Black body characteristics of a LEO (draft)

Abstract

Long-term observations of the erratic behaviour of an old amateur radio satellite reveal the physical influences at work in the absence of a command and control system.

RS-15

RS-15 (1994-085A; 23439) was the last of the Soviet Union's amateur radio satellites, designed and built by a group of amateurs from Kaluga and launched on 1994-12-26 from Baikonur Cosmodrome into a 1894x1176km orbit with an inclination of 83 degrees. Its onboard systems (primarily a 145MHz up, 29MHz down transponder, with two CW engineering beacons) failed some time ago, but a signal can still sometimes be heard from its 29.3525MHz beacon. The beacon originally sent the identifier RS15 and housekeeping information such as solar panel and battery voltages, power consumption, and temperature in morse. Now it sends only pulses, generally from 2s to 12s on, 2s to 12s off, while the spacecraft is in sunlight. The pulses are usually fairly consistent in length and spacing until they cease when the spacecraft is eclipsed, indicating that the battery and control system have failed but the solar panels are still in reasonable condition.

Estimating beacon frequency

After monitoring RS-15's beacon for a few weeks, it became clear that its frequency was decreasing. Its instability made it difficult to accurately measure, so I wrote some software which modelled the frequency (fig 1) in a way which could easily be compared with a spectrogram plot of the real beacon (fig 2). The vertical lines on the spectrograph are RF interference from the computer.

Graphic model of RS-15's beacon.

Fig 1: Graphic model of RS-15's beacon

Spectrogram of RS-15's beacon.

Fig 2: Spectrogram of RS-15's beacon

The model and the spectrogram were then compared at the beginning and end of each trace (where the frequency can most accurately be estimated), and the mean of the difference (to the nearest 25Hz) applied to the receiver frequency. Fig 3 shows the beacon frequency measured in this way from 2007 May to July (May 1 is day 121, June 1 is day 152, July 1 is day 182). Although its frequency varied somewhat from orbit to orbit there was a clear downward trend, but what particularly caught my attention was the apparent small peak around day 170, so I decided to gather more data and investigate further.

RS-15's beacon frequency.

Fig 3: RS-15's beacon frequency

Beacon frequency and solar elevation

Further observation showed that around day 200 the beacon frequency started increasing again, and the next investigation used the satellite's solar elevation as an approximation to the amount of sunlight RS-15 had received in the period under study. Fig 4 shows the beacon frequency and solar elevation to the end of August. As RS-15 is not spin-stabilised, the absolute value of the solar elevation can be used here to make more compact plots.

RS-15's beacon frequency and solar elevation against time.

Fig 4: RS-15's beacon frequency and solar elevation against time

This suggested that the beacon frequency was indeed varying with the amount of energy RS-15 was receiving from the sun. Fig 5 shows clearly how the beacon frequency not only falls but becomes less stable during eclipse seasons.

RS-15's beacon frequency against solar elevation.

Fig 5: RS-15's beacon frequency against solar elevation

Beacon frequency and solar energy

Like many LEOs in near-polar orbits, RS-15 alternates between periods of continuous sunlight and longer periods in which part of every orbit is eclipsed. While solar elevation gives an approximate indication of satellite illumination, a more accurate estimate of the solar energy reaching the satellite could be more revealing.

I used a "brute force" method to do this, dividing a period of time equal to the satellite's orbital period before the observed TCA into slices, determining whether or not the spacecraft was in sunlight at each slice, then using the mean of these values as the proportion of the preceding orbit which was lit.

RS-15 beacon frequency against illumination coefficient.

Fig 6: RS-15 beacon frequency against illumination coefficient

The illumination coefficient followed remarkably closely the observed beacon frequency. Modelling the satellite as a black body, assuming the solar irradiance (sometimes referred to as the solar constant) at the satellite to be 1368W/m^2 and (based on its description as a 1m diameter sphere) the satellite's cross-section to be pi/4m^2, suggested a clear relationship between the beacon frequency and the energy input from the sun during the preceding orbit. (Fig 7).

RS-15 beacon frequency against energy input.

Fig 7: RS-15 beacon frequency against energy input

Looking back at fig 6, the relatively deep trough in the frequency plot around day 200 after 80 days of eclipses, compared with the shallower trough around day 140 suggests that the frequency is being affected by energy input over a very long period.

Beacon reliability

As more observations were made it became noticeable that while the beacon was active almost continuously throughout the spacecraft's summers, it was active only erratically during eclipse seasons. Further analysis of data from day 116 to day 318 showed that when the solar elevation was less than 50 degrees (that is, during eclipse seasons) the beacon was detected on 39 percent of passes, compared with 95 percent during the spacecraft summers when the solar elevation was greater than 50 degrees. (To prevent false negatives, apparent non-appearances where the satellite reached a maximum altitude of less than 20 degrees were excluded.)

RS-15 beacon activity against solar elevation.

Fig 8: RS-15 beacon activity against solar elevation

Summary

Although RS-15 has, to most intents and purposes, failed, it has proved possible to use it for some interesting investigations, and it has prompted the development of software which could be useful for the study of other satellites. Unfortunately no details of the beacon circuit or command system have been published, so any musings on the exact nature of the failure which has enabled the transmitter frequency to vary in the way described would be pure conjecture. Clearly the solar panels are at present in a reasonable condition, but how much longer the beacon will continue to transmit is anyone's guess.

References

Satellite orbital data

Document history