Hi. Thank you very much. I'm so happy :) Now I see what I did wrong. The part about equating the same powers of $$e$$ confused me a bit. But I'm still trying to figure out how to get from $$\begin{align}a_3 &= -\tfrac{1}{2}a_1^2 \sin M + a_2 \cos M = \cdots = -\tfrac{1}{8} \sin M + \tfrac{3}{8}...
I'm reading, or more like deciphering a book about rocket science (Rocket propulsion and spaceflight dynamics from Cornelisse, Schoyer and Wakker). Most of my math skills are self taught from books and I usually figure things out but this one keeps haunting me.
It's some kind of series...