Phobos surface gravity, escape velocity and orbit calculator
Everything about orbiting a body follows from one number, its gravitational parameter GM, together with its radius. Surface gravity here is under a thousandth of Earth. A brisk jump would put you in orbit.
Escape velocity
11.33m/s
- Surface gravity
- 0.0058 m/s2
- Circular orbit speed at that altitude
- 1.84
- Orbital period
- 200:43:50
- Orbital period in minutes
- 12 043.83
- Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.
- 13
- Mean density
- 1870 kg/m3
- Orbital kinetic energy of the payload
- 1684.2
- Energy to lift the payload out of the well
- 64 169.7
Show the working
- Orbit altitude above the surface = 200
- Payload mass = 1000
- gm = 7.11e5 = 711 000
- radius = 1.108e4 = 11 080
- Surface gravity = 711 000 / 11 080^2 = 0.005 791 49
- Escape velocity = sqrt(2 * 711 000 / 11 080) = 11.3287
- orbit_radius = 11 080 + 200 * 1000 = 211 080
- Circular orbit speed at that altitude = sqrt(711 000 / 211 080) = 1.835 32
- Orbital period = 1.835 32 > 0 ? 2 * pi * 211 080 / 1.835 32 : 0 = 722 630
- Orbital period in minutes = 722 630 / 60 = 12 043.8
- Orbital kinetic energy of the payload = 1000 * 711 000 / (2 * 211 080) = 1684.2
- Energy to lift the payload out of the well = 1000 * 711 000 / 11 080 = 64 169.7
- geo_radius = (711 000 * (7.65 * 3600 / (2*pi))^2)^(1/3) = 23 904.5
- Stationary orbit altitude = (23 904.5 - 11 080) / 1000 = 12.8245
- Mean density = 711 000 / 6.6743e-11 / (4/3 * pi * 11 080^3) = 1869.63
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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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.
Surface gravity here is under a thousandth of Earth. A brisk jump would put you in orbit.
Where the numbers come from
- GM and mean radius from planetary ephemeris and spacecraft tracking solutions.
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