Mercury 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

4249.85m/s

≈ Rounded Mercury gravity and escape velocity Show in

Surface gravity: 3.7015 m/s2
Circular orbit speed at that altitude: 2889.01
Orbital period: 1:35:41
Orbital period in minutes: 95.68
Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.: 240 456
Mean density: 5427 kg/m3
Orbital kinetic energy of the payload: 4 173 200 000
Energy to lift the payload out of the well: 9 030 620 000

Show the working

Orbit altitude above the surface = 200
Payload mass = 1000
gm = 2.2032e13 = 22 032 000 000 000
radius = 2.4397e6 = 2 439 700
Surface gravity = 22 032 000 000 000 / 2 439 700^2 = 3.701 53
Escape velocity = sqrt(2 * 22 032 000 000 000 / 2 439 700) = 4249.85
orbit_radius = 2 439 700 + 200 * 1000 = 2 639 700
Circular orbit speed at that altitude = sqrt(22 032 000 000 000 / 2 639 700) = 2889.01
Orbital period = 2889.01 > 0 ? 2 * pi * 2 639 700 / 2889.01 : 0 = 5740.96
Orbital period in minutes = 5740.96 / 60 = 95.6827
Orbital kinetic energy of the payload = 1000 * 22 032 000 000 000 / (2 * 2 639 700) = 4 173 200 000
Energy to lift the payload out of the well = 1000 * 22 032 000 000 000 / 2 439 700 = 9 030 620 000
geo_radius = (22 032 000 000 000 * (1407.6 * 3600 / (2*pi))^2)^(1/3) = 242 895 000
Stationary orbit altitude = (242 895 000 - 2 439 700) / 1000 = 240 456
Mean density = 22 032 000 000 000 / 6.6743e-11 / (4/3 * pi * 2 439 700^3) = 5426.88

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.