Unit 6 · 6.6 — Motion of Orbiting Satellites

Everything to learn here

• Concept: Gravity provides the sole centripetal force for circular orbits; angular momentum is conserved relative to the central massive body in both circular and elliptical orbits.
• Concept: In an elliptical orbit, a satellite travels fastest at perihelion (periapsis) and slowest at aphelion (apoapsis) to conserve angular momentum (L = mvr).
• Concept: The total mechanical energy of an orbiting satellite is conserved, exchanging kinetic energy and gravitational potential energy in elliptical paths.
• Equation: $$v=\sqrt{\frac{GM}{r}}\text{(Orbital velocity for a circular orbit)}$$
• Vocabulary: Escape Velocity — The absolute minimum initial speed required to reach an infinite distance from a massive body with zero residual kinetic energy.
• Skill: Derivation — Setting F_c = F_G to symbolically derive circular orbital velocity and relating it to Kepler's Third Law for the period of orbit.
• Skill: Mathematical Routines — Applying the energy boundary condition K_i + U_i = 0 to derive the escape velocity formula for a planet.
• Concept: Explain how two masses move when the only force acting between them is their mutual gravitational attraction.
• Vocabulary: Vocabulary: Escape Velocity — The speed v_esc = sqrt(2 * G * M / r) where the sum of kinetic and potential energy is zero.

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