what happens to the force of attraction between two planets when the distance between them is doubled? view…

Explanation:

Step1: Recall gravitational - force formula

The gravitational - force formula between two objects is $F = G\frac{m_1m_2}{r^2}$, where $F$ is the force of attraction, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them.

Step2: Consider the new distance

Let the initial distance be $r_1 = r$ and the new distance be $r_2 = 2r$. The initial force $F_1=G\frac{m_1m_2}{r_1^2}=G\frac{m_1m_2}{r^2}$, and the new force $F_2 = G\frac{m_1m_2}{r_2^2}=G\frac{m_1m_2}{(2r)^2}=G\frac{m_1m_2}{4r^2}$.

Step3: Find the ratio of the forces

$\frac{F_2}{F_1}=\frac{G\frac{m_1m_2}{4r^2}}{G\frac{m_1m_2}{r^2}}=\frac{1}{4}$, which means $F_2=\frac{1}{4}F_1$.

Answer:

The force decreases to one quarter.