the Moon 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
2376.18m/s
- Surface gravity
- 1.6249 m/s2
- Circular orbit speed at that altitude
- 1591.12
- Orbital period
- 2:07:31
- Orbital period in minutes
- 127.51
- Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.
- 86 727
- Mean density
- 3345 kg/m3
- Orbital kinetic energy of the payload
- 1 265 840 000
- Energy to lift the payload out of the well
- 2 823 110 000
Show the working
- Orbit altitude above the surface = 200
- Payload mass = 1000
- gm = 4.9048695e12 = 4 904 870 000 000
- radius = 1.7374e6 = 1 737 400
- Surface gravity = 4 904 870 000 000 / 1 737 400^2 = 1.6249
- Escape velocity = sqrt(2 * 4 904 870 000 000 / 1 737 400) = 2376.18
- orbit_radius = 1 737 400 + 200 * 1000 = 1 937 400
- Circular orbit speed at that altitude = sqrt(4 904 870 000 000 / 1 937 400) = 1591.12
- Orbital period = 1591.12 > 0 ? 2 * pi * 1 937 400 / 1591.12 : 0 = 7650.59
- Orbital period in minutes = 7650.59 / 60 = 127.51
- Orbital kinetic energy of the payload = 1000 * 4 904 870 000 000 / (2 * 1 937 400) = 1 265 840 000
- Energy to lift the payload out of the well = 1000 * 4 904 870 000 000 / 1 737 400 = 2 823 110 000
- geo_radius = (4 904 870 000 000 * (655.72 * 3600 / (2*pi))^2)^(1/3) = 88 464 700
- Stationary orbit altitude = (88 464 700 - 1 737 400) / 1000 = 86 727.3
- Mean density = 4 904 870 000 000 / 6.6743e-11 / (4/3 * pi * 1 737 400^3) = 3345.29
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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