Jupiter surface gravity, escape velocity and orbit calculator
Everything about orbiting a body follows from one number, its gravitational parameter GM, together with its radius. Jupiter has no surface. This is the gravity at the one-bar cloud level, which is the conventional radius.
Escape velocity
60 201.52m/s
- Surface gravity
- 25.9203 m/s2
- Circular orbit speed at that altitude
- 42 508.14
- Orbital period
- 2:52:43
- Orbital period in minutes
- 172.72
- Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.
- 90 098
- Mean density
- 1326 kg/m3
- Orbital kinetic energy of the payload
- 903 471 000 000
- Energy to lift the payload out of the well
- 1 812 110 000 000
Show the working
- Orbit altitude above the surface = 200
- Payload mass = 1000
- gm = 1.26686534e17 = 1.26687e+17
- radius = 6.9911e7 = 69 911 000
- Surface gravity = 1.26687e+17 / 69 911 000^2 = 25.9203
- Escape velocity = sqrt(2 * 1.26687e+17 / 69 911 000) = 60 201.5
- orbit_radius = 69 911 000 + 200 * 1000 = 70 111 000
- Circular orbit speed at that altitude = sqrt(1.26687e+17 / 70 111 000) = 42 508.1
- Orbital period = 42 508.1 > 0 ? 2 * pi * 70 111 000 / 42 508.1 : 0 = 10 363.2
- Orbital period in minutes = 10 363.2 / 60 = 172.72
- Orbital kinetic energy of the payload = 1000 * 1.26687e+17 / (2 * 70 111 000) = 903 471 000 000
- Energy to lift the payload out of the well = 1000 * 1.26687e+17 / 69 911 000 = 1 812 110 000 000
- geo_radius = (1.26687e+17 * (9.925 * 3600 / (2*pi))^2)^(1/3) = 160 009 000
- Stationary orbit altitude = (160 009 000 - 69 911 000) / 1000 = 90 098.4
- Mean density = 1.26687e+17 / 6.6743e-11 / (4/3 * pi * 69 911 000^3) = 1326.17
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.
Jupiter has no surface. This is the gravity at the one-bar cloud level, which is the conventional radius.
Where the numbers come from
- GM and mean radius from planetary ephemeris and spacecraft tracking solutions.
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