# If object A attracts object B with a gravitational force of 5N from a given distance between the two objects is half, what is the changed force of attraction between them?

Apr 15, 2014

The force of attraction would be 4 times greater, or 20N.

This question uses the formula $F = \frac{G {m}_{1} {m}_{2}}{d} ^ 2$
where F is the force of attraction between the objects
G is the universal gravitation constant (G = 6.67×10^−11 N·(m/(kg))^2)
${m}_{1}$ is the mass of the first object
${m}_{2}$ is the mass of the second object
d is the distance between the centers of the objects

We can simplify this problem considerably, because the problem does not indicate a change of masses, and G remains the same; so we can essentially eliminate them from the equation by letting 1 represent the numerator.

This means that F is proportional to $\frac{1}{d} ^ 2$.

For the purposes of this question, let's let the initial distance = 1.0 m.
If d is halved, it becomes 0.5 m
Therefore ${d}^{2}$ = 0.25
Therefore $\frac{1}{d} ^ 2$ = 1/0.25 = 4

That means, if the initial force of attraction between the masses is 5N, halving the distance between the centers of the masses would mean an increase of force by 4x to a new force of 20N.