# Orbital velocity, orbital speed, tangential velocity

My mind is going around in circles over this. I know that orbital velocity is what a satellite requires to stay in orbit and I know what the equation is but I thought velocity was a vector not a number so shouldn't it be speed and not velocity.

Then I found some sites that talk about tangential velocity as the orbital velocity. Then I found some sites that use m/s for the velocity and others use radians/s for the velocity.

Could anyone give clarification about orbital velocity, speed and tangential velocity as well as a simple example.

Okay, regarding your first paragraph, I can't stop myself to say it again: this is only because English wants to be special. Most languages don't have a different word for "speed" and "velocity". This has been discussed before, but when you talk about force, or total force, or whatever, you can either mean $\vec{F}$ or $|\vec{F}|$, and nothing happens, so this is actually not relevant. I'll only use velocity here, please don't mind.

So, for any curvilinear movement, velocity is always tangent to the trajectory. You can give only $v$ in m/s, as you do know the direction; it is the curve's one.

In sum, the conversion orbital speed ↔ orbital velocity is immediate: just add/remove the unit vector tangent to the path.

As for tangential velocity, this is a more subtle issue. As I said, velocity is always tangential to the orbit, so it looks redundant to say "tangential velocity".

However, what it means is usually another different thing. Draw the planet and the center of forces (CoF). Of course the planet is moving around.

If you draw a radius from the CoF to the planet, you will have a "natural" axis for the planet. A perpendicular one completes a suitable natural reference frame.

This reference freme (local reference frame) varies with time, because it follows the movement of the planet.

The problem here is that notation is confusing. The "radial" component is fine (it's also called "normal component"), but how do we call the other one? It is usually called "tangential component" in English, but I don't like that word because it denotes it is tangent to the orbit, while it is not (not always).

I use to call it "transversal component". I find it less confusing.

This "transversal component" is only one of the components. There can be radial component too. Speed is the modulus of the vector, which you can find squaring both components and adding them up:

$$v=\sqrt{v_t^2+v_n^2}$$

Circular orbits are the only ones without radial velocity, so their velocity is both tangent to the orbit (as always) and purely transversal. However, any other orbit will have a radial component.

The key is being aware of the distinction between

• Tangential, in the sense that $\vec{v}$ is always tangent to the orbit; and this always happens, by definition.

and

• Tangential, in the sense of transversal, perpendicular to the radial component.

Edit:

Oh I forgot about rad/s. Obviously a so called "velocity" given in rad/s is obviously $\omega$. It's because of lazyness, but the correct name is angular velocity (or speed). Always check the units, that's what will tell you.

Yes for a circular orbit the tangential velocity is the orbital velocity. The direction is along the direction of motion and is tangential to the circle describing the orbit. Tangential at the location of the orbiting body. This velocity is usually measured in meters/sec or km/sec. One can also use the angular velocity which assumes the body travels 360deg or 2*pi radians in the time it takes the body to make a complete orbit. The space station, for example, orbits the earth in about 90 minutes. So its angular velocity is 360 deg/5400 sec = 0.07 deg/sec. You can determine the velocity in meters/sec by just determining the distance body travels in one orbit. The orbit is about 400 km above the surface of the earth. So distance from the center of the earth is Re (earth radius) = 400 km. 6371 km + 400 km = 6771 km. A circle with radius R has a circumference of 2*pi*R. So 2*3.14159*6771 = 42543 km. Body travels this far in 90 minutes (5400 secs.) so speed = 7.88 km/sec. I'm sure there are much better descriptions at the sites listed in the comments. Maybe this is enough to get you going though.