Orbit Precession Angle: Find & Condition for Cycles

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    Orbit Precession
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SUMMARY

The discussion focuses on calculating the precession angle of a particle's orbit defined by the equation r(φ) = r₀ / (1 - ε cos(βφ)), where ε is a constant in the interval (0,1) and β is a constant. The precession angle is determined for values of β in the range (1,2). Additionally, the condition for the trajectory to be totally cyclic is established as β being an integer. This analysis is crucial for understanding orbital mechanics in physics.

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  • Understanding of orbital mechanics and precession angles
  • Familiarity with polar coordinates and their graphical representation
  • Knowledge of mathematical constants such as e and their applications
  • Basic proficiency in calculus for solving equations
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  • Research the derivation of precession angles in orbital mechanics
  • Study the implications of integer values of β on cyclic trajectories
  • Explore the mathematical properties of polar equations
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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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