Ceres 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

514.62m/s

≈ Rounded Ceres gravity and escape velocity Show in

Surface gravity: 0.2799 m/s2
Circular orbit speed at that altitude: 305.06
Orbital period: 3:51:01
Orbital period in minutes: 231.02
Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.: 719
Mean density: 2117 kg/m3
Orbital kinetic energy of the payload: 46 532 300
Energy to lift the payload out of the well: 132 415 000

Show the working

Orbit altitude above the surface = 200
Payload mass = 1000
gm = 6.26325e10 = 62 632 500 000
radius = 4.73e5 = 473 000
Surface gravity = 62 632 500 000 / 473 000^2 = 0.279 948
Escape velocity = sqrt(2 * 62 632 500 000 / 473 000) = 514.617
orbit_radius = 473 000 + 200 * 1000 = 673 000
Circular orbit speed at that altitude = sqrt(62 632 500 000 / 673 000) = 305.065
Orbital period = 305.065 > 0 ? 2 * pi * 673 000 / 305.065 : 0 = 13 861.3
Orbital period in minutes = 13 861.3 / 60 = 231.021
Orbital kinetic energy of the payload = 1000 * 62 632 500 000 / (2 * 673 000) = 46 532 300
Energy to lift the payload out of the well = 1000 * 62 632 500 000 / 473 000 = 132 415 000
geo_radius = (62 632 500 000 * (9.074 * 3600 / (2*pi))^2)^(1/3) = 1 191 830
Stationary orbit altitude = (1 191 830 - 473 000) / 1000 = 718.83
Mean density = 62 632 500 000 / 6.6743e-11 / (4/3 * pi * 473 000^3) = 2117.01

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.