(Each plot can be obtained as a *.pdf file by clicking on it or "saving target as".)
First we can plot the positions of all three payloads with respect to the center of mass. To use a coordinate system that allows us to use some physical reasoning we use a Vertical, East, North coordinate system, as opposed to ECEF. The scales on each axis are +/- 900 meters, and we use our standard color scheme, which means that we use BLACK for the MAIN payload, RED for the FORWARD and BLUE for the AFT. We also plot the velocity vector of the payloads (direction only, since it is scaled to fit on the plot) two seconds before the paylaod separations begin, and we have the apogee IGRF magnetic field vector direction plotted as the magenta line. On this plot we have also plotted the projectons onto the North-East and Vertical-East planes to aid in visualization.
Things to note here are that the aft payload is the lowest in altitude and generally northward, and the forward P/L is highest and generally goes eastward. The nominal plan is to eject all three payloads in the plane of the IGRF magnetic field at apogee, while sending the AFT north and the FWD east. It is apparent from this plot that we came very close to this goal.
We can see the altitude difference more clearly when we look at an North_Vertical projection directly...
Also we can look at the East-North projection to get an idea of how close we got to North and East with the AFT and FWD payloads. Also we can see the angle between the AFT and FWD with respect to the CM is very close to 90 degrees, as it should be.
Now, since it was our goal to have the payloads eject into the IGRF magnetic field plane (defined at apogee), we can determine how close to that plane we go by using the GPS data. To do this as a function of time, we take the vectors from the aft to the main and the fwd to the main, then cross them to get a vector perpendicular to the plane of the three spacecraft. Then we can simply find the angle between that vector and the vector of the magnetic IGRF field. We see that we are around 30 degrees out of the plane of the magnetic field.
Next, we can do some simple coordinate transformations to change from VEN coordinates to a new system, where the magnetic field at apogee is along -V and the payload velocity vector (projected into the magnetic field plane) is along N. We use this new coordinate system for the three plots below. (Note: The CM is still at the origin.)
Here we have the positions of the payloads, but in the new coordinate system. Yellow is the magnetic field vector, green is geographic North, and magenta is the apogee CM velocity vector direction. The cyan line is the direction of true vertical. (The idea here is that Cyan (Vertical) and Green (North) give us an indication of how far we rotated from the previous VEN coordianate system.
Now since our intention was to be in the magnetic field plane, lets look at a couple of projections in this coordinate system.
The first is the North-Vertical projection. Here we can clearly see that the AFT (blue) is below the B-plane (yellow) and the FWD(red) is above. The main is quite close to being in the plane. Note also that teh CM velocity (magenta) is perpendicular to vertical (cyan), because we are using the CM velocity at apogee.
In the East-North B-Plane, we still see that the AFT and FWD are moving at about 90 degrees from the CM, which is good. Also notice that the FWD payload is East of the main, and the AFT appears to be North-East of the main, instead of just North, due to the FWD eject. BUT since the FWD eject happens AFTER the AFT eject, we should compare the AFT to the CM, and it appears to be going North at the start and then at an angle off to the East of the CM (which is primarily due to a skin section that is ejected East that is not accounted for, which really shifts the CM that we calculate westward). So it seems that we were within 10 degrees or so in azimuth, and the skin section would need to be accounted for to get more accurate angles.
Finally for now, we show the area formed by the three payloads as a function of time in this magnetic plane system. The Green lines are the North Direction which moves in this coordinate system because the velocity of the CM changes in time.
One more thing to note. The aspect magnetometer calculations show we were much closer to the magnetic field plane than is determined above. [ Magnetic aspect determination plots. ] If you wish to visualize in 3D... [ WonderCube 3D visualizaton tool. ]