How this calculator works
Escape speed is the minimum initial speed for an unpowered object to approach infinity with zero remaining speed in a two-body Newtonian model. Radius is measured from the central body's centre. The circular speed at the same location is smaller by sqrt(2). The model omits atmosphere, rotation, finite burns and other masses; it is unsuitable near compact relativistic objects.
Formula
vescape = sqrt(2GM/r) = sqrt(2mu/r); vcircular = sqrt(mu/r). r = 2mu/vescape²; M = vescape²r/(2G).
Worked example
For mu = 100 m3/s2 and radius 2 m, escape speed is 10 m/s and circular speed is 7.0711 m/s. Reducing escape speed to 5 m/s at the same mu requires radius 8 m.
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Frequently asked questions
Does the spacecraft mass matter?
It cancels when its mass is negligible relative to the central body.
Must an escaping rocket instantly reach this speed?
No. This is an unpowered ballistic energy threshold; a powered trajectory can add energy over time.
Can I enter altitude?
Convert it to centre-to-object radius by adding the body's radius first.