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

According to Universal law of gravitation, the force of attraction between two bodies is,

$$F = G \frac{m_1 m_2}{r^2}$$

Where,

$$m_1 \ and \ m_2$$ are the masses of the two bodies.

G is the gravitational constant.

r is the distance between the two bodies.

Given if the distance is reduced to half then,

r = $$\frac{1}{2}$$ r

$$\therefore F = \frac{Gm_1 m_2}{ ( \frac{r}{2} )^2 } \$$
$$\Rightarrow \ F =4 \frac{G m_1 m_2}{r^2} \$$
$$\Rightarrow \ F = 4 F$$

Therefore once the space between the objects is reduced to half, then the force of gravitation will increase by fourfold the first force.