[Physics] Orbital velocity, orbital speed, tangential velocity

kinematicsorbital-motionvectorsvelocity

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.

Best Answer

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.

Radial and tangential components

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.

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