Answer:
It increases by 16 times
Explanation:
The magnitude of the gravitational force between two objects is given by the equation
[tex]F=\frac{Gm_1 m_2}{r^2}[/tex]
where
G is the gravitational constant
m1, m2 are the masses of the two objects
r is their separation
In this problem, we call:
[tex]m_1 = m[/tex] is the Earth's mass
[tex]m_2 = M[/tex] is the Sun's mass
[tex]r=1AU[/tex] is the initial distance Earth-Sun
So the gravitational force between the two objects is
[tex]F=\frac{GMm}{r^2}[/tex]
Later, the Earth is moved to a distance of
r' = 0.25 AU
which is equivalent to write
[tex]r'=\frac{1}{4}r[/tex]
from the Sun.
Therefore, the new gravitational force will be:
[tex]F'=\frac{GMm}{r'^2}=\frac{GMm}{(\frac{1}{4}r)^2}=16(\frac{GMm}{r^2})=16F[/tex]
So, the gravitational force increases by a factor of 16.
