Define gravitational field strength.

The force per unit mass at a point in the field: g = F/m (unit N kg⁻¹).

State Newton's law of universal gravitation.

F = \frac{Gm1m2}{r^2}: attractive, proportional to the product of the masses and inversely proportional to the square of the distance between centres.

How does g change if the distance from a point mass is doubled?

It falls to one quarter (inverse square law).

Derive the field strength of a point mass.

g = F/m = (GMm/r²)/m = GM/r², as m cancels.

What does r mean in gravitational equations?

The distance from the centre of the mass, not the height above the surface.

Define gravitational potential.

The work done per unit mass in bringing a small mass from infinity to the point.

Why is gravitational potential negative?

It is zero at infinity and the field does work as the mass moves in, so energy must be supplied to return it to infinity.

What is a neutral point?

A point where the fields of two bodies are equal and opposite, so the resultant field strength is zero.

State one similarity between gravitational and electric fields.

Both are radial and obey an inverse square law.

State one difference between gravitational and electric forces.

Gravitational forces are always attractive; electric forces can be attractive or repulsive.

Why is gravity weak compared with electric force in an atom?

G is very small compared with k; the ratio for an electron and proton is about 10³⁹.

Gravitational fields and Newton's law of gravitationEdexcel International A Level Physics: Flashcards

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What is a gravitational field?

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What is a gravitational field?: A region where a mass experiences a force because of its mass.
Define gravitational field strength.: The force per unit mass at a point in the field: g = F/m (unit N kg⁻¹).
State Newton's law of universal gravitation.: $F = \frac{Gm_1m_2}{r^2}$ : attractive, proportional to the product of the masses and inversely proportional to the square of the distance between centres.
How does g change if the distance from a point mass is doubled?: It falls to one quarter (inverse square law).
Derive the field strength of a point mass.: g = F/m = (GMm/r²)/m = GM/r², as m cancels.
What does r mean in gravitational equations?: The distance from the centre of the mass, not the height above the surface.
Define gravitational potential.: The work done per unit mass in bringing a small mass from infinity to the point.
Give the equation for gravitational potential of a point mass.: $V = -\frac{GM}{r}$ (J kg⁻¹)
Why is gravitational potential negative?: It is zero at infinity and the field does work as the mass moves in, so energy must be supplied to return it to infinity.
What is a neutral point?: A point where the fields of two bodies are equal and opposite, so the resultant field strength is zero.
State one similarity between gravitational and electric fields.: Both are radial and obey an inverse square law.
State one difference between gravitational and electric forces.: Gravitational forces are always attractive; electric forces can be attractive or repulsive.
Why is gravity weak compared with electric force in an atom?: G is very small compared with k; the ratio for an electron and proton is about 10³⁹.

Exam questions on Gravitational fields and Newton's law of gravitation

Treat the Earth as a uniform sphere of mass 5.97 × 10²⁴ kg and radius 6.37 × 10⁶ m. A communications satellite of mass 450 kg is 3.59 × 10⁷ m above the Earth's surface. The gravitational constant G = 6.67 × 10⁻¹¹ N m² kg⁻².
Calculate the gravitational potential at the position of the satellite.2 marks
The Earth has mass 5.97 × 10²⁴ kg and the Moon has mass 7.35 × 10²² kg. The distance between their centres is 3.84 × 10⁸ m. Treat both as point masses at their centres. G = 6.67 × 10⁻¹¹ N m² kg⁻².
Calculate the gravitational field strength of the Moon at the centre of the Earth, and state its direction.2 marks
In a hydrogen atom an electron and a proton are separated by 5.3 × 10⁻¹¹ m. The electron has mass 9.11 × 10⁻³¹ kg and the proton has mass 1.67 × 10⁻²⁷ kg. Each has a charge of magnitude 1.60 × 10⁻¹⁹ C. G = 6.67 × 10⁻¹¹ N m² kg⁻² and the constant in Coulomb's law, k = 1/(4πε₀), is 8.99 × 10⁹ N m² C⁻².
Calculate the gravitational force between the electron and the proton.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).