Universal Gravitation and Vector Superposition
For point masses separated by r, Newtonian gravity has magnitude Gm1m2/r^2 along the line of centres; the net force or field is the vector sum of every source contribution.
Why this shows up in the exam
Forces from masses at polygon vertices · Null-point and symmetry calculations · Comparing gravitational attractions
Learn the idea
Every pair of masses attracts along its joining line, and all gravitational fields add as vectors. Treat each mass as pulling the test body toward itself, then combine the pulls with directions rather than magnitudes alone.
🧠 Memory hook: Add arrows, not bare inverse-square numbers.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- F₁2 = -G m1 m2 r_hat/r² — attractive pair force with a consistent radial unit vector
- g = sum_i (-G M_i r_i_hat/r_i²) — vector superposition of point-mass fields
How to approach it
- 1Mark every centre-to-centre vector
- 2Compute each contribution with its sign or components
- 3Add vectors and check symmetry
Common slip-ups that cost marks
- •Dropping vector directions
- •Using surface gap instead of centre distance
- •Counting the test mass inside gravitational field
🌟 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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