Can someone out there help explain (guide, give examples etc.), or show a solution of, the following textbook problem that I can't manage to solve?
You’ve just completed an analysis of where the Space Shuttle must be when it performs a critical maneuver. You know the shuttle is in a circular prograde orbit and has a position vector of $r0= 6275.396I + 2007.268J +1089.857K$ (vektor)
In 55 minutes, you predict the orbital parameters are $a = 1.0470357$ , $e = 0.000096$, $i= 28.5°$, $M= 278.94688°.$
Is your analysis correct?
Comments: The initial orbit is circular, but the final orbit has eccentricity different from 0, but it is small, perhaps caused by disturbances. Cape Canaveral, from which the Space Shuttle is launched has a latitude of 28.5 degrees.