Orbital Mechanics

Orbital mechanics calculators and formulas for orbits, escape velocity, and gravitation. Covers orbital period, escape velocity, and Kepler's laws calculations for spacecraft.

7Formulas

All levels Difficulty

Updated Jul 2026

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Fundamental

Kepler's Third Law (AU-Year Simplified Form)

T² = a³ (T in years, a in AU, orbiting the Sun)

Fundamental

Precession Period of the Equinoxes

P ≈ 360° / (rate of precession per year)

Fundamental

Moonrise/Moonset Daily Shift (Approx.)

Δt ≈ 50 minutes/day

Fundamental

Synodic Period (Planetary Opposition Interval)

1/S = |1/T_1 - 1/T_2|

Fundamental

Local Sidereal Time (Approx.)

LST = GST + Longitude/15

Fundamental

Escape Velocity

v_esc = √(2GM / r)

Fundamental

Kepler's Third Law

T² = (4π² / GM) a³