Mars 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

5027.05m/s

≈ Rounded Mars gravity and escape velocity Show in

Surface gravity: 3.7279 m/s2
Circular orbit speed at that altitude: 3454.21
Orbital period: 1:48:49
Orbital period in minutes: 108.82
Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.: 17 038
Mean density: 3934 kg/m3
Orbital kinetic energy of the payload: 5 965 780 000
Energy to lift the payload out of the well: 12 635 600 000

Show the working

Orbit altitude above the surface = 200
Payload mass = 1000
gm = 4.282837e13 = 42 828 400 000 000
radius = 3.3895e6 = 3 389 500
Surface gravity = 42 828 400 000 000 / 3 389 500^2 = 3.727 87
Escape velocity = sqrt(2 * 42 828 400 000 000 / 3 389 500) = 5027.05
orbit_radius = 3 389 500 + 200 * 1000 = 3 589 500
Circular orbit speed at that altitude = sqrt(42 828 400 000 000 / 3 589 500) = 3454.21
Orbital period = 3454.21 > 0 ? 2 * pi * 3 589 500 / 3454.21 : 0 = 6529.28
Orbital period in minutes = 6529.28 / 60 = 108.821
Orbital kinetic energy of the payload = 1000 * 42 828 400 000 000 / (2 * 3 589 500) = 5 965 780 000
Energy to lift the payload out of the well = 1000 * 42 828 400 000 000 / 3 389 500 = 12 635 600 000
geo_radius = (42 828 400 000 000 * (24.6229 * 3600 / (2*pi))^2)^(1/3) = 20 427 600
Stationary orbit altitude = (20 427 600 - 3 389 500) / 1000 = 17 038.1
Mean density = 42 828 400 000 000 / 6.6743e-11 / (4/3 * pi * 3 389 500^3) = 3933.96

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.