Rhea 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

635.02m/s

≈ Rounded Rhea gravity and escape velocity Show in

Surface gravity: 0.2641 m/s2
Circular orbit speed at that altitude: 399.71
Orbital period: 4:12:25
Orbital period in minutes: 252.42
Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.: 7642
Mean density: 1237 kg/m3
Orbital kinetic energy of the payload: 79 885 800
Energy to lift the payload out of the well: 201 624 000

Show the working

Orbit altitude above the surface = 200
Payload mass = 1000
gm = 1.5394e11 = 153 940 000 000
radius = 7.635e5 = 763 500
Surface gravity = 153 940 000 000 / 763 500^2 = 0.264 079
Escape velocity = sqrt(2 * 153 940 000 000 / 763 500) = 635.018
orbit_radius = 763 500 + 200 * 1000 = 963 500
Circular orbit speed at that altitude = sqrt(153 940 000 000 / 963 500) = 399.714
Orbital period = 399.714 > 0 ? 2 * pi * 963 500 / 399.714 : 0 = 15 145.4
Orbital period in minutes = 15 145.4 / 60 = 252.424
Orbital kinetic energy of the payload = 1000 * 153 940 000 000 / (2 * 963 500) = 79 885 800
Energy to lift the payload out of the well = 1000 * 153 940 000 000 / 763 500 = 201 624 000
geo_radius = (153 940 000 000 * (108.4 * 3600 / (2*pi))^2)^(1/3) = 8 405 270
Stationary orbit altitude = (8 405 270 - 763 500) / 1000 = 7641.77
Mean density = 153 940 000 000 / 6.6743e-11 / (4/3 * pi * 763 500^3) = 1237.17

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.