$$F = \frac{Gm_1m_2}{r^2}$$
where:
- F is the gravitational force in Newtons (N)
- G is the gravitational constant (6.674 × 10^-11 N·m²/kg²)
- m1 and m2 are the masses of the two objects in kilograms (kg)
- r is the distance between the centers of the two objects in meters (m)
So, if we want to know how much stronger the gravity is between two objects, we need to compare the gravitational force between them to the gravitational force between two standard objects, such as the Earth and the Moon.
For example, the gravitational force between the Earth and the Moon is:
$$F = \frac{(6.674 × 10^-11 N·m²/kg²)(5.972 × 10^24 kg)(7.348 × 10^22 kg)}{(3.844 × 10^8 m)^2} = 1.981 × 10^22 N$$
Now, let's say we want to compare the gravitational force between the Earth and the Moon to the gravitational force between two objects with masses of 1 kg each and a distance of 1 m between them. The gravitational force between these two objects would be:
$$F = \frac{(6.674 × 10^-11 N·m²/kg²)(1 kg)(1 kg)}{(1 m)^2} = 6.674 × 10^-11 N$$
So, the gravitational force between the Earth and the Moon is approximately 1.981 × 10^22 / 6.674 × 10^-11 = 2.96 × 10^32 times stronger than the gravitational force between the two 1 kg objects.
In general, the gravitational force between two objects is stronger when the objects have larger masses and are closer together.
