Detective story "Cosmos-2499"

At the beginning of last week, news about the discovery of the mysterious satellite "Kosmos-2499" passed through the network. Various sources put forward versions of the "killer satellites", "satellite-inspector", "experimental apparatus with a plasma engine" and the like interesting things. The more curious it will be to look at its orbital parameters, to try to calculate the flow rate of the characteristic speed and analyze the existing versions about the purpose and equipment of the mysterious device.

Background and correction of myths

First of all, it must be said that the object 2014-028E became suspicious a few months ago. On May 23, 2014, the Rokot carrier rocket launched three military communications satellites, Rodnik, into orbit. Together with the Briz-KM upper stage, there were four objects to be in orbit (2014-028A-D). However, a fifth object of unknown origin was discovered. It could be space junk, or another satellite. The second version seemed very logical - along with three “Springs” in 2013, an unknown device was launched, which subsequently received the number “Cosmos-2491” , and in 2012 and 2008, civilian “MiR” and “Jubilee” were launched with the main load. The situation became much more interesting when the object began to move in June. On June 24, he lowered perigee by 4 km and raised his apogee to 3.5 km. In principle, it could still be attributed to errors of publicly available orbital parameters. But in July, the changes in the orbit became obviously deliberate - the perigee fell almost 90 kilometers! And the maneuvers of the apparatus forced us to assume that he was going to get close to the spent "Breeze-KM" (object 2014-028D). Indeed, on November 9, the device approached the upper stage closer than one kilometer. Due to the small difference in the parameters of the orbit, the objects diverged again, and their new convergence is expected in late November-early December. And journalists raised a stir about a week after the first rapprochement.

Data acquisition and calculation of orbital parameters

What is the use of the Strategic Command of the US Armed Forces for an ordinary person? Mainly - to obtain data on the orbital parameters of satellites. The fact is, they have a website http://www.space-track.org/ , where they publish publicly available data about satellites flying in space. Anyone after registration can access this data. We use their services:
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The result will be a footcloth unintelligible to the uninitiated person figures:

  1 39765U 14028E 14143.85155363 .00000010 00000-0 00000 + 0 0 18
 2 39765 082.4519 349.4209 0018110 317.1560 042.8029 12.42900902 33
 1 39765U 14028E 14143.93205085 .00000010 00000-0 00000 + 0 0 36
 2 39765 082.4452 349.3605 0017028 316.2609 043.7103 12.42903492 40
 1 39765U 14028E 14143.93205141 .00000010 00000-0 00000 + 0 0 28
 2 39765 082.4533 349.3598 0018514 317.1806 042.7856 12.42904273 43 

This is the so-called TLE , the format for describing the orbit of a space object in two lines. We save data as a CSV file and read it with a spreadsheet processor.
Task one is time format conversion. "14143.85155363" is 2014, 143 is the day of the year, and 0.85155363 is hours, minutes and seconds as the proportion of a full day. Using functions of the tabular processor, it is rather simple to receive date.
Task two is to obtain data on apogee and perigee. Here we need formulas from orbital mechanics. The second-to-last parameter of the second line in TLE stores the frequency of circulation in revolutions per day (12.42900902). Using the formulas from here , we can get the value of the semi-major axis of the ellipse of the orbit as:

a = (8681663.653 / n0) ^ (2/3)
Where:
n0 is the frequency of circulation (average movement) in revolutions per day.

Knowing the semi-major axis of the ellipse we can get the values ​​of the apogee and perigee as:

hp = a (1 - e0) - 6371
ha = a (1 + e0) - 6371
Where:
e0 is the eccentricity of the orbit (the fifth parameter in the second line is 0018514, converted to 0.0018514).
6371 is the radius of the earth.

I made a file with calculations, ODS format , for normal display, do not try to open it in Google Drive, download and watch locally.

The result is the following interesting graph:



Single outliers are most likely data glitches. It can be seen that the mysterious satellite has been very actively maneuvering since summer. Let's try to calculate the cost of fuel for maneuvers.

Calculation of fuel consumption for orbital maneuvers

We take here this training manual from the site of the Technical University of Michigan. We make the following assumptions:

• The height of the apocenter is considered constant.
• The change in speed is calculated as deceleration from a circular orbit.

Use for the calculation of the formula from example 9-2:



where μ is the gravitational parameter (for the Earth - 398 600,4415)



If there are experts in ballistics who know more convenient formulas, write, recount.

The total change in speed is 185 m / s (approximate estimate). The calculations are indirectly confirmed by an estimate of 190 m / s in other sources .

Let's try to estimate the fuel consumption for such maneuvers. If we assume that the satellite has an engine on high-boiling components (UDMH / AT), then, taking the estimated satellite mass of 50 kg and a specific impulse of 3200 m / s, like in the Breeze-KM engine , we will get only 2.8 kg of fuel.

Attempt to answer some questions

Where does the satellite mass 50 kg come from?

From where this mass was taken by an unnamed expert “Interfax” is not known for certain, however, this figure is very plausible. The MiR and Yubileiny spacecrafts, which were launched by passing loads to the three Strel / Rodniki, weighed 60 and 48 kg, respectively.

Plasma engine?

The latest news about the new generation of plasma engines thrilled the public. However, data on satellite maneuvers do not provide grounds for such conclusions. All ERD have a very small, order millinewton. Such a thrust will not allow a speed change of ~ 30 m / s, as we can see from TLE. Considering that the news speaks of an unnamed satellite JSC ISC named after. Reshetnev, plasma engines can stand on "Springs" (hardly), or on one of the recently launched geostationary vehicles, for example, "Meridian" or "Express-AM6", which were launched in October. The second option is most likely - geostationary satellites, firstly, have a large amount of energy from solar panels, and, secondly, they need a constant correction of the disturbing influence of the moon.

Satellite assignment?

Most likely, this is a test of the so-called. satellite-inspector - a device that can get closer to another satellite and examine it. This version is supported by the secrecy surrounding Kosmos-2499. A lot of countries were engaged in such satellites. For example, in 2000, the British satellite SNAP-1 , launched from the Plesetsk cosmodrome, using a compressed butane engine, photographed the Nadezhda and Tsinghua-1 satellites, which were launched by the same launch vehicle. In the USA, similar tasks were solved by DART in 2006, ASTRO / NEXTSAT in 2007. China also launched several maneuvering satellites in recent years.

The next most likely option is testing a new engine for small satellites. Creating effective low thrust rocket engines is not easier to create powerful engines. The main problem is engine cooling. If a large thrust rocket engine uses, for example, bronze, as the material of the combustion chamber wall, thrusters are forced to experiment with refractory rhenium and iridium.

The least likely are the remaining options - experiments to study the possibility of repair / refueling / convergence from the orbit of spent satellites, experiments with miniature TV systems and other electronics.

Bonus

Telemetry is coming from Cosmos-2499, a radio amateur Dmitry Pashkov has recorded it and laid it out for everyone to see - you can listen to the "singing" of the device:



Maybe enthusiasts will even be able to decipher something?

Information sources

The main source of information is a topic on the “Cosmonautics News” forum . Follow the news there.
- a photo of the satellite Tango, made by the Mango satellite flying with him, the PRISMA project .