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Finding the eccentric anamoly 
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#1
Sep2513, 05:56 PM

P: 2

So I'm in need of some more help for my astronomy class again.
My professor wants us to write a program that outputs a table with the distance of Mars from the sun (r) and it's true anomaly. The problem is that i need to compute the Eccentric Anomaly (E) from the Mean Anomaly (M). Kepler's equation is E = M + εsin(E), but I can't get it down in terms of E. Seeing as how I'm using c++, it is kind of a necessity. One website seemed to have an equation involving Einitial and Efinals, but it didn't do me any good. Is the idea to set the original Einitial equal to 0 at t=0 (the perihelion point) and find E final in terms of that? At the end of each iteration (I'm running a while loop) the Eintial of the next iteration would be set to the Efinal of the current loop. Anybody got any ideas? Thanks 


#2
Sep2513, 06:14 PM

P: 366

The correct equation is [tex]M = E  e*sin(E)[/tex]
Solve using the Newton Method: [tex]E_{n+1} = E_{n}  \frac{f(E)}{f'(E)}[/tex] where f(E) = E  e * sin(E)  M and f'(E) = 1  e * cos(E) Loop the above equations until: [tex]\frac{f(E)}{f'(E)} < 0.00001[/tex]Or some substantially low number not zero. Also,[tex]r = \frac{a * (1  e ^ 2)}{(1 + e * cos(TA))}[/tex] where TA  True Anomaly and a  SemiMajor Axis of Mars 


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