OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(b) gravitational field strength g r GM 2 =- for a point mass
Full specification wording
Newton’s law of gravitation: (b) gravitational field strength g r GM 2 =- for a point mass
Gravitational field strength g at a point is the force per unit mass on a small test mass placed there.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 2 of 3
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Gravitational field strength g at a point is the force per unit mass on a small test mass placed there. For a point mass M, or any spherically symmetric body treated as one, the field at distance r from its centre has magnitude g = GM/r², where G is the gravitational constant. The field is directed towards the mass, so the vector form carries a minus sign when r is measured outwards from the mass: g = −GM/r². Because r appears squared in the denominator, doubling the distance quarters the field strength. For example, at twice the Earth's surface radius from the centre, g falls to about one quarter of its surface value. The expression applies outside the body; inside a uniform sphere the field varies linearly with distance from the centre.
What earns the marks
- States that g is the gravitational force per unit mass at a point, with units N kg⁻¹.
- Recalls the magnitude relation g = GM/r² for a point mass or spherically symmetric mass.
- Explains that the minus sign in g = −GM/r² indicates the field points towards the mass when r is measured outwards.
- Applies the inverse-square dependence, so doubling r reduces g by a factor of 4.
- Recognises that the expression holds outside the body and that a uniform sphere behaves as a point mass at its centre for external points.
Common mistakes and how to put them right
Writing g = GM/r instead of g = GM/r².
Put it right: The field obeys an inverse-square law, so the correct denominator is r².
Treating r as the height above the surface rather than the distance from the centre of the mass.
Put it right: For a planet, r must be measured from its centre.
Ignoring the direction of the field and claiming g is a scalar with no sign.
Put it right: The vector form g = −GM/r² shows the field acts towards the mass.
Assuming the formula applies inside a solid sphere in the same way.
Put it right: Inside a uniform sphere the field is proportional to r, not to 1/r².
Exam tips
- Check whether the question gives distance from the surface or from the centre, and convert to centre distance before substituting.
- Keep G, M and r in SI units (N m² kg⁻², kg, m) so that g comes out in N kg⁻¹.
- When comparing two points, use ratios such as g₂/g₁ = (r₁/r₂)² to avoid unnecessary arithmetic.
- State the direction of g explicitly when a vector answer is expected, using the minus sign convention given in the specification.
Try the lesson
The start of the Newton’s law of gravitation: (b) gravitational field strength g r GM 2 =- for a point mass lesson, made from checked teaching notes for this specification point.
Listen
Gravitational field strength g at a point is the force per unit mass on a small test mass placed there. For a point mass M, or any spherically symmetric body treated as one, the field at distance r from its centre has magnitude g = GM/r², where G is the gravitational constant. The field is directed towards the mass, so the vector form carries a minus sign when r is measured outwards from the mass: g = −GM/r². Because r appears squared in the denominator, doubling the distance quarters the field strength. For example, at twice the Earth's surface radius from the centre, g falls to about one quarter of its surface value. The expression applies outside the body; inside a uniform sphere the field varies linearly with distance from the centre. A strong answer earns marks for these points. States that g is the gravitational force per unit mass at a point, with units N kg⁻¹. Recalls the magnitude relation g = GM/r² for a point mass or spherically symmetric mass. Explains that the minus sign in g = −GM/r² indicates the field points towards the mass when r is measured outwards. Applies the inverse-square dependence, so doubling r reduces g by a factor of 4. Exam tip: Check whether the question gives distance from the surface or from the centre, and convert to centre distance before substituting.
Key words
Say what each word means before you turn the card.
Gravitational field strength
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Inverse-square law
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Vector nature of gravitational fields
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Application outside the body
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See every definition
- Gravitational field strength
- The force per unit mass on a small test mass placed at a point, with units N kg⁻¹.
- Inverse-square law
- Because r appears squared in the denominator, doubling the distance quarters the field strength.
- Vector nature of gravitational fields
- The field is directed towards the mass, so the vector form carries a minus sign when r is measured outwards from the mass.
- Application outside the body
- The expression applies outside the body, and a uniform sphere behaves as a point mass at its centre for external points.
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