Pluto 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

1210.77m/s

≈ Rounded Pluto gravity and escape velocity Show in

Surface gravity: 0.6168 m/s2
Circular orbit speed at that altitude: 792.08
Orbital period: 3:03:33
Orbital period in minutes: 183.55
Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.: 17 681
Mean density: 1857 kg/m3
Orbital kinetic energy of the payload: 313 693 000
Energy to lift the payload out of the well: 732 980 000

Show the working

Orbit altitude above the surface = 200
Payload mass = 1000
gm = 8.71e11 = 871 000 000 000
radius = 1.1883e6 = 1 188 300
Surface gravity = 871 000 000 000 / 1 188 300^2 = 0.616 831
Escape velocity = sqrt(2 * 871 000 000 000 / 1 188 300) = 1210.77
orbit_radius = 1 188 300 + 200 * 1000 = 1 388 300
Circular orbit speed at that altitude = sqrt(871 000 000 000 / 1 388 300) = 792.077
Orbital period = 792.077 > 0 ? 2 * pi * 1 388 300 / 792.077 : 0 = 11 012.7
Orbital period in minutes = 11 012.7 / 60 = 183.546
Orbital kinetic energy of the payload = 1000 * 871 000 000 000 / (2 * 1 388 300) = 313 693 000
Energy to lift the payload out of the well = 1000 * 871 000 000 000 / 1 188 300 = 732 980 000
geo_radius = (871 000 000 000 * (153.29 * 3600 / (2*pi))^2)^(1/3) = 18 869 600
Stationary orbit altitude = (18 869 600 - 1 188 300) / 1000 = 17 681.3
Mean density = 871 000 000 000 / 6.6743e-11 / (4/3 * pi * 1 188 300^3) = 1856.72

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.