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Buzzoni, A., Guichard, J., Alessi, E.M., Altavilla, G., Figer, A., Carbognani, A. & Tommei, G.:
"Spectrophotometric and dynamical properties of the soviet/russian constellation of Molniya satellites"
2020, Journal of Space Safety Engineering, 7, 255


Summary:
We report on the extended observing campaign of the surviving Soviet/Russian spacecraft Molniya, carried out in the years 2014–17 at Mexican and Italian telescopes. Spectrophotometry and astrodynamical analysis have been carried out for all the 43 demised payloads still in uncontrolled HEO orbit at late 2017, in order to assess dynamical and reflectance properties of such a wide family of virtually identical orbiting objects, as well as their long-term orbit evolution, according to full historic Two-Line Elements (TLE) datasets in synergy with mathematical modeling to properly size up the prevailing effect of lunisolar perturbation and atmospheric drag.


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   Browse figures in hires (click on the thumbnails)
Figure 1 -
An illustrative example of Molniya orbit ground track. Two 12-hr orbits are displayed to span a full day. The nominal orbital parameters are assumed, for illustrative scope, according to [2]. Note the extremely asymmetric location of the ascending (AN) and descending (DN) nodes, due to the high eccentricity of the orbit, and the perigee location (P), always placed in the Southern hemisphere. Along the two daily apogees (A), the satellite hovers first Russia and then Canada/US. The visibility horizon (i.e. the “foot print”) attained from the “Russian apogee”, is marked by the yellow line. Notice, in this example, that both Washington (W) and Moscow (M) are in sight from the spacecraft.
Figure 2 -
A sketch of a Molniya spacecraft with its characteristic “daisy” look, as inspired by the six big solar panels. The spacecraft sports a size of 4.4×8.2×8.2 m, with a typical mass about 1500–1700 kg. Note that the two high-gain antennas, symmetrically placed at the two sides of the bus, are not displayed in this figure.
Figure 3 -
(Left panel): a 30 sec R-band frame tracking Molniya 1-63 across the sky of Loiano, during a 2016 observing session. Note the repeated dot-dashed pattern along the satellite trace. (Right panel): the extracted track of Molniya 1-63 from an I-band LFOSC frame taken in Cananea, on 2016 March 7. The 7 sec exposure clearly shows a repeating pattern over timescales about 4 s. The very short (but finite) time for the CCD shutter to start/stop the exposure makes the exact gcut hof the track (both in pixel/time and magnitude) somewhat uncertain, as discussed in the text. The adopted satellite track, taking a total of 137 bona fide "switched-on" pixels, is marked in red for this example.
Figure 4 -
A PDM score plot for a set of I-band frames of Molniya 1–63 (one of which is shown in the right panel of Fig. 3), in search for the likely periodicity values. Note the period clustering around the value of P~4 s and its corresponding 1/2x and 2x “aliases” around P~2 and 8 s, respectively, as discussed in the text. According to our analysis, the spacecraft appears eventually to spin with a period P = 4.031 s.
Figure 5 -
The folded I- and R-band lightcurve of Molniya 1–63, as seen from Cananea (left panel) and Loiano (right panel), along two 2016 observing runs. In both cases (and throughout in this paper) apparent magnitudes are scaled to a fixed reference distance of 30,000 km. Note the quite different pattern, with the flashing behavior of the Loiano observations, as discussed in the text.
Figure 6 -
The R-band lightcurve of Molniya 2–09 (left) and 3–42 (right), respectively as from Cananea observations of 2015 September 20 and Loiano 2014 October 17. The same pattern can easily be recognized in both plots, as a sort of bona fide “photometric signature” of Molniya satellites.
Figure 7 -
The reflectance spectra of Molniya 1–91 (black curve) and 3–41 (blue curve), as from BFOSC spectroscopic observations in Loiano. Molniya 1–91 has been observed through grism GR3, while Molniya 3–41 data are from the GR3+GR5 combination (R~400). Both spectra have been smoothed (yellow- red moving average on the plots) for better display. The solar spectrum is overplotted (within arbitrary offset), for comparison (red dotted curve). The absorption features in the satellite spectra are due to the Sun or the telluric absorptions, in the near infrared, mainly by water vapor and Oxygen, as singled out in the lower sketch. Note the fairly “reddish” color of both Molniyas, compared to the Sun.
Figure 8 -
The observed color path of Molniya 1–63 along its rotation, as from the 2016 Loiano observations (see Fig. 5, right panel) in the (Rc−Ic) vs. (B−Rc) diagram. The lightcurve maxima (that is when solar pads are reflecting) are singled out in green (primary peak) and red (secondary peak), while the black line mainly traces satellite bus reflectance. The big blue and yellow triangles mark respectively the time- and luminosity-averaged colors. For comparison, the (Rc−Ic) vs. (B−Rc) locus for Main-Sequence stars of different spectral type after [15] is also displayed on the plot, marking the Sun’s location.
Figure 9 -
The historical track of Molniya 2–09 and 2–10, the two oldest satellites in orbit since 1974, are reported according to [11]. Orbit evolution is assessed in terms of drag and lunisolar perturbation acting on the satellite semi-major axis (taking period as a proxy) and eccentricity (with perigee altitude as a proxy). The FOP semi-analytical orbital propagator [19] has been used for our analysis. The historical data are in black, while the Moon and Sun perturbation is singled out, respectively by the green and blue curves and dots. Solar activity is sketched below in each panel (red histogram). Note the 7.5, 11 and 24-yr “breathing pulse” on satellite eccentricity induced by the lunisolar perturbation, as discussed in the text. For Molniya 2–09 notice as well the period switch, leaving the original 2:1 resonance during two deep excursions of perigee into the atmospheric drag, about year 1990 and 2015.


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