The Kosmos-2561/2562 pair has now been in orbit for about 2.5 months. Kosmos-2561 has gradually decayed from its initial 407x420 km orbit to a 401x413 km orbit and has so far not performed any orbit corrections (see attachment 1 from Celestrak). Kosmos-2562 has carried out three burns to slightly lower its orbit, two in late October and another in mid-November. There is also a small spike in the semi-major axis just before December 14, but that may have been due to inaccuracies in the data (see attachment 2). The satellite is currently being tracked in a 377x395 km orbit.
Space-Track.Org gives the radar cross section of Kosmos-2561 as “large” (more than 1 m2) and that of Kosmos-2562 as “small” (between 0.1 and 1 m2). The fact that these are not two identical satellites is also evident from the fact that they have different military designators (14F164 and 14F172), which were leaked by an insider on the NK forum shortly before launch and had never been seen before. European radio amateurs have picked up signals from Kosmos-2561 in the S-band at 2280 MHz. This is the same frequency used by the so-called inspector satellites, but it is not necessarily a sign of commonality. The S-band is commonly used for downlinking telemetry.
The purpose of these satellites remains a mystery and all we can do is try and make some educated guesses. It is logical to assume that the two satellites were launched together because their missions are somehow interrelated. Having maneuvered to a slightly lower orbit, Kosmos-2562 orbits the Earth slightly faster than Kosmos-2561 and regularly overtakes it, with the two occasionally passing each other at a relatively close range. This may have been done deliberately to allow them to regularly interact with one another, albeit at a distance. Keeping them close together in exactly the same orbit would require much more fuel.
As I have speculated earlier in the thread, there is a possibility that the satellites are part of a project named Numizmat, initiated in 2014 with a contract awarded by the Ministry of Defense to CNIIHM. Online procurement documentation related to this project makes it possible to conclude with a fairly high degree of certainty that one of the payloads is an ultra wideband (UWB) radar developed by the Sedakov Scientific Research Institute of Measuring Systems (NIIIS) and most likely designed to detect other objects in orbit. More on that in the Numizmat thread here:
https://forum.nasaspaceflight.com/index.php?topic=47851.0Articles published by NIIIS (some of the authors of which have signed procurement documents for Numizmat) discuss the need to study how the propagation of such UWB radar signals is affected by the ionosphere. In 2014 NIIIS published a drawing of a satellite equipped with a so-called “spectrum analyzer” designed to do just that (see attachment 3). However, this was published before NIIIS was assigned to Numizmat in early 2015, so it is not necessarily representative of the satellite’s ultimate design.
If Kosmos-2561 and 2562 belong to Numizmat, one could carry the radar and the other could serve as a target to reflect the radar signals or analyze the signals itself. The signals would probably have to travel some distance through the ionosphere for a proper analysis to be made, which could explain why the two satellites pass one another at considerable distances. The timing of this mission during a period of increased solar activity may not be coincidental because the ionosphere is now more susceptible to disturbances, especially in the polar regions, which the satellites regularly pass in their 97° inclination orbits.
Right now Numizmat looks like the best candidate to explain this mission from the
known Russian military space projects that has not yet seen a flight earlier. Also, with the project having started in 2014, its first mission is certainly overdue. But, of course, Kosmos-2561 and 2562 might just as well be part of a totally different project that has not yet been uncovered.