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    How can I calculate the ”eccentric anomaly” of an orbit? (2 posts)

  • Avatar Image Rylie4 years, 1 month said ago:

    I’m trying to figure out how to plot “positon versus time” of an orbit. I have 18400 as period T, e = 0.5, Mean Motion n = 2PI/T. I think I have Mean Anamoly M plotted as n(t-T),where t is .05 increments of T. But M + E – eSIN(E) in my book from library, how do I plot E and how do I use E to find position and velocity of satellite?

  • Avatar Image victor4 years, 1 month said ago:

    Your equation should read M = E – esin(E). The problem with this equation is that it can’t be directly solved for E in terms of M. One approach is to use an iteration formula, such as
    E1 = E0 + (M + esin(E0) – E0)/(1 – ecos(E0))
    where E0 is your first approximation for E and E1 is a better one. Repeat by substituting E1 for E0 until the required accuracy is achieved. Remember to work in radians.
    There is some information here: http://en.wikipedia.org/wiki/Ellipse#Eccentric_anomaly about how to use the eccentric anomaly to derive the satellite’s position.