Orbit (follow up)

[Thomas Klemm]

(12-31-2014 02:40 PM)SlideRule Wrote:  NASA (NTRS) - Introduction to orbital flight planning

That's an interesting workbook. Thanks for sharing.

Quote:B.2. POSITION IN PLANE OF ORBIT FOR NEARLY CIRCULAR ORBITS
For small eccentricities (e), the true anomaly may be found from the formula,
\[\Theta=M+2e\sin M+\frac{5}{4}e^2\sin 2M+\frac{e^3}{12}(13\sin 3M-3\sin M)\]
p. 48

While it's clearly not the focus of the book to understand all the formulas but to apply them to real world problems you still might be wondering how they were found.
A few years ago I posted the somewhat related article Sunrise and Sunset wherein I referenced a paper where you can find the derivation of that formula:

Quote:(...)
Wir setzen also im weiteren
\[\delta(t):=2\sin(t)\kappa+\frac{5}{4}\sin(2t)\kappa^2\]
p. 158

Cheers
Thomas