Answer:
the force increases by 9/4
Explanation:
The gravitational force between two stars is given by:
[tex]F=G\frac{m_1 m_2}{r^2}[/tex]
where
G is the gravitational constant
m1 and m2 are the masses of the two stars
r is the separation between the two stars
In this problem, the distance between the two stars is decreased by 1/3, which means that the new distance is
[tex]r'=r-\frac{1}{3}r=\frac{2}{3}r[/tex]
So, the new gravitational force will be
[tex]F'=G\frac{m_1 m_2}{(2/3)^2}=G\frac{m_1 m_2}{\frac{4}{9}r^2}=\frac{9}{4}F[/tex]
