Science calculator

Escape and orbital speed.

Calculate escape speed, circular orbital speed and gravitational field at a chosen distance from the centre of a spherical body.

Central mass M

Distance from centre r

Escape speed vₑNewtonian

—

minimum launch speed without further thrust

Circular orbital speed: —
Gravitational field strength: —

Speed unitDisplay precision

v_{e} = \sqrt{\frac{2 G M}{r}}

v_{o} = \sqrt{\frac{G M}{r}}

vₑ escape speed · vₒ circular orbital speed · G gravitational constant · M central mass · r distance from its centre

Assumptions

Newtonian gravity and a spherically symmetric central body; outside it, the mass acts as though concentrated at the centre.
Radius r is measured from the body's centre, not altitude above its surface.
Escape speed assumes no atmosphere, rotation, thrust after launch or gravity from other bodies, and zero speed at infinite distance.
The orbital result is for an instantaneous circular orbit at the same radius; a physical orbit must lie outside the body.

How it works

Escape speed follows by equating launch kinetic energy with the gravitational potential energy needed to reach infinite distance.

A circular orbit instead balances gravitational acceleration with centripetal acceleration. At the same radius its speed is escape speed divided by √2.

Enter mass and centre-to-centre radius. The Earth defaults are useful for checking scale, but rotation and atmospheric drag matter for real launches.

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