Orbital Velocity & Escape Velocity Calculator
Orbital velocity is the speed needed to stay in a circular orbit at a given height. Escape velocity is the speed needed to leave Earth for good without more thrust. Escape velocity is always √2 times the circular speed.
Standards:
- NGSS HS-ESS1-4
- NGSS HS-PS2-4
- IB D.1
Our alignment; not reviewed by the standards bodies.
The equation
Worked example
- Given
- Altitude above Earth (km): 400 km
- Answer
- Circular orbital velocity: 7.669 km/s
- Escape velocity: 10.845 km/s
- Check
- At the surface this gives 11.18 km/s for escape and 7.905 km/s for circular speed. NASA’s Earth fact sheet lists 11.186 km/s because it uses the 6,371 km mean radius instead of the 6,378.137 km equatorial radius used here. The build checks both.
Assumptions
Spherical Earth, no air drag, no Earth rotation bonus.
Go deeper
Sources
- H. D. Curtis, Orbital Mechanics for Engineering Students, 4th ed., Butterworth-Heinemann (Elsevier), 2020.
- R. R. Bate, D. D. Mueller, J. E. White, W. W. Saylor, Fundamentals of Astrodynamics, 2nd ed., Dover, 2020.
- NASA JPL Solar System Dynamics, planetary physical parameters.
- NASA NSSDCA, Planetary Fact Sheets.