Titania 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

760.90m/s

≈ Rounded Titania gravity and escape velocity Show in

Surface gravity: 0.3672 m/s2
Circular orbit speed at that altitude: 480.53
Orbital period: 3:35:24
Orbital period in minutes: 215.40
Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.: 14 054
Mean density: 1666 kg/m3
Orbital kinetic energy of the payload: 115 454 000
Energy to lift the payload out of the well: 289 485 000

Show the working

Orbit altitude above the surface = 200
Payload mass = 1000
gm = 2.2823e11 = 228 230 000 000
radius = 7.884e5 = 788 400
Surface gravity = 228 230 000 000 / 788 400^2 = 0.367 18
Escape velocity = sqrt(2 * 228 230 000 000 / 788 400) = 760.901
orbit_radius = 788 400 + 200 * 1000 = 988 400
Circular orbit speed at that altitude = sqrt(228 230 000 000 / 988 400) = 480.529
Orbital period = 480.529 > 0 ? 2 * pi * 988 400 / 480.529 : 0 = 12 923.9
Orbital period in minutes = 12 923.9 / 60 = 215.398
Orbital kinetic energy of the payload = 1000 * 228 230 000 000 / (2 * 988 400) = 115 454 000
Energy to lift the payload out of the well = 1000 * 228 230 000 000 / 788 400 = 289 485 000
geo_radius = (228 230 000 000 * (208.9 * 3600 / (2*pi))^2)^(1/3) = 14 842 200
Stationary orbit altitude = (14 842 200 - 788 400) / 1000 = 14 053.8
Mean density = 228 230 000 000 / 6.6743e-11 / (4/3 * pi * 788 400^3) = 1665.86

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.