Gravitational Force Between Point Masses (CIE A Level Physics)

• 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
  • Recall that the mass of a uniform sphere can be considered to be a point mass at its centre
• 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:

• 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)

Newton's law of gravitation

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 1/r² 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