Exact symbolic verification of Kepler's third law for circular orbits. Equation of motion centripetal: m·v²/a = G·M·m/a² → v² = G·M/a exactly. Orbital period: T = 2π·a/v = 2π·a·√(a/(GM)) = 2π·a^{3/2}/√(GM). Squaring: T² = 4π²·a³/(GM). …
Exact symbolic verification of Kepler's third law for circular orbits. Equation of motion centripetal: m·v²/a = G·M·m/a² → v² = G·M/a exactly. Orbital period: T = 2π·a/v = 2π·a·√(a/(GM)) = 2π·a^{3/2}/√(GM). Squaring: T² = 4π²·a³/(GM). …