Deimos 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

5.62m/s

≈ Rounded Deimos gravity and escape velocity Show in

Surface gravity: 0.0025 m/s2
Circular orbit speed at that altitude: 0.69
Orbital period: 522:01:56
Orbital period in minutes: 31 321.93
Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.: 25
Mean density: 1471 kg/m3
Orbital kinetic energy of the payload: 237.633
Energy to lift the payload out of the well: 15 806.5

Show the working

Orbit altitude above the surface = 200
Payload mass = 1000
gm = 9.8e4 = 98 000
radius = 6.2e3 = 6200
Surface gravity = 98 000 / 6200^2 = 0.002 549 43
Escape velocity = sqrt(2 * 98 000 / 6200) = 5.622 54
orbit_radius = 6200 + 200 * 1000 = 206 200
Circular orbit speed at that altitude = sqrt(98 000 / 206 200) = 0.689 396
Orbital period = 0.689 396 > 0 ? 2 * pi * 206 200 / 0.689 396 : 0 = 1 879 320
Orbital period in minutes = 1 879 320 / 60 = 31 321.9
Orbital kinetic energy of the payload = 1000 * 98 000 / (2 * 206 200) = 237.633
Energy to lift the payload out of the well = 1000 * 98 000 / 6200 = 15 806.5
geo_radius = (98 000 * (30.3 * 3600 / (2*pi))^2)^(1/3) = 30 911.4
Stationary orbit altitude = (30 911.4 - 6200) / 1000 = 24.7114
Mean density = 98 000 / 6.6743e-11 / (4/3 * pi * 6200^3) = 1470.81

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.