Dione 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
510.36m/s
- Surface gravity
- 0.2320 m/s2
- Circular orbit speed at that altitude
- 309.88
- Orbital period
- 4:17:18
- Orbital period in minutes
- 257.31
- Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.
- 4135
- Mean density
- 1478 kg/m3
- Orbital kinetic energy of the payload
- 48 012 200
- Energy to lift the payload out of the well
- 130 233 000
Show the working
- Orbit altitude above the surface = 200
- Payload mass = 1000
- gm = 7.3113e10 = 73 113 000 000
- radius = 5.614e5 = 561 400
- Surface gravity = 73 113 000 000 / 561 400^2 = 0.231 98
- Escape velocity = sqrt(2 * 73 113 000 000 / 561 400) = 510.359
- orbit_radius = 561 400 + 200 * 1000 = 761 400
- Circular orbit speed at that altitude = sqrt(73 113 000 000 / 761 400) = 309.878
- Orbital period = 309.878 > 0 ? 2 * pi * 761 400 / 309.878 : 0 = 15 438.4
- Orbital period in minutes = 15 438.4 / 60 = 257.306
- Orbital kinetic energy of the payload = 1000 * 73 113 000 000 / (2 * 761 400) = 48 012 200
- Energy to lift the payload out of the well = 1000 * 73 113 000 000 / 561 400 = 130 233 000
- geo_radius = (73 113 000 000 * (65.686 * 3600 / (2*pi))^2)^(1/3) = 4 696 000
- Stationary orbit altitude = (4 696 000 - 561 400) / 1000 = 4134.6
- Mean density = 73 113 000 000 / 6.6743e-11 / (4/3 * pi * 561 400^3) = 1478.03
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.
Related calculators
- Weight on Dione
- Orbital period
- Rocket equation
- Earth gravity and escape velocity
- Enceladus gravity and escape velocity
- Eris gravity and escape velocity
- Europa gravity and escape velocity
- Ganymede gravity and escape velocity
- Haumea gravity and escape velocity
- Iapetus gravity and escape velocity
- Io gravity and escape velocity
- Jupiter gravity and escape velocity
- All astronomy & space calculators →