Question

how would the force of gravity change between the sun and mercury if mercury were 5 times further from the sun? (hint: this is the same amount by which the suns brightness would change).
5 times stronger
1/25 as strong
25 times stronger
1/5 as strong
10 times stronger

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 Mercury in this case), and $r$ is the distance between them.

Step2: Analyze the change in distance

Let the initial distance be $r_1$ and the new distance be $r_2 = 5r_1$. The initial force $F_1=G\frac{Mm}{r_1^{2}}$, and the new force $F_2 = G\frac{Mm}{r_2^{2}}=G\frac{Mm}{(5r_1)^{2}}=G\frac{Mm}{25r_1^{2}}$.

Step3: Find the ratio of the forces

$\frac{F_2}{F_1}=\frac{G\frac{Mm}{25r_1^{2}}}{G\frac{Mm}{r_1^{2}}}=\frac{1}{25}$. So $F_2=\frac{1}{25}F_1$.

Answer:

B. 1/25 as strong