Eris surface gravity, escape velocity and orbit calculator
Everything about orbiting a body follows from one number, its gravitational parameter GM, together with its radius.
Escape velocity
1380.37m/s
- Surface gravity
- 0.8192 m/s2
- Circular orbit speed at that altitude
- 901.62
- Orbital period
- 2:38:18
- Orbital period in minutes
- 158.31
- Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.
- 36 155
- Mean density
- 2519 kg/m3
- Orbital kinetic energy of the payload
- 406 456 000
- Energy to lift the payload out of the well
- 952 709 000
Show the working
- Orbit altitude above the surface = 200
- Payload mass = 1000
- gm = 1.108e12 = 1 108 000 000 000
- radius = 1.163e6 = 1 163 000
- Surface gravity = 1 108 000 000 000 / 1 163 000^2 = 0.819 182
- Escape velocity = sqrt(2 * 1 108 000 000 000 / 1 163 000) = 1380.37
- orbit_radius = 1 163 000 + 200 * 1000 = 1 363 000
- Circular orbit speed at that altitude = sqrt(1 108 000 000 000 / 1 363 000) = 901.617
- Orbital period = 901.617 > 0 ? 2 * pi * 1 363 000 / 901.617 : 0 = 9498.47
- Orbital period in minutes = 9498.47 / 60 = 158.308
- Orbital kinetic energy of the payload = 1000 * 1 108 000 000 000 / (2 * 1 363 000) = 406 456 000
- Energy to lift the payload out of the well = 1000 * 1 108 000 000 000 / 1 163 000 = 952 709 000
- geo_radius = (1 108 000 000 000 * (378 * 3600 / (2*pi))^2)^(1/3) = 37 318 400
- Stationary orbit altitude = (37 318 400 - 1 163 000) / 1000 = 36 155.4
- Mean density = 1 108 000 000 000 / 6.6743e-11 / (4/3 * pi * 1 163 000^3) = 2519.45
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.
Where the numbers come from
- GM and mean radius from planetary ephemeris and spacecraft tracking solutions.
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