Question

what happens to the force of attraction between two planets when the distance between them is doubled? view available hint(s) hint 1. let the equation for gravity guide your thinking. the force decreases to half. the force remains the same. the force decreases to one quarter. the force doubles.

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.