Celestial Mechanics and Dynamics
Core concepts
Master Newtonian gravity, Kepler's laws, orbital elements, the vis-viva equation, and energy and angular momentum conservation. Understand two-body and restricted three-body problems, Lagrange points, perturbations, precession, and tidal forces. Know escape velocity, circular velocity, and the concept of orbital eccentricity and inclination.
Traps
Do not apply circular-orbit formulas to eccentric orbits without adjustment. Remember that the vis-viva equation uses the semimajor axis, not the current radius. Watch for confusion between specific energy and total energy. Distinguish the barycenter from the primary's center.
Worked example
A satellite at 7,000 km from Earth's center moves at 7.5 km/s. Vis-viva: v^2 = GM(2/r - 1/a). With GM ≈ 3.986×10^14 m^3/s^2, 2/r ≈ 2.86×10^-7, and v^2 ≈ 5.6×10^7, solve for 1/a ≈ 2.86×10^-7 - 1.4×10^-7 ≈ 1.46×10^-7, so a ≈ 6.85×10^6 m. Rule of thumb: circular speed at a given radius is √(GM/r).
Rule of thumb
Escape velocity equals √2 times the circular velocity at the same radius.