Physics C: Mechanics · Unit 7: Gravitation · 14 min read · Updated 2026-05-11
Orbits of planets and satellites — AP Physics C: Mechanics
AP Physics C: Mechanics · Unit 7: Gravitation · 14 min read
1. Circular Orbits and Centripetal Force Balance★★☆☆☆⏱ 4 min
For a circular orbit, gravitational force from the central body provides exactly the centripetal force required to maintain constant speed along the circular path. We can ignore acceleration of the central body around the shared center of mass due to the large difference in mass.
2. Kepler's Laws of Planetary Motion★★★☆☆⏱ 4 min
Kepler derived three empirical laws from observational data before Newton developed gravitational theory, and Newton's law of universal gravitation confirms all three for two-body orbits with a dominant central mass.
**Law of Orbits**: All planets move in elliptical orbits with the central body at one focus of the ellipse. Eccentricity $e$ describes orbit shape: $e=0$ = perfect circle, $0<e<1$ = bound elliptical orbit, $e \geq 1$ = unbound orbit. Closest distance (perihelion/perigee) is $r_p = a(1-e)$, farthest distance (aphelion/apogee) is $r_a = a(1+e)$, where $a$ = semi-major axis.
**Law of Areas**: A line joining the orbiting body and central body sweeps out equal areas in equal time intervals. This is a direct consequence of conservation of angular momentum: gravity exerts zero torque, so $L$ is constant, meaning speed is higher at smaller $r$.
**Law of Periods**: The square of the orbital period is proportional to the cube of the semi-major axis: $T^2 = \frac{4 \pi^2 a^3}{G M}$, which generalizes the circular orbit result (where $a=r$).
3. Orbital Energy and Escape Velocity★★★☆☆⏱ 3 min
For all bound orbits (circular or elliptical, $0 \leq e < 1$), total mechanical energy is always negative. We define gravitational potential energy $U=0$ at $r \to \infty$, so $U$ is negative, and has twice the magnitude of the orbit's kinetic energy.
4. AP-Style Practice Worked Examples★★★★☆⏱ 3 min
Common Pitfalls
Why: Problems often give altitude, and students confuse height above ground with the center-to-center distance required for all gravitational formulas.
Why: Students remember kinetic energy is positive and forget gravitational potential energy is negative and has a larger magnitude for bound orbits.
Why: The proportionality only holds when the central mass $M$ is the same, since the constant of proportionality depends on $M$.
Why: Students mix up the definitions of the two axes for ellipses.
Why: Students forget the factor of 2 from the energy derivation, mixing up the two formulas.