Orbit state vectors not reproducible?

[Starstrider42]

I found something weird when trying to debug a new feature in Custom Asteroids (https://github.com/Starstrider42/Custom-Asteroids/issues/26). Can somebody explain this to me?

1. Load Custom Asteroids with the following config only:
   Spoiler

   AsteroidSets
   {
       ASTEROIDGROUP
       {
           name = xy
           title = X-Y Plane

           centralBody = Sun

           spawnRate = 1.0

           orbitSize
           {
               type = SemimajorAxis
               min  = Ratio(Jool.sma, 0.9)
               max  = Ratio(Jool.sma, 0.9)
           }

           inclination
           {
               avg = 0
           }

           periapsis
           {
               type = Longitude
               min = 90.0
               max = 90.0
           }

           ascNode
           {
               min = 90.0
               max = 90.0
           }

           orbitPhase
           {
               type = MeanLongitude
               epoch = Now
               min = 0.0
               max = 0.0
           }
       }

   }

   (For those not familiar with CA config syntax, this creates asteroids on a fixed orbit, always spawning at the same place).

2. Start a new KSP (1.1.0) game and let the spawner log the orbital elements and state vectors of new asteroids:

   Spoiler

   orbit: a = 61896183895.8152 m, e = 0, i = 0, argPe = 0, lAn = 90, mEp = -1.5707963267949 at epoch 84989.5893112183
   UT = 84989.5893112183
   x_0 (relativePositionAtUT) = [-39771554371.5685, 47427429233.872, 0]
   v_0 (orbitalVelocityAtUT) = [-3334.71870588347, -2796.41900991061, 0]
   x_0 (positionAtUT) = [-48493074463.4069, 1014.90997314453, 57861748376.7216]
   x_0 (truePositionAtUT) = [-48493074463.4069, 1014.90997314453, 57861748376.7216]
   v_0 (frameVelAtUT) = [-3334.71870588347, -2796.41900991061, 0]

   orbit: a = 61896183895.8152 m, e = 0, i = 0, argPe = 0, lAn = 90, mEp = -1.5707963267949 at epoch 219281.928708191
   UT = 219281.928708191
   x_0 (relativePositionAtUT) = [-39771554371.5685, 47427429233.872, 0]
   v_0 (orbitalVelocityAtUT) = [-3334.71870588347, -2796.41900991061, 0]
   x_0 (positionAtUT) = [-48493074463.4069, 1014.90997314453, 57861748376.7216]
   x_0 (truePositionAtUT) = [-48493074463.4069, 1014.90997314453, 57861748376.7216]
   v_0 (frameVelAtUT) = [-3334.71870588347, -2796.41900991061, 0]

    

3. Exit KSP, restart KSP, load the game from step 2, and let some more asteroids spawn:

   Spoiler

   orbit: a = 61896183895.8152 m, e = 0, i = 0, argPe = 0, lAn = 90, mEp = -1.5707963267949 at epoch 330370.966731021
   UT = 330370.966731021
   x_0 (relativePositionAtUT) = [39152943915.2026, -47939384264.2724, 0]
   v_0 (orbitalVelocityAtUT) = [3370.71554502888, 2752.92296311742, 0]
   x_0 (positionAtUT) = [49392906256.6498, 1014.90997314453, -56890084838.7397]
   x_0 (truePositionAtUT) = [49392906256.6498, 1014.90997314453, -56890084838.7397]
   v_0 (frameVelAtUT) = [3370.71554502888, 2752.92296311742, 0]

   orbit: a = 61896183895.8152 m, e = 0, i = 0, argPe = 0, lAn = 90, mEp = -1.5707963267949 at epoch 455458.894602115
   UT = 455458.894602115
   x_0 (relativePositionAtUT) = [39152943915.2026, -47939384264.2724, 0]
   v_0 (orbitalVelocityAtUT) = [3370.71554502888, 2752.92296311742, 0]
   x_0 (positionAtUT) = [49392906256.6498, 1014.90997314453, -56890084838.7397]
   x_0 (truePositionAtUT) = [49392906256.6498, 1014.90997314453, -56890084838.7397]
   v_0 (frameVelAtUT) = [3370.71554502888, 2752.92296311742, 0]

    

The tracking station shows the asteroids spawning on the same orbit in the same spot. The orbital elements are identical. Yet the state vectors have not only absolute values different by about a percent, but OPPOSITE SIGNS in the two sessions. Why is this?

In case anybody wants it, the code behind the logging:

Spoiler

double ut = Planetarium.GetUniversalTime();
Vector3d x = orbit.getRelativePositionAtUT(ut);
Vector3d v = orbit.getOrbitalVelocityAtUT(ut);

Debug.Log("Transforming orbit from frame " + plane);
Debug.Log("orbit: a = " + orbit.semiMajorAxis + " m, e = " + orbit.eccentricity + ", i = " + orbit.inclination
    + ", argPe = " + orbit.argumentOfPeriapsis + ", lAn = " + orbit.LAN + ", mEp = " + orbit.meanAnomalyAtEpoch + " at epoch " + orbit.epoch);
Debug.Log("UT = " + ut);
Debug.Log("x_0 (relativePositionAtUT) = " + x);
Debug.Log("v_0 (orbitalVelocityAtUT) = " + v);
Debug.Log("x_0 (positionAtUT) = " + orbit.getPositionAtUT(ut));
Debug.Log("x_0 (truePositionAtUT) = " + orbit.getTruePositionAtUT(ut));
Debug.Log("v_0 (frameVelAtUT) = " + orbit.GetFrameVelAtUT(ut));

 

Edited April 30, 2016 by Starstrider42

[Starstrider42]

For those who might stumble across this post later:

It turns out that, while the coordinates do change between game instances, KSP always handles them self-consistently in the sense that the statement

orbit.UpdateFromStateVectors(orbit.getRelativePositionAtUT(ut), orbit.getOrbitalVelocityAtUT(ut), orbit.referenceBody, ut);

never changes the orbit. However, the coordinates are in the frame given by Planetarium.ZupRotation, so any attempts to transform those coordinates need to include rotations by ZupRotation and/or its inverse.