Orbit Precession Angle: Find & Condition for Cycles

In summary, the problem asks to consider a particle with a specific orbit described by ##r(\phi)=\frac{r_0}{1-\epsilon \cos (\beta \phi)}##, where ##\epsilon \in ]0,1[## and ##\beta=cte##. The task is to find the precession angle and determine the condition for the trajectory to be totally cyclic. The answer for b) is ##\beta=integer##, with c representing the speed of light and e representing the mathematical constant 2.71828182846. The variables and their meanings are not clearly defined, making it difficult to provide a more detailed solution.
  • #1
alejandrito29
150
0
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##?
 
Last edited:
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  • #2
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.

Homework Statement


Homework Equations


The Attempt at a Solution

 

1. What is orbit precession angle?

Orbit precession angle is the angle between the ascending node and the point of perihelion of an orbit. It determines the orientation of an orbit in space.

2. How is the orbit precession angle calculated?

The orbit precession angle can be calculated using the formula arctan(tan(i) * sin(Ω) * sin(ω) / (cos(i) * cos(ω))), where i is the inclination, Ω is the longitude of the ascending node, and ω is the argument of perihelion.

3. What is the significance of the orbit precession angle?

The orbit precession angle is important in understanding the dynamics of a celestial object's orbit. It can affect the orientation of the orbit, the stability of the orbit, and the timing of orbital events.

4. How can I find the orbit precession angle for a specific orbit?

You can find the orbit precession angle by knowing the orbital elements of the object, such as the inclination, longitude of the ascending node, and argument of perihelion. These can be obtained from observational data or through simulations.

5. What are the conditions for cycles in orbit precession angle?

Cycles in orbit precession angle occur when the rate of change of the angle is periodic. This can happen when there is a resonance between the orbital periods of two objects, or when there is a gravitational pull from a third body affecting the orbit.

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