What are the orbital velocities of the other planets? For objects in a 'Low-Earth-Orbit' around planets other than Earth, e.g.?

Question

I was pondering this question recently, but most sites I can find only mention the speeds/velocities of the planets around the Sun when I look for 'orbital velocities' of the planets.

I tried examining the velocities of moons around other planets, or NASA satellites, but these are all over the proverbial map, and often in very eccentric orbits.

Is there a 'Low-Jupiter-Orbit' like there is for Earth (LEO)? What is its altitude and speed?

What about a Juno-synchronous or Jupiter-stationary high(er) orbit, as there is for Earth?

P.S.: Are there (simple) equations for these orbits?

Answer 1

The formula for orbital velocity is $\sqrt{GM/r}$ and for a "low" orbit you would mean orbit at, or close to the surface, ie with a radius equal to the radius of the planet. This makes calculating the velocity possible (SI units metres and seconds):

Body	GM	r	v
Sun	1.33E+20	696340000	436561
Mercury	2.20E+13	2439500	3005
Venus	3.25E+14	6052000	7327
Earth	3.99E+14	6378000	7905
Moon	4.90E+12	1737500	1680
Mars	4.28E+13	3396000	3551
Ceres	6.26E+10	473000	364
Jupiter	1.27E+17	71492000	42096
Saturn	3.79E+16	60268000	25087
Uranus	5.79E+15	25559000	15056
Neptune	6.84E+15	24764000	16615
Pluto	8.71E+11	1188000	856
Eris	1.11E+12	1163000	976

For planets with an atmosphere, a practical low orbit will have a slightly larger radius, and so lower velocity. There may be practical issues with a "low solar orbit"!

If you multiply these orbital velocities by $\sqrt2$, you will get the escape velocity from the surface.

There would be a "Jovistationary" orbit, but note that different parts of Jupiter rotate at different speeds. On the other hand, Venus rotates so slowly that a "veneralstationary" orbit would be so far from the planet that you would no longer be able to orbit.

Answer 2

"Low-Earth-Orbit" is kind of arbitrarily defined, and I don't believe there's a widely accepted general definition of a low orbit that can be applied to other planets.

If you know what the radius of your orbit is, your satellite is of negligible mass compared to the body it orbits, and the orbit is roughly circular, you can approximate the orbital velocity with

\begin{equation} \ v = \sqrt\frac{GM}{r} \end{equation}

If we assume the altitude of a Low-Jupiter-Orbit is about the same as the minimum altitude of the Juno spacecraft's orbit, we'd get a velocity of around 41 km/s for a circular orbit.

The simple equation for a stationary orbit's radius would be \begin{equation} \ r = \sqrt[3]\frac{GMT^2}{4\pi^2} \end{equation}

(r being the orbit's radius, G being the gravitational constant, M being the mass of the body you're orbiting, and T being that body's rotational period for both equations.)

Note that because Jupiter isn't a solid body, different parts of its surface rotate at different speeds, so I'm not sure you could really call a Jupiter orbit "stationary".