I'm in the process of comparing the data in the USSC's SATCAT DB with the ESA's DISCOS DB. Unfortunately, the Americans use modified Keplerian orbit descriptions that look like:
{
"PERIOD": "96.19",
"INCLINATION": "65.10",
"APOGEE": "938",
"PERIGEE": "214",
}
I'm planning on working with the classical keplerian descriptions that the ESA uses that look like:
{
"raan": 0,
"inc": 26.13,
"sma": 24124000,
"ecc": 0.72566885,
"aPer": 0
}
With those parameters being the right ascension ascending node, inclination, semi-major axis, eccentricity and argument of periapsis.
Now, I think I can do the following:
eccentricity = eccentricity = (apogee - perigee) / (apogee + perigee)
semiMajorAxis = (period^2 * gravitational parameter of central body) / (4 * pi^2)
apoapsis = apogee + radius of central body
periapsis = perigee + radius of central body
But leaves me with no idea how to get the raan
given there's seemingly nothing to do with this angle in the SATCAT's orbit model.
Am I missing something here? Can I actually derive this value from the four provided values (and maybe some known constants).
In my search I came across this paper from JPL that seems to describe some of these relationships.
However, I'm confused even further by this as the parameter I need is seemingly circularly defined:
The symbols are defined as:
And further we see: