Iapetus 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

572.88m/s

≈ Rounded Iapetus gravity and escape velocity Show in

Surface gravity: 0.2234 m/s2
Circular orbit speed at that altitude: 359.14
Orbital period: 4:32:29
Orbital period in minutes: 272.49
Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.: 51 611
Mean density: 1088 kg/m3
Orbital kinetic energy of the payload: 64 489 000
Energy to lift the payload out of the well: 164 098 000

Show the working

Orbit altitude above the surface = 200
Payload mass = 1000
gm = 1.2053e11 = 120 530 000 000
radius = 7.345e5 = 734 500
Surface gravity = 120 530 000 000 / 734 500^2 = 0.223 415
Escape velocity = sqrt(2 * 120 530 000 000 / 734 500) = 572.884
orbit_radius = 734 500 + 200 * 1000 = 934 500
Circular orbit speed at that altitude = sqrt(120 530 000 000 / 934 500) = 359.135
Orbital period = 359.135 > 0 ? 2 * pi * 934 500 / 359.135 : 0 = 16 349.4
Orbital period in minutes = 16 349.4 / 60 = 272.49
Orbital kinetic energy of the payload = 1000 * 120 530 000 000 / (2 * 934 500) = 64 489 000
Energy to lift the payload out of the well = 1000 * 120 530 000 000 / 734 500 = 164 098 000
geo_radius = (120 530 000 000 * (1903.9 * 3600 / (2*pi))^2)^(1/3) = 52 345 100
Stationary orbit altitude = (52 345 100 - 734 500) / 1000 = 51 610.6
Mean density = 120 530 000 000 / 6.6743e-11 / (4/3 * pi * 734 500^3) = 1087.99

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.