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Orbital and escape velocity calculator

Compute escape velocity, circular orbital speed and orbital period for any body from its mass and radius.

Earth 5.972e24

Escape velocity
11.186 km/s
Circular orbital speed7.9097 km/s
Orbital period84.348 minutes
Surface gravity at this radius9.82 m/s²
Escape / orbital ratio1.414 (always √2)

Escape velocity is the speed at which an object’s kinetic energy exactly equals the gravitational potential energy binding it to a body. Launch faster than that, ignoring drag, and it never comes back.

v_escape = √(2GM / r)   v_orbit = √(GM / r)

Notice that mass of the escaping object cancels out. A pebble and a spacecraft need the same speed. What differs is the energy required to get there, which is why rockets are large.

Escape speed is always √2 times orbital speed

The two formulas differ only by a factor of two under the root. Circular orbit around Earth’s surface would need about 7.9 km/s; escaping needs 11.2 km/s. That fixed ratio holds for every body in the universe.

Direction does not matter, drag does

Escape velocity is a scalar. Fired at any upward angle, an object at that speed will leave. This is only true because the derivation is purely energetic and ignores the atmosphere. In reality no rocket travels at escape velocity near the ground — it would burn up — so launches accelerate gradually as the air thins, and the concept is used as an energy budget rather than a literal speed.

Some figures

BodyEscape velocity
Moon2.38 km/s
Mars5.03 km/s
Earth11.19 km/s
Jupiter59.5 km/s
Sun617.5 km/s

A body whose escape velocity would exceed the speed of light is a black hole, and setting v = c in this formula gives the Schwarzschild radius — which is, remarkably, the correct answer despite the derivation being entirely Newtonian.