the Sun surface gravity, escape velocity and orbit calculator
Everything about orbiting a body follows from one number, its gravitational parameter GM, together with its radius. The photosphere is not a surface you could stand on, so treat this as the gravity at that radius.
Escape velocity
617 674.70m/s
- Surface gravity
- 274.2001 m/s2
- Circular orbit speed at that altitude
- 436 699.20
- Orbital period
- 2:46:53
- Orbital period in minutes
- 166.88
- Stationary orbit altitude Where an orbit matches the rotation period. Meaningless for a retrograde or very slow rotator.
- 24 588 790
- Mean density
- 1410 kg/m3
- Orbital kinetic energy of the payload
- 95 353 100 000 000
- Energy to lift the payload out of the well
- 190 761 000 000 000
Show the working
- Orbit altitude above the surface = 200
- Payload mass = 1000
- gm = 1.32712440018e20 = 1.32712e+20
- radius = 6.957e8 = 695 700 000
- Surface gravity = 1.32712e+20 / 695 700 000^2 = 274.2
- Escape velocity = sqrt(2 * 1.32712e+20 / 695 700 000) = 617 675
- orbit_radius = 695 700 000 + 200 * 1000 = 695 900 000
- Circular orbit speed at that altitude = sqrt(1.32712e+20 / 695 900 000) = 436 699
- Orbital period = 436 699 > 0 ? 2 * pi * 695 900 000 / 436 699 : 0 = 10 012.5
- Orbital period in minutes = 10 012.5 / 60 = 166.876
- Orbital kinetic energy of the payload = 1000 * 1.32712e+20 / (2 * 695 900 000) = 95 353 100 000 000
- Energy to lift the payload out of the well = 1000 * 1.32712e+20 / 695 700 000 = 190 761 000 000 000
- geo_radius = (1.32712e+20 * (609.12 * 3600 / (2*pi))^2)^(1/3) = 25 284 500 000
- Stationary orbit altitude = (25 284 500 000 - 695 700 000) / 1000 = 24 588 800
- Mean density = 1.32712e+20 / 6.6743e-11 / (4/3 * pi * 695 700 000^3) = 1409.78
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.
The photosphere is not a surface you could stand on, so treat this as the gravity at that radius.
Where the numbers come from
- GM and mean radius from planetary ephemeris and spacecraft tracking solutions.
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