Venus surface gravity, escape velocity and orbit calculator
Everything about orbiting a body follows from one number, its gravitational parameter GM, together with its radius. Venus rotates backwards, which is why its rotation period is written as a negative number.
Escape velocity
10 361.44m/s
- Surface gravity
- 8.8700 m/s2
- Circular orbit speed at that altitude
- 7208.50
- Orbital period
- 1:30:49
- Orbital period in minutes
- 90.82
- Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.
- 1 530 509
- Mean density
- 5243 kg/m3
- Orbital kinetic energy of the payload
- 25 981 200 000
- Energy to lift the payload out of the well
- 53 679 700 000
Show the working
- Orbit altitude above the surface = 200
- Payload mass = 1000
- gm = 3.24859e14 = 324 859 000 000 000
- radius = 6.0518e6 = 6 051 800
- Surface gravity = 324 859 000 000 000 / 6 051 800^2 = 8.870 04
- Escape velocity = sqrt(2 * 324 859 000 000 000 / 6 051 800) = 10 361.4
- orbit_radius = 6 051 800 + 200 * 1000 = 6 251 800
- Circular orbit speed at that altitude = sqrt(324 859 000 000 000 / 6 251 800) = 7208.5
- Orbital period = 7208.5 > 0 ? 2 * pi * 6 251 800 / 7208.5 : 0 = 5449.29
- Orbital period in minutes = 5449.29 / 60 = 90.8215
- Orbital kinetic energy of the payload = 1000 * 324 859 000 000 000 / (2 * 6 251 800) = 25 981 200 000
- Energy to lift the payload out of the well = 1000 * 324 859 000 000 000 / 6 051 800 = 53 679 700 000
- geo_radius = (324 859 000 000 000 * (-5832.5 * 3600 / (2*pi))^2)^(1/3) = 1 536 560 000
- Stationary orbit altitude = (1 536 560 000 - 6 051 800) / 1000 = 1 530 510
- Mean density = 324 859 000 000 000 / 6.6743e-11 / (4/3 * pi * 6 051 800^3) = 5242.6
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.
Venus rotates backwards, which is why its rotation period is written as a negative number.
Where the numbers come from
- GM and mean radius from planetary ephemeris and spacecraft tracking solutions.