Question

How does the force of gravitation between two objects change when the distance between them is reduced to half?

Answer 1

Answer:

it is 1 / square root of the change in distance

Explanation:

since the equation of the gravitational force is

$F=G{\frac{m_1m_2}{r^2}}$

then F and r are inversely related, by the equation

$F \alpha \frac{1}{r^2}$

this means when F is multiplied by 2 then r^2 is multiplied by half

so when r is multiples by half we first square the number (0.5) ^ 2 = 0.25

so

$F \alpha \frac{1}{(0.25)r^2}$

which means F is multiples by 1/0.25 or 4 when the radius is halfed