Ganymede surface gravity, escape velocity and orbit calculator
Everything about orbiting a body follows from one number, its gravitational parameter GM, together with its radius. The largest moon in the solar system, bigger than Mercury.
Escape velocity
2739.99m/s
- Surface gravity
- 1.4251 m/s2
- Circular orbit speed at that altitude
- 1867.85
- Orbital period
- 2:38:53
- Orbital period in minutes
- 158.89
- Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.
- 43 106
- Mean density
- 1935 kg/m3
- Orbital kinetic energy of the payload
- 1 744 440 000
- Energy to lift the payload out of the well
- 3 753 780 000
Show the working
- Orbit altitude above the surface = 200
- Payload mass = 1000
- gm = 9.887834e12 = 9 887 830 000 000
- radius = 2.6341e6 = 2 634 100
- Surface gravity = 9 887 830 000 000 / 2 634 100^2 = 1.425 07
- Escape velocity = sqrt(2 * 9 887 830 000 000 / 2 634 100) = 2739.99
- orbit_radius = 2 634 100 + 200 * 1000 = 2 834 100
- Circular orbit speed at that altitude = sqrt(9 887 830 000 000 / 2 834 100) = 1867.85
- Orbital period = 1867.85 > 0 ? 2 * pi * 2 834 100 / 1867.85 : 0 = 9533.49
- Orbital period in minutes = 9533.49 / 60 = 158.892
- Orbital kinetic energy of the payload = 1000 * 9 887 830 000 000 / (2 * 2 834 100) = 1 744 440 000
- Energy to lift the payload out of the well = 1000 * 9 887 830 000 000 / 2 634 100 = 3 753 780 000
- geo_radius = (9 887 830 000 000 * (171.7 * 3600 / (2*pi))^2)^(1/3) = 45 739 900
- Stationary orbit altitude = (45 739 900 - 2 634 100) / 1000 = 43 105.8
- Mean density = 9 887 830 000 000 / 6.6743e-11 / (4/3 * pi * 2 634 100^3) = 1935.13
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.
The largest moon in the solar system, bigger than Mercury.
Where the numbers come from
- GM and mean radius from planetary ephemeris and spacecraft tracking solutions.
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