5.7.4 Newton's Law of Gravitation

• The gravitational force between two masses, e.g., between the Earth and the Sun, is defined by Newton’s Law of Gravitation

• Newton’s Law of Gravitation states:

The gravitational force F between two masses m₁ and m₂ is proportional to the product of their masses and inversely proportional to the square of their separation, r

• In equation form, this is written as:

• Where:
  • F = gravitational force between two point masses m₁ and m₂ (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)

• The 1/r² relation is called the ‘inverse square law’
  • This means that if the distance between two masses doubles, r becomes 2r
  • Therefore, 1/r² becomes 1/(2r)², which is equal to 1/4r²
  • Hence, the gravitational force between the two masses reduces by a factor of four

• The negative sign indicates that the gravitational force F between the two point masses m₁ and m₂ is attractive

The gravitational force between two masses is defined by Newton’s Law of Gravitation