I am familiar with the general approach to propagate orbits using orbital parameters, and how to account for basic J2 perturbations. I am looking to perform some analysis on large walker constellations (>100 satellites) in circular LEO orbits.

Some questions to analyze:

  1. Access intervals/duration
  2. Amount of coverage (%)
  3. elevation angles

I know that when you consider the special case of circular orbits the propagation/position determination versus time simplifies greatly. Specifically since e=0 causes many terms to go to either 0 or 1 and Mean, Eccentric, and true anomaly all become equal.

I have done some research and can't find any direct answers but what I am trying to find out is

  1. For a circular orbit are there equations that produce satellite geodetic sub-satellite longitude and latitude vs time as a function of basic Kepler elements, while also account for J2 affects on Arg. Perigee and RAAN?

  2. If those equations exist and someone wants to calculate access intervals (start and stop) I am aware there are methods that take into account basic minimum elevation angle and sensor FOV, but can you use the equations for Walker Constellations and combine them with the equations in 1 to perform an efficient coverage analysis for the constellation?

My thoughts are that with this very specific case there might be a more efficient manner of analysis then propagation every single orbit individually.


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