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.

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.

Doppler shift graph of radio transmissions
Doppler shift measurements of the EQUiSat radio transmissions  made by an amateur radio operator. Each vertical line is a data packet reception and the smooth curve is the best fit of the measurements to the predicted orbit. Credit: cgbsat / SatNOGS

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.

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