finding the eccentric anamoly


by smmSTV
Tags: anamoly, eccentric
smmSTV
smmSTV is offline
#1
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 Phys.org
A star's early chemistry shapes life-friendly atmospheres
Unique pair of supermassive black holes in an ordinary galaxy discovered
Red stars and big bulges: How black holes shape galaxies
Philosophaie
Philosophaie is offline
#2
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