Tethys 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

393.94m/s

≈ Rounded Tethys gravity and escape velocity Show in

Surface gravity: 0.1461 m/s2
Circular orbit speed at that altitude: 237.42
Orbital period: 5:22:28
Orbital period in minutes: 322.47
Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.: 2497
Mean density: 984 kg/m3
Orbital kinetic energy of the payload: 28 184 200
Energy to lift the payload out of the well: 77 595 600

Show the working

Orbit altitude above the surface = 200
Payload mass = 1000
gm = 4.1211e10 = 41 211 000 000
radius = 5.311e5 = 531 100
Surface gravity = 41 211 000 000 / 531 100^2 = 0.146 103
Escape velocity = sqrt(2 * 41 211 000 000 / 531 100) = 393.943
orbit_radius = 531 100 + 200 * 1000 = 731 100
Circular orbit speed at that altitude = sqrt(41 211 000 000 / 731 100) = 237.42
Orbital period = 237.42 > 0 ? 2 * pi * 731 100 / 237.42 : 0 = 19 348.1
Orbital period in minutes = 19 348.1 / 60 = 322.468
Orbital kinetic energy of the payload = 1000 * 41 211 000 000 / (2 * 731 100) = 28 184 200
Energy to lift the payload out of the well = 1000 * 41 211 000 000 / 531 100 = 77 595 600
geo_radius = (41 211 000 000 * (45.307 * 3600 / (2*pi))^2)^(1/3) = 3 028 280
Stationary orbit altitude = (3 028 280 - 531 100) / 1000 = 2497.18
Mean density = 41 211 000 000 / 6.6743e-11 / (4/3 * pi * 531 100^3) = 983.988

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.