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.

Projection of antenna beam
A projection of the antenna beam to the ground stations at 06:19:20 UTC.

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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.

pass map
Map showing some of the ground stations that heard a packet on 8 Nov 2018 at 06:18:40.701 UTC and the position of the satellite at the time of transmission.

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.

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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.

radio recption
Recording of radio reception on Nov. 2, 2018 from a ground station in Europe. The receiver was tuned to the Doppler shifted signal of SiriusSat-1 but a packet from EQUiSat was also captured. Credit: Cees Bassa / SatNOGS

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.

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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.

Long term solar activity
Long term observations of sunspot number showing two dozen cycles of solar activity. The 11 year cycle is fairly consistent but there is large variability in peak height.

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.

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Project Space Track

During the early years of the space age techniques were developed to track objects in orbit and predict their future position. The mathematical technique for calculating an orbit is called a Simplified General Perturbations (SGP) model. These models were first used in the 1960s and were refined during the 1970s. This work was done by NORAD – the North American Aerospace Defense Command.

NORAD satellite tracking
“Satellite watchers in the Space Computational Center, NORAD Headquarters, track all the satellites orbiting earth.” Credit: U.S. Information Agency / National Archives, 1982

The computations were performed on large mainframe computer systems that cost several million dollars each. One of these computers was used for ballistic missile warning. A second was dedicated to space surveillance and tracking satellites. A third was available on standby as a backup system in case one of the primary computers failed. The various objects being tracked in air and space were displayed on consoles such as the one shown above.

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