Haumea surface gravity, escape velocity and orbit calculator
Everything about orbiting a body follows from one number, its gravitational parameter GM, together with its radius. Haumea spins so fast it is stretched into an ellipsoid; the radius here is the volumetric mean.
Escape velocity
827.41m/s
- Surface gravity
- 0.4389 m/s2
- Circular orbit speed at that altitude
- 521.97
- Orbital period
- 3:16:37
- Orbital period in minutes
- 196.61
- Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.
- 323
- Mean density
- 2012 kg/m3
- Orbital kinetic energy of the payload
- 136 224 000
- Energy to lift the payload out of the well
- 342 308 000
Show the working
- Orbit altitude above the surface = 200
- Payload mass = 1000
- gm = 2.67e11 = 267 000 000 000
- radius = 7.8e5 = 780 000
- Surface gravity = 267 000 000 000 / 780 000^2 = 0.438 856
- Escape velocity = sqrt(2 * 267 000 000 000 / 780 000) = 827.415
- orbit_radius = 780 000 + 200 * 1000 = 980 000
- Circular orbit speed at that altitude = sqrt(267 000 000 000 / 980 000) = 521.966
- Orbital period = 521.966 > 0 ? 2 * pi * 980 000 / 521.966 : 0 = 11 796.8
- Orbital period in minutes = 11 796.8 / 60 = 196.613
- Orbital kinetic energy of the payload = 1000 * 267 000 000 000 / (2 * 980 000) = 136 224 000
- Energy to lift the payload out of the well = 1000 * 267 000 000 000 / 780 000 = 342 308 000
- geo_radius = (267 000 000 000 * (3.915 * 3600 / (2*pi))^2)^(1/3) = 1 103 420
- Stationary orbit altitude = (1 103 420 - 780 000) / 1000 = 323.418
- Mean density = 267 000 000 000 / 6.6743e-11 / (4/3 * pi * 780 000^3) = 2012.49
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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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.
Haumea spins so fast it is stretched into an ellipsoid; the radius here is the volumetric mean.
Where the numbers come from
- GM and mean radius from planetary ephemeris and spacecraft tracking solutions.
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