# Slicing the network

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.

# Triangulation

Brown Space Engineering has started to participate in the Satellite Networked Open Ground Station (SatNOGS) project. Numerous radio receivers around the world listen for transmissions from satellites and the observations are then automatically uploaded to their website. The recordings of these receptions tipped us off to a close approach with another satellite transmitting on a nearby frequency.

We scheduled observations of EQUiSat on multiple ground stations in the eastern United States during a pass a little after 1 AM local time on November 8th. The goal is to try to understand the orientation of the antenna (and also the entire spacecraft) by comparing signal strength when two or more stations hear the same packet. The simple 70 cm dipole antenna on the spacecraft is directional. The maximum signal strength is perpendicular to the wire. We might be able to infer how the antenna was oriented at that moment by looking at which stations missed hearing the packet or received a weak signal.

# Close approach

We noticed a signal in a recording of transmissions from EQUiSat that had a very odd Doppler shift. It turned out that there was a second satellite above the horizon at the same time and it was transmitting on a similar frequency. SiriusSat-1 uses 435.57 MHz and EQUiSat uses 435.55 MHz. If the first satellite is Doppler shifted by -10 kHz and the second is +10 kHz the signals will overlap. To understand the potential for interference I examined the orbits of the two.

Both satellites were deployed from the International Space Station (ISS) during the summer. EQUiSat in mid July then SiriusSat-1 and SiriusSat-2 in mid August. Because of the similar deployment the two satellites are in nearly identical orbits. The inclination of the two orbital planes is within a few ten thousandths of a degree.

# Solar minimum

The activity of the Sun increases and decreases in a cycle that lasts approximately 11 years. When the cycle reaches a maximum there are a larger number of sunspots and an increase in solar radiation and charged particles reaching our planet. This can cause the atmosphere of the Earth to expand slightly. A satellite in low Earth orbit experiences a small amount of atmospheric drag despite the low density of air. The exact amount depends on how active the Sun is. Each cycle varies somewhat in duration. A cycle can be as short as 9 years or as long as 14. The average is about 10.7 years. These variations complicate the process of making predictions of future activity which are important for estimating the orbital decay of a satellite.

The magnitude and shape of the peaks in activity is also variable. The maximums in the early 1800s were very small, a time period known as the Dalton minimum. The next figure is a closer look at the Sun’s activity during the space age. The maximum in the late 1950s when Sputnik launched was the largest ever observed. During the Apollo missions the maximum was lower than other recent peaks but greater than the most recent maximum.

# Tracking “flocks” of CubeSats

A satellite built by undergraduate students from Brown Space Engineering (BSE) was launched by NASA and has been operating in low earth orbit since July 2018. Objects in orbit are tracked by the Space Surveillance Network.  Measurements of the position and velocity are made using optical telescopes, radar ranging, and radio reception. This data is then used to calculate the orbit. Once or twice per day a file is published for each tracked object that can be used to predict the motion a day or two in the future.  The file is called a two-line element set (TLE) and contains numbers that describe the elliptical shape of the orbital path and where the object is at a given moment. Here is a sample TLE for the ISS: the International Space Station.

```ISS (ZARYA)
1 25544U 98067A   98324.28472222 -.00003657  11563-4  00000+0 0  9996
2 25544 051.5908 168.3788 0125362 086.4185 359.7454 16.05064833    05```

Each object is given a unique designation that includes the year and number of launch followed by a letter for each piece that is in a separate orbit. The first module of the ISS (called Zarya, the Russian word for “dawn” or “sunrise”) was the 67th launch of 1998 and is cataloged as 1998-067-A. Any piece that becomes detached, either by accident or intentionally, is given a new designation to independently track it. A tool bag that floated away from an astronaut became known as 1998-067-BL and the BSE satellite named EQUiSat released by the astronauts is designated 1998-067-PA. All of the objects discussed below are considered “loose pieces” of the ISS and I’ll refer to them using just the trailing letter designation.

On July 13th EQUiSat was one of four small satellites released from the ISS. The first TLE files were published three days later. There was some early confusion about which TLE corresponded to which satellite. EQUiSat was initially identified as NZ on July 17 but was later found to be better matched to PA on July 22. The remainder of this post is a detailed analysis of the computed orbital elements in the published TLE files.