EXERCISE

This closing exercise set tests every idea developed in the unit, across five question formats:

• Multiple-choice questions probing conceptual understanding -- Kepler's laws, the inverse-square force, gravitational potential energy sign, variation of $g$, escape speed, weightlessness, and satellite energy.
• Short-answer questions requiring precise statements and definitions -- Kepler's laws, Newton's law of gravitation, gravitational field/potential/potential-energy definitions, escape speed, geostationary/polar satellites, weight, eclipses, and Earth's spin.
• Long-answer questions requiring full derivations and detailed explanations -- the features of the law of gravitation, deriving gravitational potential energy and $U=mgh$, escape speed, the three variations of $g$, satellite time period and energy, weightlessness, geostationary/polar satellites, the heliocentric-vs-geocentric argument, and the Eratosthenes and lunar-umbra measurement methods.
• Numerical exercises applying every formula in the unit to concrete calculations -- Kepler's third law, gravitational force and field, gravitational potential, angular momentum and torque, satellite energy, escape velocity, and the variation of $g$. …