orbital-mechanics

# Orbital Mechanics Orbital mechanics is the branch of celestial mechanics that answers: where will this object be at time t, given its position and velocity now? The foundational discoveries were Kepler's three laws (1609, 1619) and Newton's derivation of them from universal gravitation (1687). Modern practice adds perturbation theory for multi-body problems and relativistic corrections for high-precision ephemerides. This skill covers the classical core: the six orbital elements, Kepler's laws, the vis-viva equation, orbit types, transfer orbits, gravity assists, and a handful of strategies for computing positions in practice. **Agent affinity:** hubble (catalog cross-reference), payne-gaposchkin (binary star orbits and dynamical masses) **Concept IDs:** astro-keplers-laws, astro-earth-moon-sun-geometry, astro-planetary-motion ## The Two-Body Problem Two point masses interacting only via gravity produce a relative motion that is exactly solvable. The relative orbit is a conic section — circle, ellipse, parabola, or hyperbola — with the total mass concentrated at one focus. **Assumptions:** - Only two bodies (all others negligible) - Point masses (or spherically symmetric) - No radiation pressure, atmosphere, or non-gravitational forces - Newtonian gravity (relativistic correction needed for Mercury's perihelion, binary pulsars) When these assumptions hold, the motion is fully determined by six constants — the **orbital elements** — and an epoch. ## The Six Orbital ...