Understanding the Law of Universal Gravitation

The force of gravity between two objects is described by Newton's Law of Universal Gravitation:

* F = G * (m1 * m2) / r²

Where:

* F is the force of gravity

* G is the gravitational constant (approximately 6.674 x 10^-11 N m²/kg²)

* m1 and m2 are the masses of the two objects

* r is the distance between the centers of the two objects

The Problem

You're told that the force of gravity (F) is 500 Newtons, and the mass of one of the objects (let's say m1) is doubled. We need to find the new force of gravity.

Solution

1. Original Force: Let's assume the original masses are m1 and m2. The original force is:

* F = G * (m1 * m2) / r² = 500 N

2. Doubling the Mass: Now, m1 is doubled, becoming 2m1. The new force is:

* F' = G * (2m1 * m2) / r²

3. Relationship: Notice that the new force (F') is simply double the original force (F):

* F' = 2 * (G * (m1 * m2) / r²) = 2 * F

Answer

If the mass of one object is doubled, the new gravitational attraction will be 1000 Newtons.