Originally Posted by **DesertFox**
Two weeks ago, I read a text, where the author talks about "free movement (circulation) in gravitational orbit" and he (the author) 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 (the notorious formulation)
I can't grasp his idea... I searched all the google and and all the textbooks, which i have at home... but i can't find information about the author's primary formulation: **p = miv/(2πl) = const**
I can't post the original text, because it is written in bulgarian. the literal translation will be difficult for me. English is not my native language, but i hope I asked my question clearly... So I am looking for some comments, which will explain me the formulation... I will be very thankful for every explanation....
Have a nice day! |

Hi DesertFox,

Welcome to the forum. Your English is alright so don't worry about that. I am practically a layperson also but have managed to pick up some advanced maths skills here and there and have learned a lot just doing what you are doing.

I looks like

**p = miv/(2πl) = const** might be a statement about conservation of angular momentum as $\displaystyle \mathbf{r} \times \mathbf{P} = \mathbf{L}$ or perhaps more understandable as $\displaystyle r P sin(\theta) = L$ which, using circular motion as an example, is the radius of motion and P is the momentum and theta is the angle between the radius of motion and the direction of P and L is angular momentum which is generally conserved. Here is basic explanation of angular momentum

This Url Link. Others on this forum may have better sources.