Io surface gravity, escape velocity and orbit calculator

Everything about orbiting a body follows from one number, its gravitational parameter GM, together with its radius.

Orbit altitude above the surface

Payload mass

Escape velocity

2558.05m/s

≈ Rounded Io gravity and escape velocity Show in

Surface gravity: 1.7961 m/s2
Circular orbit speed at that altitude: 1717.01
Orbital period: 2:03:18
Orbital period in minutes: 123.30
Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.: 13 401
Mean density: 3527 kg/m3
Orbital kinetic energy of the payload: 1 474 060 000
Energy to lift the payload out of the well: 3 271 800 000

Show the working

Orbit altitude above the surface = 200
Payload mass = 1000
gm = 5.959916e12 = 5 959 920 000 000
radius = 1.8216e6 = 1 821 600
Surface gravity = 5 959 920 000 000 / 1 821 600^2 = 1.796 11
Escape velocity = sqrt(2 * 5 959 920 000 000 / 1 821 600) = 2558.05
orbit_radius = 1 821 600 + 200 * 1000 = 2 021 600
Circular orbit speed at that altitude = sqrt(5 959 920 000 000 / 2 021 600) = 1717.01
Orbital period = 1717.01 > 0 ? 2 * pi * 2 021 600 / 1717.01 : 0 = 7397.8
Orbital period in minutes = 7397.8 / 60 = 123.297
Orbital kinetic energy of the payload = 1000 * 5 959 920 000 000 / (2 * 2 021 600) = 1 474 060 000
Energy to lift the payload out of the well = 1000 * 5 959 920 000 000 / 1 821 600 = 3 271 800 000
geo_radius = (5 959 920 000 000 * (42.46 * 3600 / (2*pi))^2)^(1/3) = 15 222 400
Stationary orbit altitude = (15 222 400 - 1 821 600) / 1000 = 13 400.8
Mean density = 5 959 920 000 000 / 6.6743e-11 / (4/3 * pi * 1 821 600^3) = 3526.85

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

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.