Engineering
Orbital velocity, escape velocity & Kepler's 3rd Law satellite period formulas
Calculate circular orbital speed SQRT(mu/r), local escape speed SQRT(2*mu/r), and orbital period in minutes from gravitational parameter mu and altitude.
Always add planetary radius R to altitude h before computing orbital mechanics!
Use distance from the center: planetary radius plus altitude, in km. With mu=398600 km^3/s^2 and radius 6378+400=6778 km, circular speed is 7.67 km/s and period is 92.56 minutes.
This ideal two-body model assumes a spherical central body and negligible satellite mass. It omits atmosphere, rotation, oblateness and other bodies. Escape speed is a local speed, not a launch delta-v budget. The period formula uses orbital radius only for circular orbits; elliptical orbits require the semimajor axis. A zero-altitude calculation is a theoretical surface limit, not a viable orbit.
| Astrodynamics Quantity (400 km LEO, r = 6,778 km) | Formula (mu = 398,600 km^3/s^2) | Value |
|---|---|---|
| Circular Orbital Velocity (v_orb) | SQRT(398600 / 6778) | 7.67 km/s |
| Local Escape Velocity (v_esc) | SQRT(2 * 398600 / 6778) | 10.85 km/s |
| Kepler Orbital Period (Minutes) | 2 * PI() * SQRT(6778^3 / 398600) / 60 | 92.56 min |
| Surface Escape Velocity (h = 0, r = 6,378 km) | SQRT(2 * 398600 / 6378) | 11.18 km/s |
Circular orbital velocity (km/s) at altitude h
A2=GravitationalParameter mu (398600 km^3/s^2), B2=PlanetRadius_km (6378), C2=Altitude_km (400).
=IF(OR(COUNT(A2:C2)<>3,A2<=0,B2<=0,C2<0),"Invalid inputs",ROUND(SQRT(A2 / (B2 + C2)), 2))Kepler's 3rd Law orbital period in minutes
Divides 2 * PI() * SQRT(r^3 / mu) seconds by 60 to express orbit duration in minutes.
=IF(OR(COUNT(A2:C2)<>3,A2<=0,B2<=0,C2<0),"Invalid inputs",LET(orbitalRadius, B2 + C2, ROUND((2 * PI() * SQRT((orbitalRadius ^ 3) / A2)) / 60, 2)))Try the example
Use the original values or change them to test your understanding.