AS 91524 · 2025 paper · momentum & circular motion

Question 1(d) Merit to Excellence

Practises Gravitation & orbital mechanics

Titan is the largest of Saturn's moons. Ignore every other body, and assume Titan is in a perfectly circular orbit.

M Saturn	5.68×10²⁶ kg
r Saturn	5.82×10⁷ m
M Titan	1.35×10²³ kg
centre-to-centre	1.22×10⁹ m

Astronauts on the International Space Station appear weightless, even though Earth's gravity is still acting on them.

Explain why astronauts appear weightless yet can stay in orbit.

The 2025 paper, page 4 ↗ Marking schedule, page 2 ↗

Work it out

Try it on paper first. Stuck? Take one hint at a time.

1 Is gravity weak where the ISS is?
No. Low Earth orbit is close to the surface compared with Earth’s radius, so gravity there is still close to its full surface strength. The question says so too: Earth’s gravity is still acting on them.
2 So what is that gravity doing to the station and the astronaut?
It is the centripetal force that keeps both of them moving in a circle: F_g = F_c. They are falling towards Earth all the time, but they move sideways so fast that the curved surface drops away beneath them as they fall. That is what an orbit is.
3 What do you actually feel as your weight?
Not gravity itself, but the push back from whatever holds you up: the floor’s reaction force.
4 The station and the astronaut fall together. What push does the floor give the astronaut?
They are both in free fall with the same acceleration, so the floor never pushes on the astronaut. With no reaction force there is nothing to feel as weight, so they appear weightless.

Answer Gravity still acts on the astronauts and provides exactly the centripetal force their orbit needs, so they and the ISS are both in free fall around Earth, accelerating together. Because nothing pushes back on them, there is no reaction force, and that missing support force is why they appear weightless.

What the marker wanted

Achieved One idea: they are in free fall; there is no reaction force on them; or gravity is what provides the centripetal force (written as F_c = F_g is fine, if it is about this orbit).
Merit Two of those ideas explained in full, or one in full and two in part.
Excellence The whole explanation: gravity supplies the centripetal force that keeps them in orbit, they and the station fall at the same rate, so no reaction force acts on them, and that missing push is what “weightless” means.

In our words, from NZQA’s 2025 marking schedule.

Common mistake

Explaining it like the top of a roller-coaster loop. NZQA’s 2025 report says leaning on Earth-bound analogies, roller-coaster physics in particular, kept many answers from the higher grades. Start from what gravity is doing in orbit.

How did it go?

Got it moves it further out. Review brings it back tomorrow.