Satellite State

The classical Keplarian set of parameters that describe the state of the satellite is given by:

1. \(a\) : Semimajor Axis

2. \(e\) : eccentricity

3. \(i\) : inclination

4. \(\Omega\) : longitude of acending node

5. \(\omega\) : argument of perigee

6. \(\nu\) : 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:

\[\begin{split} e = \sqrt{1 - \frac{p}{a}}\\ e = \sqrt{1 + \frac{2 \xi L^2}{\mu^2}} \end{split}\]