Escape & Circular Velocity
Escape and circular orbital speed and period at your chosen altitude.
About this tool
Choose a body or enter its mass M and radius R. Enter altitude h above that radius in km, then calculate. Results are the speed required to escape, circular orbital speed and circular orbital period at r = R + h. Altitude may be zero; mass and radius must be positive. Editing mass or radius selects Custom body; changing body keeps the altitude. Reset restores Earth at 400 km.
The two-body spherical model uses vₑ = √(2GM/r), v꜀ = √(GM/r), T = 2πr/v꜀, and g = GM/r². Speeds are relative to the body’s centre in a nonrotating frame. Escape speed is √2 times circular speed, not the extra speed needed when already in orbit. Earth at 400 km has a circular speed about 7.67 km/s and period 92.6 min.
Details shows gravity at the selected altitude, surface gravity and GM. Compare altitudes uses the surface, your selected altitude and heights R and 3R; it recalculates them for this body. These are ideal mathematical orbits, including the surface row, not a claim that a spacecraft can orbit through terrain or atmosphere.
Preset planet/dwarf masses and equatorial radii are rounded JPL values. The Moon uses its mean radius and mass inferred from JPL GM; the Sun uses its photospheric radius and mass inferred from JPL GM. G = 6.67430 × 10⁻¹¹ SI. Rotation, oblateness, atmosphere, other bodies, thrust and relativity are omitted; this is not a launch delta-v budget. Very compact bodies require relativity. Floating-point arithmetic limits extreme inputs.