Oberon 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

734.22m/s

≈ Rounded Oberon gravity and escape velocity Show in

Surface gravity: 0.3540 m/s2
Circular orbit speed at that altitude: 462.03
Orbital period: 3:37:54
Orbital period in minutes: 217.90
Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.: 18 398
Mean density: 1663 kg/m3
Orbital kinetic energy of the payload: 106 735 000
Energy to lift the payload out of the well: 269 543 000

Show the working

Orbit altitude above the surface = 200
Payload mass = 1000
gm = 2.0523e11 = 205 230 000 000
radius = 7.614e5 = 761 400
Surface gravity = 205 230 000 000 / 761 400^2 = 0.354 01
Escape velocity = sqrt(2 * 205 230 000 000 / 761 400) = 734.225
orbit_radius = 761 400 + 200 * 1000 = 961 400
Circular orbit speed at that altitude = sqrt(205 230 000 000 / 961 400) = 462.028
Orbital period = 462.028 > 0 ? 2 * pi * 961 400 / 462.028 : 0 = 13 074.2
Orbital period in minutes = 13 074.2 / 60 = 217.904
Orbital kinetic energy of the payload = 1000 * 205 230 000 000 / (2 * 961 400) = 106 735 000
Energy to lift the payload out of the well = 1000 * 205 230 000 000 / 761 400 = 269 543 000
geo_radius = (205 230 000 000 * (323.1 * 3600 / (2*pi))^2)^(1/3) = 19 159 600
Stationary orbit altitude = (19 159 600 - 761 400) / 1000 = 18 398.2
Mean density = 205 230 000 000 / 6.6743e-11 / (4/3 * pi * 761 400^3) = 1663.06

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.