How is orbital velocity related to escape velocity?

Escape velocity is sqrt(2) times orbital velocity at the same radius: v_escape = sqrt(2) * v_orbital.

Does a satellite in orbit need fuel to stay in orbit?

In an ideal vacuum, no. In low Earth orbit, atmospheric drag gradually slows the satellite, requiring periodic boosts.

What happens if an orbiting object speeds up?

It moves to a higher orbit. If it reaches escape velocity, it leaves the gravitational field entirely.

Free Orbital Velocity Calculator

Calculate the velocity required for a circular orbit using v = sqrt(G * M / r).

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Mass of Central Body

Orbital Radius

Orbital Velocity

7,672.49 m/s

Orbital Period5,545 s

Orbital Velocity vs Mass of Central Body

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Orbital Velocity

For a circular orbit, gravitational force provides the centripetal force.

Derivation

Setting G*M*m/r² = m*v²/r and solving:

v = sqrt(G * M / r)

The orbital period is T = 2*pi*r / v.

Example Calculation

Low Earth orbit at 400 km altitude (r = 6,371 + 400 = 6,771 km).

01v = sqrt(G * M / r)
02v = sqrt(6.6743e-11 * 5.972e24 / 6.771e6)
03v = sqrt(5.888e7)
04v ≈ 7,674 m/s
05T = 2*pi*r / v ≈ 5,541 s ≈ 92.3 minutes

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