Gravity and Weight Above a Planet
Outside a spherical planet, g(h) = GM/(R+h)^2 = g0[R/(R+h)]^2; for h much smaller than R, the first-order approximation is g(h) approximately g0(1-2h/R).
Why this shows up in the exam
Altitude-dependent weight · Matching gravity at height and depth · Small percentage weight changes
Learn the idea
At altitude h, use distance R+h from the centre, so gravity falls by [R/(R+h)]². Altitude is measured from the surface, but the inverse-square law measures distance from the planet's centre.
🧠 Memory hook: Add altitude before squaring.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- g(h) = g0 [R/(R+h)]² — exact altitude dependence
- g(h) approx g0(1 - 2h/R) — small-altitude approximation h much less than R
How to approach it
- 1Convert height to centre distance
- 2Choose exact or small-h formula deliberately
- 3Use a ratio and verify gravity decreases
Common slip-ups that cost marks
- •Using h instead of R+h
- •Using the linear approximation for large h
- •Confusing weight change with mass change
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A satellite moves in a circular orbit where GM = 4 x 10^14 m^3/s^2 and orbital radius is 2 x 10^6 m. Find its orbital speed.
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