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Finding the eccentric anamoly

by smmSTV
Tags: anamoly, eccentric
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Sep25-13, 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
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Sep25-13, 06:14 PM
P: 368
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 - Semi-Major Axis of Mars

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