Explain why the gravitational field strength at the surface of the Moon is less than the gravitational field strength at the surface of the Earth, even though the Moon has a smaller radius.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
The Moon has a mass of approximately 7.3 × 10²² kg and a mean radius of 1.7 × 10⁶ m. The Earth has a mass of approximately 6.0 × 10²⁴ kg and a mean radius of 6.4 × 10⁶ m.
Model answer (4 marks)
Gravitational field strength at a surface is given by g = GM/R².
The Moon’s mass (7.3×10²² kg) is about 80 times smaller than the Earth’s mass (6.0×10²⁴ kg). This large reduction in M lowers g on the Moon.
A smaller radius (1.7×10⁶ m vs 6.4×10⁶ m) would tend to increase g because g ∝ 1/R², but the effect is small compared with the mass difference.
Thus the decrease in g caused by the Moon’s much smaller mass outweighs the increase from its smaller radius, giving a weaker surface gravitational field on the Moon.
The Moon’s mass (7.3×10²² kg) is about 80 times smaller than the Earth’s mass (6.0×10²⁴ kg). This large reduction in M lowers g on the Moon.
A smaller radius (1.7×10⁶ m vs 6.4×10⁶ m) would tend to increase g because g ∝ 1/R², but the effect is small compared with the mass difference.
Thus the decrease in g caused by the Moon’s much smaller mass outweighs the increase from its smaller radius, giving a weaker surface gravitational field on the Moon.
Examiner tips
- Use the formula g=GM/R² explicitly; mention both M and R. Show the mass ratio (~1/80) and explain its effect. Explain the opposing effect of the radius. Conclude that mass dominates over radius.
- common_mistakes
- :
- Forgetting to include the mass term in the explanation. Claiming the radius alone determines g without noting the mass effect. Using incorrect units or not specifying the formula.
Mark scheme (4 marks)
- Gravitational field strength at a surface is given by g = GM/R², where M is the mass of the body and R is its radius.
- The Moon's mass is very much smaller than the Earth's mass (by a factor of about 80), which acts to reduce g significantly.
- A smaller radius alone would increase g (since g ∝ 1/R²), so the Moon's smaller radius partially counteracts the effect of its smaller mass.
- The reduction in g due to the Moon's much smaller mass outweighs the increase in g from its smaller radius, so the Moon's surface gravitational field strength is smaller overall.
Key terms in this question
Related
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