Europa 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
2025.83m/s
- Surface gravity
- 1.3147 m/s2
- Circular orbit speed at that altitude
- 1348.67
- Orbital period
- 2:16:43
- Orbital period in minutes
- 136.72
- Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.
- 18 131
- Mean density
- 3013 kg/m3
- Orbital kinetic energy of the payload
- 909 456 000
- Energy to lift the payload out of the well
- 2 051 990 000
Show the working
- Orbit altitude above the surface = 200
- Payload mass = 1000
- gm = 3.202739e12 = 3 202 740 000 000
- radius = 1.5608e6 = 1 560 800
- Surface gravity = 3 202 740 000 000 / 1 560 800^2 = 1.3147
- Escape velocity = sqrt(2 * 3 202 740 000 000 / 1 560 800) = 2025.83
- orbit_radius = 1 560 800 + 200 * 1000 = 1 760 800
- Circular orbit speed at that altitude = sqrt(3 202 740 000 000 / 1 760 800) = 1348.67
- Orbital period = 1348.67 > 0 ? 2 * pi * 1 760 800 / 1348.67 : 0 = 8203.22
- Orbital period in minutes = 8203.22 / 60 = 136.72
- Orbital kinetic energy of the payload = 1000 * 3 202 740 000 000 / (2 * 1 760 800) = 909 456 000
- Energy to lift the payload out of the well = 1000 * 3 202 740 000 000 / 1 560 800 = 2 051 990 000
- geo_radius = (3 202 740 000 000 * (85.22 * 3600 / (2*pi))^2)^(1/3) = 19 691 700
- Stationary orbit altitude = (19 691 700 - 1 560 800) / 1000 = 18 130.9
- Mean density = 3 202 740 000 000 / 6.6743e-11 / (4/3 * pi * 1 560 800^3) = 3012.91
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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