D. the gravitational force increases by a factor of 4
Explanation:
The magnitude of the gravitational force between two objects is given by:
where
is the gravitational constant
m1, m2 are the masses of the two objects
r is the separation between them
Here let's call F the initial gravitational force between the two objects. Later, the distance between the objects is halved, so the new distance is:
Substituting into the equation, we find the new force:
Therefore, the gravitational force increases by a factor of 4.
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