Gravitational Force Between Point Masses (Cambridge (CIE) A Level Physics): Revision Note

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

• In equation form, this can be written as:

$F_G=\frac{G{m}_1{m}_2}{r^2}$

• Where:

  • F_G = gravitational force between two masses (N)

  • G = Newton’s gravitational constant

  • m₁ and m₂ = two points masses (kg)

  • r = distance between the centre of the two masses (m)

Gravitational force between two point masses

The gravitational force between two point masses outside a uniform field is defined by Newton’s law of gravitation

• Newton’s law of gravitation applies to orbiting bodies, e.g. planets orbiting the Sun

• Although stars and planets are very large, they can be considered to be point masses as:

  • they are approximately uniform spheres

  • their separation is much larger than their radii

• The $\frac{1}{r^2}$ relation is called the inverse square law

• This means that when a mass is twice as far away from another, the gravitational force reduces by a quarter, i.e. ${\left(\frac{1}{2}\right)}^2=\frac{1}{4}$