CIE A Level Physics (9702) 2019-2021

Revision Notes

15.1.2 Gravitational Force Between Point Masses

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
    • 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 their separation

  • In equation form, this can be written as:

Newton's Law of Gravitation equation 1

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

  • Where:
    • FG = 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)

 

  • 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

Worked example: Newton’s law of gravitationWorked example - Newton's law of gravitation, downloadable AS & A Level Physics revision notes

Exam 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.

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