I'm still trying to figure it out (if anyone spots something, please do tell), but it seems that if I do:
sqrt((-14.8928060532)^2 + (1.52614057064)^2 + (-0.37974858284)^2) = 14.9756130481
I'll always get a value that always falls within the min/max distance from orbit center (14.95 - 14.99).
Since that's specified in orbit center radii, I'll need to multiply it by 69173 * 1000 to get the SI unit:
14.9756130481 * 69173 * 1000 = 1.0359080813762213 * 10^9 meters
Since pyEphem deals in distances with AU:
print (1.0359080813762213 * 10**9) / ephem.meters_per_au # 0.00692461785302
At the same time, the Earth-Jupiter distance was 5.79160547256
AU.
Now, to get the distance, I should either add or subtract depending on the sign of the z
coordinate:
5.79160547256 - 0.00692461785302 = 5.78468085470698 AU
Running the same code for today (now) returns 6.03799937821
which seems to very close to the value of 6.031
that WolframAlpha is returning at the present time, it doesn't match 100% but perhaps that could be accounted for by some different underlying ephemeris library or data source. Not sure...