Gravitational force is always attractive

The gravitational force experienced by any object in a gravitational field is invariably attractive. This force, a vector quantity, is influenced by two primary factors:

• The masses of the two interacting objects.
• The distance between the centres of these objects.

Calculating gravitational force using Newton's equation

The gravitational force between two uniform spheres, which can be approximated as point masses, is computed using Newton's law of gravitation, represented by the formula:

$\text{F = }\text{ = }\frac{\text{G M m}}{\text{r}^2}$

Where:

• F = Gravitational force (N)
• G = Gravitational constant (6.67 x 10^-11 N m² kg^-2)
• M, m = Masses of the objects (kg)
• r = Distance between the centres of the masses (m)

Worked example - Calculating gravitational force between the Earth and the Moon

Calculate the gravitational force between the Earth and the Moon. The Earth has a mass of 5.97 x 10²⁴ kg and the Moon has a mass of 7.35 x 10²² kg. The average distance between the centres of the Earth and Moon is 3.84 x 10⁸ meters.

Step 1: Formula

$\text{F = }\frac{\text{G M m}}{\text{r}^2}$

Step 2: Substitution and correct evaluation

$\text{F = }\frac{6.67 \times 10^{-11} \times 5.97 \times 10^{24} \times 7.35 \times 10^{22}}{(3.84 \times 10^{8})^2} = 1.99 \times 10^{20} \text{ N}$

Newton's law follows an inverse square relationship

Newton's law of gravitation is characterised by an inverse square relationship. If the distance between two masses doubles, the gravitational force decreases to one quarter of its original value.