Orbit Precession Angle: Find & Condition for Cycles

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    Orbit Precession
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The discussion revolves around calculating the precession angle for a particle with a specified orbital equation, r(φ) = r0/(1 - ε cos(βφ)), where ε is a small parameter and β is a constant. Participants express confusion about how to derive the precession angle despite observing graphical evidence of precession for β values between 1 and 2. The condition for the trajectory to be totally cyclic is suggested to be that β must be an integer. Clarification is sought on the meanings of variables such as c (speed of light) and e (Euler's number), as well as the role of time in the calculations. The conversation emphasizes the need for a clear understanding of the mathematical framework to solve the problem effectively.
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the problem says:

"consider a particle with orbit

##r(\phi)=\frac{r_0}{1-\epsilon \cos (\beta \phi)}##

##\epsilon \in ]0,1[## and ##\beta=cte##

a) Find the precession angle.

b) What is the condition to the trayectory is totally cyclic??
__________________

I don't understand why i calculare the precession angle. If I draw ##r(\phi)## i view that the grraphics precesse for ##\beta \in ]1,2[##, but i need calculate the angle.

the answer of b) is ##\beta=integer##?
 
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c being the speed of light, e= 2.71828182846, t being time?
Do try and make it possible to help you: follow the template and explain what variables mean.

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