Why does weight change on the Moon but not mass?

Mass is the amount of matter, while weight is mass times g; lunar g of 1.6 means the same body weighs about six times less.

How is Kepler third law used?

The period squared scales with radius cubed, so doubling the period needs 1.59 times the radius, a quick way to compare satellites.

S6 Physics Gravitation, Paper 3: inverse square and Kepler ratios

2026-11-02

Tutor Prep Guide · Primary English

Ten graded items on weight on the Moon and other planets, g ratios, orbital radii from period ratios, plus escape and orbital speed.

Focus　Surface g varies with mass and with the square of the radius, and Kepler ratios give radius as the two thirds power of the period.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: S6 Physics: Gravitation
Level	Four basic, three advanced, two challenge and one error-repair item

02　Questions (10 items)

FoundationThe Moon has surface g of 1.6 m/s^2. Find the weight of a 50 kg astronaut there.
FoundationTwo 5 kg spheres are 1 m apart. Find the gravitational force between them.
FoundationA planet has radius 5.0 x 10^6 m and surface g of 8.0 m/s^2. Find its mass.
FoundationAt three Earth radii from the centre, what is g if the surface value is 9.8 m/s^2?
IntermediateA satellite circles at 7.0 x 10^6 m from Earth centre. Find its period, with Earth mass 6.0 x 10^24 kg.
IntermediateFind the escape speed of Earth, with mass 6.0 x 10^24 kg and radius 6.4 x 10^6 m.
IntermediateA planet has twice the Earth mass and twice the radius. Find its surface g, taking the Earth value as 9.8 m/s^2.
ChallengeTwo satellites orbit the same planet and the outer period is twice the inner one. Compare their orbital radii.
ChallengeA planet has three times the Earth mass but the same radius. Find its surface g, taking the Earth value as 9.8 m/s^2.
Error redoA student gets 7.9 km/s for the Earth escape speed using root gR. Find the mistake and the correct value.

03　Answers and one-line notes

#	Answer	One-line note
1	80 N	Weight is mass times surface gravity, so the astronaut weighs 80 newtons on the Moon.
2	About 1.67 x 10^-9 N	Five kilograms each at one metre apart gives about 1.67 times ten to the minus ninth newtons.
3	About 3.0 x 10^24 kg	Rearranging g equals GM over R squared gives a mass of about 3.0 times ten to the twenty-fourth kilograms.
4	About 1.09 m/s^2	Distance triples, so g falls to one ninth of 9.8, about 1.09 metres per second squared.
5	About 5.8 x 10^3 s, roughly 97 minutes	The period works out near 5800 seconds, about 97 minutes, typical of a low Earth orbit.
6	About 11.2 km/s	The square root of twice GM over R gives about 11.2 kilometres per second, the well known Earth value.
7	Half, 4.9 m/s^2	Doubling both mass and radius halves g, giving 4.9 metres per second squared.
8	About 1.59 times	Since the period scales as r to the three halves, doubling the period needs about 1.59 times the radius.
9	29.4 m/s^2	Mass triples at the same radius, so g triples to 29.4 metres per second squared.
10	Root gR is orbital speed; escape speed is root two times that, 11.2 km/s, about 1.41 times larger	Root gR is the circular orbital speed; escape speed needs the extra factor root two, giving 11.2 kilometres per second.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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