Titan 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

2640.86m/s

≈ Rounded Titan gravity and escape velocity Show in

Surface gravity: 1.3544 m/s2
Circular orbit speed at that altitude: 1798.81
Orbital period: 2:41:32
Orbital period in minutes: 161.53
Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.: 73 001
Mean density: 1882 kg/m3
Orbital kinetic energy of the payload: 1 617 860 000
Energy to lift the payload out of the well: 3 487 060 000

Show the working

Orbit altitude above the surface = 200
Payload mass = 1000
gm = 8.978138e12 = 8 978 140 000 000
radius = 2.5747e6 = 2 574 700
Surface gravity = 8 978 140 000 000 / 2 574 700^2 = 1.354 36
Escape velocity = sqrt(2 * 8 978 140 000 000 / 2 574 700) = 2640.86
orbit_radius = 2 574 700 + 200 * 1000 = 2 774 700
Circular orbit speed at that altitude = sqrt(8 978 140 000 000 / 2 774 700) = 1798.81
Orbital period = 1798.81 > 0 ? 2 * pi * 2 774 700 / 1798.81 : 0 = 9691.94
Orbital period in minutes = 9691.94 / 60 = 161.532
Orbital kinetic energy of the payload = 1000 * 8 978 140 000 000 / (2 * 2 774 700) = 1 617 860 000
Energy to lift the payload out of the well = 1000 * 8 978 140 000 000 / 2 574 700 = 3 487 060 000
geo_radius = (8 978 140 000 000 * (382.7 * 3600 / (2*pi))^2)^(1/3) = 75 575 800
Stationary orbit altitude = (75 575 800 - 2 574 700) / 1000 = 73 001.1
Mean density = 8 978 140 000 000 / 6.6743e-11 / (4/3 * pi * 2 574 700^3) = 1881.53

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.