Surface Gravity and Planet Scaling
For a spherical planet of mass M and radius R, surface gravitational acceleration is GM/R^2; if its mean density is rho, substituting M = 4 pi rho R^3/3 gives g = 4 pi G rho R/3.
Why this shows up in the exam
Comparing planets · Compression at fixed mass · Density-radius scaling
Learn the idea
Surface gravity depends on M/R², or equivalently on rho R for a uniform spherical planet. A larger planet does not automatically have stronger surface gravity; both its mass and the square of its radius matter.
🧠 Memory hook: At the surface: M over R squared, or density times R.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- g_s = GM/R² — surface gravitational acceleration
- g_s = (4 pi/3) G rho R — surface gravity in terms of mean density
- W = m g_s — true gravitational weight at the surface
How to approach it
- 1List which of M, R, and rho remain fixed
- 2Form a ratio before inserting numbers
- 3Check the result against physical scaling
Common slip-ups that cost marks
- •Scaling with radius alone
- •Confusing diameter and radius factors
- •Keeping density fixed when mass is stated fixed
🌟 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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