All subjects · Physics · WPH15 (Unit 5)

Gravitational fields and Newton's law of gravitation

Gravity holds planets in orbit and keeps us on the ground. Newton's law of gravitation describes it, and it has a lot in common with Coulomb's law.

Gravitational fields

A gravitational field is a region where a mass experiences a force. The gravitational field strength is the force per unit mass:

g = F / m (N/kg)

Near the Earth's surface, g = 9.81 N/kg. Field lines point towards the mass that creates the field.

Newton's law of gravitation

Two point masses m_1 and m_2 a distance r apart attract each other with a force

F = Gm_1m_2 / r2

with G = 6.67 x 10-11 N m2 kg-2. Spherical bodies such as planets act as point masses at their centres. It is an inverse square law.

Field of a point mass

Putting F = GMm / r2 into g = F / m gives

g = GM / r2

so g falls with the square of the distance from the centre. At a height h above a planet of radius R, use r = R + h.

Comparing gravitational and electric fields

Worked example

Find g at the Earth's surface. (M = 5.97 x 1024 kg, R = 6.37 x 106 m)

  1. g = GM / r2 = 6.67 x 10-11 x 5.97 x 1024 / (6.37 x 106)2
  2. = 3.98 x 1014 / 4.06 x 1013

Answer: g = 9.81 N/kg

Key idea: g = F/m; F = Gm_1m_2/r2 (always attractive); g = GM/r2; like electric fields, inverse square, but mass not charge.

Check yourself

  1. Find the gravitational force between two 1000 kg masses whose centres are 3.0 m apart, in units of 10-6 N, to 3 s.f.
    Show answer

    7.41 x 10-6 N. F = 6.67 x 10-11 x 1000 x 1000 / 9.0 = 7.41 x 10-6 N.

  2. Mars has mass 6.42 x 1023 kg and radius 3.39 x 106 m. Find g at its surface in N/kg, to 3 s.f.
    Show answer

    3.73 N/kg. g = GM / r2 = 6.67 x 10-11 x 6.42 x 1023 / (3.39 x 106)2 = 3.73 N/kg.

  3. Find g at 400 km above the Earth's surface. (M = 5.97 x 1024 kg, R = 6.37 x 106 m) Answer in N/kg, to 3 s.f.
    Show answer

    8.69 N/kg. r = 6.37 x 106 + 0.40 x 106 = 6.77 x 106 m; g = 3.98 x 1014 / (6.77 x 106)2 = 8.69 N/kg.

  4. Find the gravitational force between the Earth (5.97 x 1024 kg) and the Moon (7.35 x 1022 kg), 3.80 x 108 m apart, in units of 1020 N, to 3 s.f.
    Show answer

    2.03 x 1020 N. F = 6.67 x 10-11 x 5.97 x 1024 x 7.35 x 1022 / (3.80 x 108)2 = 2.03 x 1020 N.

  5. Find the ratio of the electric force to the gravitational force between two protons, in units of 1036, to 3 s.f.
    Show answer

    1.24 x 1036. Ratio = ke2 / (Gm_p2) = (8.99 x 109 x 2.56 x 10-38) / (6.67 x 10-11 x 2.79 x 10-54) = 1.24 x 1036. The distance cancels.

  6. Which statement correctly compares gravitational and electric forces?
    • Gravitational forces are always attractive; electric forces can attract or repel
    • Electric forces are always attractive; gravitational forces can repel
    • Only gravitational forces follow an inverse square law
    • Gravitational forces act on charge
    Show answer

    Gravitational forces are always attractive; electric forces can attract or repel. There is only one kind of mass, but two kinds of charge.

  7. The distance from the centre of a planet is tripled. What happens to g?
    • It becomes 1/3 as large
    • It becomes 3 times as large
    • It becomes 1/9 as large
    • It stays the same
    Show answer

    It becomes 1/9 as large. g is proportional to 1/r2, and (1/3)2 = 1/9.

  8. What is a gravitational field?
    • A region where a charge experiences a force
    • The path of an orbiting satellite
    • The force on a 1 kg mass at the Earth's surface
    • A region where a mass experiences a force
    Show answer

    A region where a mass experiences a force. That is the definition in the specification.

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Last updated 7 November 2026. Spotted a mistake? Tell us.