Charon 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
590.91m/s
- Surface gravity
- 0.2881 m/s2
- Circular orbit speed at that altitude
- 362.31
- Orbital period
- 3:52:58
- Orbital period in minutes
- 232.96
- Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.
- 8739
- Mean density
- 1700 kg/m3
- Orbital kinetic energy of the payload
- 65 632 800
- Energy to lift the payload out of the well
- 174 587 000
Show the working
- Orbit altitude above the surface = 200
- Payload mass = 1000
- gm = 1.058e11 = 105 800 000 000
- radius = 6.06e5 = 606 000
- Surface gravity = 105 800 000 000 / 606 000^2 = 0.288 098
- Escape velocity = sqrt(2 * 105 800 000 000 / 606 000) = 590.91
- orbit_radius = 606 000 + 200 * 1000 = 806 000
- Circular orbit speed at that altitude = sqrt(105 800 000 000 / 806 000) = 362.306
- Orbital period = 362.306 > 0 ? 2 * pi * 806 000 / 362.306 : 0 = 13 977.8
- Orbital period in minutes = 13 977.8 / 60 = 232.964
- Orbital kinetic energy of the payload = 1000 * 105 800 000 000 / (2 * 806 000) = 65 632 800
- Energy to lift the payload out of the well = 1000 * 105 800 000 000 / 606 000 = 174 587 000
- geo_radius = (105 800 000 000 * (153.29 * 3600 / (2*pi))^2)^(1/3) = 9 345 150
- Stationary orbit altitude = (9 345 150 - 606 000) / 1000 = 8739.15
- Mean density = 105 800 000 000 / 6.6743e-11 / (4/3 * pi * 606 000^3) = 1700.49
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.
Where the numbers come from
- GM and mean radius from planetary ephemeris and spacecraft tracking solutions.
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