled, $r_2 = 2r_1$. The new force $F_2=G\frac{Mm}{r_2^{2}}=G\frac{Mm}{(2r_1)^{2}}=G\frac{Mm}{4r_1^{2}}$.

Step3: Compare the initial and new forces

We can see that $F_2=\frac{1}{4}F_1$.

Answer:

A. It becomes one - fourth as strong