Pallas 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

334.24m/s

≈ Rounded Pallas gravity and escape velocity Show in

Surface gravity: 0.2182 m/s2
Circular orbit speed at that altitude: 177.09
Orbital period: 4:29:39
Orbital period in minutes: 269.65
Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.: 403
Mean density: 3049 kg/m3
Orbital kinetic energy of the payload: 15 679 800
Energy to lift the payload out of the well: 55 859 400

Show the working

Orbit altitude above the surface = 200
Payload mass = 1000
gm = 1.43e10 = 14 300 000 000
radius = 2.56e5 = 256 000
Surface gravity = 14 300 000 000 / 256 000^2 = 0.218 201
Escape velocity = sqrt(2 * 14 300 000 000 / 256 000) = 334.244
orbit_radius = 256 000 + 200 * 1000 = 456 000
Circular orbit speed at that altitude = sqrt(14 300 000 000 / 456 000) = 177.087
Orbital period = 177.087 > 0 ? 2 * pi * 456 000 / 177.087 : 0 = 16 179.3
Orbital period in minutes = 16 179.3 / 60 = 269.655
Orbital kinetic energy of the payload = 1000 * 14 300 000 000 / (2 * 456 000) = 15 679 800
Energy to lift the payload out of the well = 1000 * 14 300 000 000 / 256 000 = 55 859 400
geo_radius = (14 300 000 000 * (7.813 * 3600 / (2*pi))^2)^(1/3) = 659 284
Stationary orbit altitude = (659 284 - 256 000) / 1000 = 403.284
Mean density = 14 300 000 000 / 6.6743e-11 / (4/3 * pi * 256 000^3) = 3048.75

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.