Triton 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
1452.46m/s
- Surface gravity
- 0.7794 m/s2
- Circular orbit speed at that altitude
- 958.65
- Orbital period
- 2:49:41
- Orbital period in minutes
- 169.69
- Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.
- 19 689
- Mean density
- 2060 kg/m3
- Orbital kinetic energy of the payload
- 459 508 000
- Energy to lift the payload out of the well
- 1 054 820 000
Show the working
- Orbit altitude above the surface = 200
- Payload mass = 1000
- gm = 1.4276e12 = 1 427 600 000 000
- radius = 1.3534e6 = 1 353 400
- Surface gravity = 1 427 600 000 000 / 1 353 400^2 = 0.779 389
- Escape velocity = sqrt(2 * 1 427 600 000 000 / 1 353 400) = 1452.46
- orbit_radius = 1 353 400 + 200 * 1000 = 1 553 400
- Circular orbit speed at that altitude = sqrt(1 427 600 000 000 / 1 553 400) = 958.653
- Orbital period = 958.653 > 0 ? 2 * pi * 1 553 400 / 958.653 : 0 = 10 181.3
- Orbital period in minutes = 10 181.3 / 60 = 169.688
- Orbital kinetic energy of the payload = 1000 * 1 427 600 000 000 / (2 * 1 553 400) = 459 508 000
- Energy to lift the payload out of the well = 1000 * 1 427 600 000 000 / 1 353 400 = 1 054 820 000
- geo_radius = (1 427 600 000 000 * (141.0 * 3600 / (2*pi))^2)^(1/3) = 21 042 500
- Stationary orbit altitude = (21 042 500 - 1 353 400) / 1000 = 19 689.1
- Mean density = 1 427 600 000 000 / 6.6743e-11 / (4/3 * pi * 1 353 400^3) = 2059.84
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
Scenarios & local history
Compare a saved scenario
Recent calculations
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.