Hi there!
Recall Newton's Law of Universal Gravitation:
[tex]\large\boxed{F_g = \frac{Gm_1m_2}{r^2}}[/tex]
G = Gravitational Constant
m1, m2 = mass of objects (kg)
r = distance between objects (m)
There is an INVERSE-SQUARE relationship between the gravitational force and the distance between the objects, so:
[tex]F_g = \frac{Gm_1m_2}{(\frac{1}{4}r)^2} = F_g = \frac{Gm_1m_2}{\frac{1}{16}r^2}[/tex]
[tex]= 16G\frac{m_1m_2}{r^2} = 16F_g[/tex]
Thus, the gravitational force between the objects would INCREASE by a factor of 16.
