Mimas surface gravity, escape velocity and orbit calculator

Everything about orbiting a body follows from one number, its gravitational parameter GM, together with its radius.

Orbit altitude above the surface

Payload mass

Escape velocity

158.91m/s

≈ Rounded Mimas gravity and escape velocity Show in

Surface gravity: 0.0637 m/s2
Circular orbit speed at that altitude: 79.28
Orbital period: 8:46:00
Orbital period in minutes: 526.00
Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.: 550
Mean density: 1150 kg/m3
Orbital kinetic energy of the payload: 3 142 390
Energy to lift the payload out of the well: 12 626 600

Show the working

Orbit altitude above the surface = 200
Payload mass = 1000
gm = 2.5026e9 = 2 502 600 000
radius = 1.982e5 = 198 200
Surface gravity = 2 502 600 000 / 198 200^2 = 0.063 706 6
Escape velocity = sqrt(2 * 2 502 600 000 / 198 200) = 158.913
orbit_radius = 198 200 + 200 * 1000 = 398 200
Circular orbit speed at that altitude = sqrt(2 502 600 000 / 398 200) = 79.2766
Orbital period = 79.2766 > 0 ? 2 * pi * 398 200 / 79.2766 : 0 = 31 559.9
Orbital period in minutes = 31 559.9 / 60 = 525.999
Orbital kinetic energy of the payload = 1000 * 2 502 600 000 / (2 * 398 200) = 3 142 390
Energy to lift the payload out of the well = 1000 * 2 502 600 000 / 198 200 = 12 626 600
geo_radius = (2 502 600 000 * (22.6 * 3600 / (2*pi))^2)^(1/3) = 748 660
Stationary orbit altitude = (748 660 - 198 200) / 1000 = 550.46
Mean density = 2 502 600 000 / 6.6743e-11 / (4/3 * pi * 198 200^3) = 1149.7

Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.

Scenarios & local history

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.