Callisto surface gravity, escape velocity and orbit calculator
Everything about orbiting a body follows from one number, its gravitational parameter GM, together with its radius.
Escape velocity
2440.73m/s
- Surface gravity
- 1.2358 m/s2
- Circular orbit speed at that altitude
- 1658.42
- Orbital period
- 2:44:50
- Orbital period in minutes
- 164.83
- Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.
- 69 896
- Mean density
- 1834 kg/m3
- Orbital kinetic energy of the payload
- 1 375 180 000
- Energy to lift the payload out of the well
- 2 978 590 000
Show the working
- Orbit altitude above the surface = 200
- Payload mass = 1000
- gm = 7.179289e12 = 7 179 290 000 000
- radius = 2.4103e6 = 2 410 300
- Surface gravity = 7 179 290 000 000 / 2 410 300^2 = 1.235 77
- Escape velocity = sqrt(2 * 7 179 290 000 000 / 2 410 300) = 2440.73
- orbit_radius = 2 410 300 + 200 * 1000 = 2 610 300
- Circular orbit speed at that altitude = sqrt(7 179 290 000 000 / 2 610 300) = 1658.42
- Orbital period = 1658.42 > 0 ? 2 * pi * 2 610 300 / 1658.42 : 0 = 9889.51
- Orbital period in minutes = 9889.51 / 60 = 164.825
- Orbital kinetic energy of the payload = 1000 * 7 179 290 000 000 / (2 * 2 610 300) = 1 375 180 000
- Energy to lift the payload out of the well = 1000 * 7 179 290 000 000 / 2 410 300 = 2 978 590 000
- geo_radius = (7 179 290 000 000 * (400.5 * 3600 / (2*pi))^2)^(1/3) = 72 306 500
- Stationary orbit altitude = (72 306 500 - 2 410 300) / 1000 = 69 896.2
- Mean density = 7 179 290 000 000 / 6.6743e-11 / (4/3 * pi * 2 410 300^3) = 1833.89
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- g = GM / r^2
- escape velocity = sqrt(2 GM / r)
- circular orbit speed = sqrt(GM / r)
- period = 2 pi r / v
- escape velocity is always sqrt(2) times the circular orbit speed at the same radius
Escape velocity assumes no atmosphere and no further thrust. It is the speed at which kinetic energy equals the depth of the gravity well.
Mean density is derived by dividing GM by G, so it inherits the uncertainty in G — about one part in twenty thousand.
Where the numbers come from
- GM and mean radius from planetary ephemeris and spacecraft tracking solutions.
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