Vesta surface gravity, escape velocity and orbit calculator
Everything about orbiting a body follows from one number, its gravitational parameter GM, together with its radius.
Escape velocity
362.88m/s
- Surface gravity
- 0.2507 m/s2
- Circular orbit speed at that altitude
- 193.33
- Orbital period
- 4:10:35
- Orbital period in minutes
- 250.58
- Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.
- 283
- Mean density
- 3415 kg/m3
- Orbital kinetic energy of the payload
- 18 687 900
- Energy to lift the payload out of the well
- 65 841 600
Show the working
- Orbit altitude above the surface = 200
- Payload mass = 1000
- gm = 1.729e10 = 17 290 000 000
- radius = 2.626e5 = 262 600
- Surface gravity = 17 290 000 000 / 262 600^2 = 0.250 73
- Escape velocity = sqrt(2 * 17 290 000 000 / 262 600) = 362.882
- orbit_radius = 262 600 + 200 * 1000 = 462 600
- Circular orbit speed at that altitude = sqrt(17 290 000 000 / 462 600) = 193.328
- Orbital period = 193.328 > 0 ? 2 * pi * 462 600 / 193.328 : 0 = 15 034.6
- Orbital period in minutes = 15 034.6 / 60 = 250.576
- Orbital kinetic energy of the payload = 1000 * 17 290 000 000 / (2 * 462 600) = 18 687 900
- Energy to lift the payload out of the well = 1000 * 17 290 000 000 / 262 600 = 65 841 600
- geo_radius = (17 290 000 000 * (5.342 * 3600 / (2*pi))^2)^(1/3) = 545 108
- Stationary orbit altitude = (545 108 - 262 600) / 1000 = 282.508
- Mean density = 17 290 000 000 / 6.6743e-11 / (4/3 * pi * 262 600^3) = 3415.2
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.
Where the numbers come from
- GM and mean radius from planetary ephemeris and spacecraft tracking solutions.