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For Students · Escape Velocity

Escape Velocity for a star cluster

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a star cluster live below — adjust the inputs and watch it respond, right in your browser.

Escape & Orbital VelocityLive

how fast to leave a world

Escape velocity — Earth

11.19km/s

7.91

orbital km/s

1.00

surface g (× Earth)

Controls

Custom body

Presets

Escape velocity v = √(2GM/R) is the speed needed to break free of a body's gravity from its surface, ignoring air resistance. Circular orbital velocity is √(GM/R) — a factor of √2 smaller. Both depend only on mass and radius, not on the mass of the escaping object.

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Data Inspector

Escape velocity11.19 km/s

Orbital velocity7.91 km/s

Surface gravity9.82 m/s²

Governing equation

v_{e} = \frac{2 GM}{R} = \frac{2 ( 6.674 \times 1 0 ^{- 11} ) ( 5.97 e + 24 )}{6.37 e + 6} = 11.19 km/s

Reading this result: Leaving Earth takes 11.2 km/s no matter the spacecraft mass, while a circular orbit needs only 7.9 km/s — smaller by exactly √2 (about 1.41×).

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More with Escape Velocity

Escape Velocity for a planet orbit Escape Velocity for a binary star Escape Velocity for a black hole Escape Velocity for a galaxy rotation Escape Velocity for a comet path Escape Velocity for a solar eclipse Escape Velocity for a supernova Escape Velocity for a star's life

Frequently asked questions

Is this good for students?: Yes — this version of "Escape Velocity for a star cluster" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.