Energy of a Circular Orbit
Combining circular-force balance with U=-GMm/r gives K=-U/2 and E=K+U=U/2=-GMm/(2r), under the point-mass or spherical-source approximation.
Why this shows up in the exam
Orbital energy ratios · Energy needed to raise a circular orbit · Matching orbital quantities
Learn the idea
A circular orbit has K=GMm/(2r), U=-GMm/r, and total energy E=-GMm/(2r). Half the magnitude of gravitational potential energy appears as kinetic energy; the remaining half keeps the orbit bound.
🧠 Memory hook: Circular orbit: positive half, negative one, total negative half.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- K = GMm/(2r) — circular-orbit kinetic energy
- U = -GMm/r — circular-orbit potential energy
- E = -GMm/(2r) — total mechanical energy
How to approach it
- 1Write r from the centre
- 2Use the three linked energy expressions
- 3Check that a larger circular orbit has less-negative total energy
Common slip-ups that cost marks
- •Setting total energy equal to kinetic energy
- •Using surface radius for an elevated orbit
- •Forgetting satellite mass in energy ratios
🌟 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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