Here's why:
* Newton's Law of Universal Gravitation: This law states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
* Mathematical Expression:
F = G * (m1 * m2) / r²
where:
* F is the force of gravity
* G is the gravitational constant
* m1 and m2 are the masses of the two objects
* r is the distance between their centers
* Doubling the Distance: If you double the distance (r becomes 2r), the force becomes:
F' = G * (m1 * m2) / (2r)² = G * (m1 * m2) / (4r²) = (1/4) * [G * (m1 * m2) / r²] = (1/4) * F
Therefore, doubling the distance between two masses weakens the gravitational force by a factor of four.
