Saturn surface gravity, escape velocity and orbit calculator
Everything about orbiting a body follows from one number, its gravitational parameter GM, together with its radius. Saturn is less dense than water, so its surface gravity is barely above Earth despite its size.
Escape velocity
36 093.78m/s
- Surface gravity
- 11.1860 m/s2
- Circular orbit speed at that altitude
- 25 478.44
- Orbital period
- 4:00:10
- Orbital period in minutes
- 240.16
- Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.
- 54 007
- Mean density
- 687 kg/m3
- Orbital kinetic energy of the payload
- 324 575 000 000
- Energy to lift the payload out of the well
- 651 380 000 000
Show the working
- Orbit altitude above the surface = 200
- Payload mass = 1000
- gm = 3.7931187e16 = 3.79312e+16
- radius = 5.8232e7 = 58 232 000
- Surface gravity = 3.79312e+16 / 58 232 000^2 = 11.186
- Escape velocity = sqrt(2 * 3.79312e+16 / 58 232 000) = 36 093.8
- orbit_radius = 58 232 000 + 200 * 1000 = 58 432 000
- Circular orbit speed at that altitude = sqrt(3.79312e+16 / 58 432 000) = 25 478.4
- Orbital period = 25 478.4 > 0 ? 2 * pi * 58 432 000 / 25 478.4 : 0 = 14 409.8
- Orbital period in minutes = 14 409.8 / 60 = 240.163
- Orbital kinetic energy of the payload = 1000 * 3.79312e+16 / (2 * 58 432 000) = 324 575 000 000
- Energy to lift the payload out of the well = 1000 * 3.79312e+16 / 58 232 000 = 651 380 000 000
- geo_radius = (3.79312e+16 * (10.656 * 3600 / (2*pi))^2)^(1/3) = 112 239 000
- Stationary orbit altitude = (112 239 000 - 58 232 000) / 1000 = 54 006.9
- Mean density = 3.79312e+16 / 6.6743e-11 / (4/3 * pi * 58 232 000^3) = 687.095
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.
Saturn is less dense than water, so its surface gravity is barely above Earth despite its size.
Where the numbers come from
- GM and mean radius from planetary ephemeris and spacecraft tracking solutions.
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