Satellite State#
The classical Keplarian set of parameters that describe the state of the satellite is given by:
\(a\) : Semimajor Axis
\(e\) : eccentricity
\(i\) : inclination
\(\Omega\) : longitude of acending node
\(\omega\) : argument of perigee
\(\nu\) : True anomaly
Elliptical and Circular Orbits#
For elliptical and circular orbits we don’t have to worry about some of the parameters going out of bound.
\(a\) can be determined from the following relations can be established:
\[\begin{split}
a = \frac{r_a + r_p}{2}\\
r_p = a(1-e)\\
r_a = a(1+e)\\
p = \frac{b^2}{a} = a(1-e^2)
\end{split}\]
\(e\) from the following:
\[\begin{split}
e = \sqrt{1 - \frac{p}{a}}\\
e = \sqrt{1 + \frac{2 \xi L^2}{\mu^2}}
\end{split}\]