Makemake 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

747.96m/s

≈ Rounded Makemake gravity and escape velocity Show in

Surface gravity: 0.3912 m/s2
Circular orbit speed at that altitude: 467.52
Orbital period: 3:24:57
Orbital period in minutes: 204.95
Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.: 2532
Mean density: 1957 kg/m3
Orbital kinetic energy of the payload: 109 290 000
Energy to lift the payload out of the well: 279 720 000

Show the working

Orbit altitude above the surface = 200
Payload mass = 1000
gm = 2.0e11 = 200 000 000 000
radius = 7.15e5 = 715 000
Surface gravity = 200 000 000 000 / 715 000^2 = 0.391 217
Escape velocity = sqrt(2 * 200 000 000 000 / 715 000) = 747.958
orbit_radius = 715 000 + 200 * 1000 = 915 000
Circular orbit speed at that altitude = sqrt(200 000 000 000 / 915 000) = 467.525
Orbital period = 467.525 > 0 ? 2 * pi * 915 000 / 467.525 : 0 = 12 296.9
Orbital period in minutes = 12 296.9 / 60 = 204.949
Orbital kinetic energy of the payload = 1000 * 200 000 000 000 / (2 * 915 000) = 109 290 000
Energy to lift the payload out of the well = 1000 * 200 000 000 000 / 715 000 = 279 720 000
geo_radius = (200 000 000 000 * (22.83 * 3600 / (2*pi))^2)^(1/3) = 3 246 600
Stationary orbit altitude = (3 246 600 - 715 000) / 1000 = 2531.6
Mean density = 200 000 000 000 / 6.6743e-11 / (4/3 * pi * 715 000^3) = 1957.12

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.