In a previous post I described an idea on how to triangulate on the orientation of the Brown Space Engineering (BSE) satellite EQUiSat using simultaneous observations from multiple SatNOGS ground stations. We’re running simulation software to model how the antenna beam might be changing orientation as the spacecraft spins. The gyroscope is reporting about 7 degrees per second around one axis. This seems very fast and we’re not sure if the readings are accurate. This initial modeling assumes they are correct.

In the figures below the antenna beam is shown by a torus surrounding the satellite. The pattern is projected to the ground as rainbow colored lines. The red lines are the center of the beam. This does not show how signal strength varies on the surface. We’ll get to that later. It is merely projecting the geometry of a dipole antenna to illustrate where the center of the beam could be and how it might be rotating as the spacecraft spins.

The figure above shows the position at the moment that multiple distant ground stations received the same packet and the line of site range to three receivers. This is only one possible orientation that matches a small subset of the observations. We’ll need to examine many more to understand how it was really aimed at the moment of transmission. This first exercise is just to visualize how fast the beam might be moving if the gyro data is reasonable. This will inform us as to what to expect as we starting mining the observation data. This snapshot is of the same November 8th packet that I examined in the prior post.

The spacecraft is currently in low power mode where it only transmits every 40 seconds. The figure above shows the position exactly 40 seconds before the previous figure when the prior packet was transmitted. At this range we would have expected to hear a packet at Ladd but didn’t. The nearby Grove #98 just barely detected it but it was far weaker than the other detection. Two stations to the southwest received a strong signal. It could be that the antenna was tilted towards the south and then rotated to a better angle.

There are many factors that impact reception that were not included here. Disentangling those will be a challenge. This example merely shows that the antenna orientation can change dramatically between packets and we need to take that into account when analyzing the data.

We expect to find instances where the orientation of the antenna is aligned with two or more stations that are distant from the satellite but receive a strong signal. At the same moment our control group in New England fails to detect it despite being closer. This is illustrated above. As the antenna beam slices through the network we should see alignments that cut across the map. Just by inspecting a small number of waterfall plots visually shows some interesting correlations.

This is easier to visualize with an animation.The antenna axis is shown by a dark double arrow and the dipole radiation pattern is the wireframe torus. The red vector is the face of the cube with the antenna. When it point away from the globe the satellite chassis blocks the signal.

The first shows a real-time view of the changing orientation of the antenna. It should be noted that the transmitter does not send continuously so we can’t see this in the observations. The movie is at satnogs-pass-rt.wmv.

The second animation shows orientation at the 20 second time steps which is the transmitting interval in normal power mode. The orientation jumps between packets. After passing over the United States it then travels over the northern Atlantic and Europe. The two minute movie is at satnogs-pass-20s.wmv.

Now that we have an idea of what we’re looking for the BSE team is now working on software to process these observations automatically.