finding the eccentric anamoly

by smmSTV
Tags: anamoly, eccentric
smmSTV is offline
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
Phys.Org News Partner Astronomy news on
Unique pair of supermassive black holes in an ordinary galaxy discovered
Red stars and big bulges: How black holes shape galaxies
Image: X-raying the cosmos
Philosophaie is offline
Sep25-13, 06:14 PM
P: 365
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

Register to reply

Related Discussions
HELP - Anamoly in Stress concentration Engineering Systems & Design 0
MATLAB: sparse matrices in matlab anamoly? Math & Science Software 0
eccentric circular cam Mechanical Engineering 2
Two Car Eccentric Impact Engineering, Comp Sci, & Technology Homework 31
Why eccentric orbits? General Astronomy 2