Why do astronauts feel weightless?

The craft and crew fall together, so gravity supplies exactly the centripetal force and there is no support force.

Must a geostationary satellite be over the equator?

Yes, only a circular orbit above the equator keeps the satellite fixed relative to the ground.

S6 Physics Gravitation, Paper 1: the law and g

2026-11-02

Tutor Prep Guide · Primary English

Ten graded items on the inverse square law, surface gravity, orbital speed, geostationary radius and Kepler third law.

Focus　Measure r from the centre of the planet, use GM over R squared for g, the square root of GM over r for orbital speed and remember T squared goes as r cubed.

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)

FoundationEarth has mass 6.0 x 10^24 kg and radius 6.4 x 10^6 m. Find g at the surface, with G as 6.67 x 10^-11.
FoundationTwo 10 kg spheres are 1 m apart. Find the gravitational force between them.
FoundationThe distance between two stars grows from r to 3r. What fraction of the original force remains?
FoundationThe Moon has mass 7.3 x 10^22 kg and radius 1.74 x 10^6 m. Find g on its surface.
IntermediateA space station orbits 7.0 x 10^6 m from Earth centre. Find its orbital speed, with Earth mass 6.0 x 10^24 kg.
IntermediateA geostationary satellite has a period of 86400 s. Find its orbital radius, with Earth mass 6.0 x 10^24 kg.
IntermediateA satellite orbital radius grows fourfold. By what factor does the period change?
ChallengeMars has mass 6.4 x 10^23 kg and radius 3.4 x 10^6 m. Find g on its surface.
ChallengeAn object rises to a height equal to the Earth radius. What fraction of its surface weight remains and what is g there?
Error redoA student claims doubling the orbital radius doubles the period. What is the correct factor?

03　Answers and one-line notes

#	Answer	One-line note
1	9.77 m/s^2	Gravitational constant times Earth mass over the square of the radius gives about 9.77 metres per second squared.
2	6.67 x 10^-9 N	The force is 6.67 times ten to the minus ninth newtons, far too small to notice in daily life.
3	One ninth	Force falls with the square of the distance, so three times the separation leaves one ninth of the force.
4	1.61 m/s^2	Moon gravity works out at about 1.61 metres per second squared, roughly a sixth of the value on Earth.
5	7.56 km/s	Orbital speed is the square root of GM over r, giving about 7.56 kilometres per second.
6	About 4.23 x 10^7 m	Setting the gravitational force equal to the centripetal force gives a radius of about 4.23 times ten to the seventh metres.
7	Eight times	Kepler law squares the period against the cube of the radius, so four times the radius means eight times the period.
8	3.69 m/s^2	Mars gives about 3.69 metres per second squared, smaller mass but also smaller radius.
9	One quarter, 2.44 m/s^2	At twice the Earth radius the distance is doubled, so g falls to a quarter, about 2.44 metres per second squared.
10	About 2.83 times, the square root of eight	Period grows as the three halves power of the radius, so doubling the radius gives about 2.83 times, not two times.

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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