Question

what happens to the force of attraction between two planets if their masses are doubled and the distance between them is also doubled?
view available hint(s)
hint 1.
what is the gravitational force proportional to?
the force would double.
the force would remain the same.
the force would quadruple.
it would be half of the original force.

Explanation:

Step1: Recall gravitational - force formula

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

Step2: Calculate the new force

Let the original masses be $m_1$ and $m_2$, and the original distance be $r$. The original force is $F_1=G\frac{m_1m_2}{r^2}$. After the masses are doubled ($m_1' = 2m_1$, $m_2' = 2m_2$) and the distance is doubled ($r' = 2r$), the new force $F_2$ is $F_2=G\frac{(2m_1)(2m_2)}{(2r)^2}$.

Step3: Simplify the new - force expression

$F_2=G\frac{4m_1m_2}{4r^2}=G\frac{m_1m_2}{r^2}$.

Answer:

The force would remain the same.