Orbital Mechanics Calculator

This wizard covers five staple orbital-mechanics calculations, each a distinct classic formula rather than a single unified simulator. Kepler's Laws & Orbits applies Kepler's third law (T² = 4π²a³/GM) to find orbital period from semi-major axis and central mass, then uses the vis-viva equation to derive perihelion and aphelion velocities from eccentricity, and classifies the orbit's shape from that same eccentricity value. Hohmann Transfer & Delta-V computes the minimum-energy two-burn trajectory between two circular orbits: transfer-orbit velocities via vis-viva, the delta-v required at departure and arrival, transfer time as half the transfer ellipse's period, and the synodic period between launch windows — it also flags when a bi-elliptic transfer (a three-burn alternative) would be more fuel-efficient, using the classic orbit-ratio-of-11.94 threshold. Escape Velocity & Sphere of Influence computes escape velocity and surface gravity from mass and radius, then estimates two related but distinct gravitational-dominance boundaries — a Hill-sphere-style radius and a separate sphere-of-influence approximation — using different exponents, so don't expect the two figures to match.

The synchronous-orbit altitude always assumes a 24-hour rotation period regardless of the body being modeled, so it's only meaningful for Earth-like rotators. Lagrange Points approximates L1 and L2 distances using the same μ/3 cube-root formula (a first-order approximation that doesn't distinguish the small difference between the two points), and reports L4/L5 stability using the standard 0.0385 mass-ratio threshold. Relativistic Effects computes Schwarzschild radius, gravitational and velocity time dilation, and Mercury-style perihelion precession — useful for seeing how small general-relativistic corrections are for ordinary planetary orbits, and how large they become near compact objects.