Engineering tools
Space physics calculators
Every tool shows its formula, assumptions and a step-by-step solution, uses SI constants from CODATA, the IAU and JPL, and is covered by automated tests against published reference values. Results can be shared as a link.
Orbital mechanics
- Orbital VelocitySpeed needed to hold a circular orbit at any altitude around the Sun, a planet or the Moon.
v = √(μ / r)Open tool - Orbital PeriodHow long one orbit takes for a given semi-major axis around any Solar System body.
T = 2π √(a³ / μ)Open tool - Escape VelocityMinimum speed to escape a body's gravity from its surface or any altitude, without further thrust.
vₑ = √(2μ / r)Open tool - Hohmann TransferTwo-burn transfer between circular, coplanar orbits: both burns, total delta-v and transfer time.
aₜ = (r₁ + r₂)/2Open tool - Kepler's Third LawSolve for orbital period or semi-major axis, including the orbiting body's mass.
T² = 4π² a³ / (G (M + m))Open tool - Orbital EnergySpecific orbital energy and vis-viva speed at any point of an elliptical orbit.
ε = −μ / (2a)Open tool
Rocketry
- Rocket Equation (Delta-v)Tsiolkovsky rocket equation: delta-v from specific impulse and wet/dry mass.
Δv = IspOpen tool - Thrust-to-Weight RatioCan your rocket lift off? Thrust-to-weight ratio on Earth, the Moon, Mars or any body.
TWR = F / (mOpen tool - Rocket Fuel (Propellant Mass)Propellant needed to deliver a target delta-v, plus mass flow and burn time.
m_p = m_fOpen tool - Payload MassMaximum payload a single stage can carry for a given delta-v, propellant load and structure.
m_payload = m_p / (e^(Δv/(Isp·g₀)) − 1) − m_dryOpen tool
Distance & light
- Light Travel TimeHow long light or a radio signal takes to cross any distance — from the Moon to other stars.
t = d / cOpen tool - Space Travel Time EstimatorHow long a journey takes at a constant speed — from the Moon to the nearest star.
t = d / vOpen tool - Astronomical Unit (AU) ConverterConvert astronomical units to km, light-minutes, light-years and parsecs.
1 AU = 149,597,870,700 m (exact, IAU 2012)Open tool - Light-Year ConverterConvert light-years to km, AU and parsecs.
1 ly = c × 365.25 days = 9.4607 × 10¹⁵ mOpen tool - Parsec ConverterConvert parsecs to light-years, AU and km.
1 pc = 648,000/π AU ≈ 3.2616 lyOpen tool
Gravity
- Gravitational ForceNewton's law of universal gravitation: the attraction between any two masses.
F = GOpen tool - Surface GravityGravitational acceleration at the surface of any planet, moon or star from its mass and radius.
g = GOpen tool - Planetary WeightWhat you would weigh on the Moon, Mars, Jupiter and every other world.
W = mOpen tool
Power
Relativity
Stars & exoplanets
- Exoplanet Transit DepthFractional dimming when a planet crosses its star — the basis of Kepler and TESS discoveries.
δ = (R_p / R_★)²Open tool - Stellar LuminosityTotal power radiated by a star from its radius and effective temperature (Stefan–Boltzmann law).
L = 4π R² σ T⁴Open tool - Habitable Zone EstimatorConservative and optimistic habitable-zone limits around a star, plus a planet's equilibrium temperature.
S_eff = S☉ + aT★ + bT★² + cT★³ + dT★⁴Open tool