Quick answer: Gravitational potential energy is U = −GMm/r, with zero at infinity. This AP Physics C test on orbits and escape speed has 8 questions worth 20 marks, to do in 45 minutes: field strength, low Earth orbit and effect of drag. The mark scheme is on a separate page; free printable PDF.
This test covers gravitational potential energy, circular and elliptical orbits and escape speed in the style of AP Physics C: Mechanics. Show each step, use calculus where asked and give units. Take G = 6.67 × 10⁻¹¹ N m²/kg² and the data given. The total is 20 marks.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:M Unit 7
Question 1 Field strength (2 marks)
Calculate the gravitational field strength at a distance of 3R from Earth’s centre, where R = 6.37 × 10⁶ m, given that g = 9.81 m/s² at the surface.Question 2 Low Earth orbit (3 marks)
A satellite orbits 600 km above Earth (R = 6.37 × 10⁶ m, GM = 3.98 × 10¹⁴ N m²/kg²).- Write the equation linking gravity and centripetal force. (1 mark)
- Calculate the orbital speed. (1 mark)
- Calculate the period. (1 mark)
Question 3 Effect of drag (2 marks)
Explain why a satellite in a low circular orbit speeds up as air drag slowly lowers it.Question 4 Escape from the Moon (3 marks)
Derive and calculate the escape speed from the Moon (M = 7.35 × 10²² kg, R = 1.74 × 10⁶ m, G = 6.67 × 10⁻¹¹ N m²/kg²).Question 5 Energies of an orbit (3 marks)
A satellite of mass 800 kg is in a circular orbit of radius 1.2 × 10⁷ m. Calculate (a) its kinetic energy, (b) its potential energy, (c) its total energy. Use GM = 3.98 × 10¹⁴.Question 6 Comet speeds (3 marks)
Question 7 Deriving U (2 marks)
Starting from F = −GMm/r², show by integration that the gravitational potential energy is U = −GMm/r, taking U = 0 at infinity.Question 8 Kepler’s third law (2 marks)
A planet orbits a star at 4.0 times the distance of another planet. Calculate the ratio of their periods.
