OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(d) gravitational potential energy E mV r GMm g = =- at a distance r from…
Full specification wording
Gravitational potential and energy: (d) gravitational potential energy E mV r GMm g = =- at a distance r from a point mass M
Gravitational potential energy of a mass m at distance r from a point mass M is E = mV = −GMm/r, where V = −GM/r is the gravitational potential at that point.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 4 of 5
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Gravitational potential energy of a mass m at distance r from a point mass M is E = mV = −GMm/r, where V = −GM/r is the gravitational potential at that point. The expression applies outside a spherical mass, with r measured from the centre. The negative sign means the potential energy is zero at infinity and decreases as the mass moves closer, so energy is released when a mass falls towards M. Because E is inversely proportional to r, doubling the separation from r to 2r changes E from −GMm/r to −GMm/2r, an increase of GMm/2r, which equals the energy needed to move the mass outward.
For example: A satellite of mass m in orbit at radius r has E = −GMm/r, and the energy required to move it to a higher orbit is the difference between the two values.
What earns the marks
- States E = mV = −GMm/r for a mass m at distance r from a point mass M.
- Explains that E is the product of the mass and the gravitational potential at that point.
- Interprets the negative sign: E is zero at infinity and more negative closer to M.
- Calculates changes in gravitational potential energy as ΔE = E_final − E_initial using signed values.
- Applies the expression outside a spherical mass, with r measured from the centre.
Common mistakes and how to put them right
Dropping the negative sign and writing E = GMm/r.
Put it right: Gravitational potential energy is negative relative to the zero at infinity.
Using r as the height above the surface rather than the distance from the centre.
Put it right: r is the centre-to-centre separation outside the sphere.
Adding magnitudes when finding a change in energy.
Put it right: Subtract signed values, E_final − E_initial, so the direction of energy transfer is clear.
Exam tips
- Write E = mV and substitute V = −GM/r explicitly to show where the negative sign comes from.
- For energy changes, calculate both energies with signs and subtract, rather than working with magnitudes.
- Check that the mass m is the object in the field, not the source mass M.
Try the lesson
The start of the Gravitational potential and energy: (d) gravitational potential energy E mV r GMm g = =- at a distance r from a point mass M lesson, made from checked teaching notes for this specification point.
Listen
Gravitational potential energy of a mass m at distance r from a point mass M is E = mV = −GMm/r, where V = −GM/r is the gravitational potential at that point. The expression applies outside a spherical mass, with r measured from the centre. The negative sign means the potential energy is zero at infinity and decreases as the mass moves closer, so energy is released when a mass falls towards M. Because E is inversely proportional to r, doubling the separation from r to 2r changes E from −GMm/r to −GMm/2r, an increase of GMm/2r, which equals the energy needed to move the mass outward. For example, a satellite of mass m in orbit at radius r has E = −GMm/r, and the energy required to move it to a higher orbit is the difference between the two values. A strong answer earns marks for these points. States E = mV = −GMm/r for a mass m at distance r from a point mass M. Explains that E is the product of the mass and the gravitational potential at that point. Interprets the negative sign: E is zero at infinity and more negative closer to M. Calculates changes in gravitational potential energy as ΔE = E_final − E_initial using signed values. A common slip: Dropping the negative sign and writing E = GMm/r. Instead, gravitational potential energy is negative relative to the zero at infinity. Exam tip: Write E = mV and substitute V = −GM/r explicitly to show where the negative sign comes from.
See it
Key words
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Gravitational potential energy
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Negative sign
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Inverse-distance dependence
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See every definition
- Gravitational potential energy
- The product of the mass and the gravitational potential at that point, given by E = mV = −GMm/r at a distance r from a point mass M.
- Negative sign
- It means the potential energy is zero at infinity and decreases as the mass moves closer, so energy is released when a mass falls towards M.
- Inverse-distance dependence
- Because E is inversely proportional to r, doubling the separation from r to 2r changes E from −GMm/r to −GMm/2r, an increase of GMm/2r.
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