Newton's Law of Gravitation

The gravitational force between two bodies outside a uniform field, e.g. between the Earth and the Sun, is defined by Newton’s Law of Gravitation
Newton’s Law of Gravitation states that:

The gravitational force between two point masses is proportional to the product of the masses and inversely proportional to the square of their separation

All planets and stars are assumed to be point masses
In equation form, this can be written as:

$F = \frac{G m_{1} m_{2}}{r^{2}}$

Where:
- F = gravitational force between two masses (N)
- G = Newton's Gravitational Constant
- m₁ and m₂ = mass of body 1 and mass of body 2 (kg)
- r = distance between the centre of the two masses (m)

Newton's law of gravitation, downloadable AS & A Level Physics revision notes

The gravitational force between two masses outside a uniform field is defined by Newton’s Law of Gravitation

Although planets are not point masses, their separation is much larger than their radius
- Therefore, Newton’s law of gravitation applies to planets orbiting the Sun
The $F \propto \frac{1}{r^{2}}$ relation is called the inverse square law
This means that when a mass is twice as far away from another, its force due to gravity reduces by (½)² = ¼

Worked example

A satellite of mass 6500 kg orbits at 2000 km above the Earth's surface. The gravitational force between the Earth and the satellite is 37 kN.

Calculate the mass of the Earth.

Radius of the Earth = 6400 km

Answer:

Examiner Tip

A common mistake in exams is to forget to add together the distance from the surface of the planet and its radius to obtain the value of r. The distance r is measured from the centre of the mass, which is from the centre of the planet.

Make sure to square the separation r in the equation!

Newton's Law of Gravitation (SL IB Physics)

Revision Note