# B (orbital) momentum

1. Jul 4, 2017

### DesertFox

Hello everybody!
I'm layman in physics, but recently I have very strong interest. Now I am struggling to obtain some knowledge all by myself. That's so complex, probably impossible for me... that's why i decided to sign up in the forum and I hope to get help from people who are versed and educated in physics.

Here is the first question which I hope to get answer....
I know about the notorious formulation: p = m x v
p - momentum;
m - mass;
v - velocity.

Two weeks ago, I read a text about "free moving (circulation) in gravitational orbit". In the text they talk about orbital momentum. The formulation of orbital momentum was presented as: p = miv/(2πl) = const
p - orbital momentum;
m - mass;
iv - orbital velocity, also: velocity of circulation (it was represented as a kind of imaginary velocity; i - imaginary unit ???)
2πl - orbital length (circumference).

I searched in the physics textbooks, which I have at home... I searched in google... but i can't find information (and explanation) about this formulation.
"p = m x v" is derived from "p = miv/(2πl)"? Or "p = miv/(2πl)" is derived from "p = m x v"?
I will be very thankful for every comment about this mysterious formulation ( p = miv/(2πl) )....

Have a nice day everybody!

P.S. English is not my native language, but I hope I managed to ask my questions clearly enough..

2. Jul 4, 2017

### BvU

Hello Fox,

Your i has nothing to do with imaginary numbers. Check out angular momentum and perhaps it becomes clearer.

Your notation is understandable but leads to confusion: physicists use x for vector products and bold face for vectors (or an arrow above a vector quantity).
So translational momentum vector $\vec p$ is defined as $\vec p \equiv m\vec v$
And angular momentum $\vec L \equiv \vec r \times \vec v$ as you find in Wikipedia.

Talking about orbital momentum is confusing. Could you refer us to the precise wording or post a piece of context ?
looks weird dimensionally: mass/time ?

3. Jul 4, 2017

### DesertFox

The original text is written in bulgarian language, so it is difficult to translate it literally.
I will try one more time to represent the question and i will make some corrections in my questions.

Here it is in short:
He (the author) talks about a free movement (circulation) in gravitational orbit and he describes the momentum like this: p = miv/(2πl) = const
p - momentum;
iv - orbital velocity (velocity of circulation);
2πl - orbital length (perimeter of circumference).

After that, he says:
when we have 2πl= i (imaginary number), we get: p = mv

I can't grasp his idea. The final formulation (p = mv) is OK, it is notorious.But his primary formulation ( p = miv/(2πl) = const )... I can't understand it...

I hope I made my question more clear and I look for help.

4. Jul 6, 2017

### BvU

Can't say it helps me understand better. $2\pi l = i$ simply can't be meaningful to me either.

Is there a connection with the Kepler laws in the bul.. (sorry about the pun) story ?