Rapid tumbling of the Chang'e 2 r/b (2010-050B) and Rollercoaster orbital evolution

(click image to enlarge)

Recently, I have posted several times about my tracking of two extremely remote pieces of space junk: 2010-050B and 2013-070B, the CZ-3C upper stages of the Chinese Chang'e 2 and 3 Lunar missions. These orbit in orbits with (currently) perigee just within, and apogee beyond one Lunar distance, i.e. a trans-Lunar orbit.

In a recent post I discussed the tumbling behaviour of 2013-070B, the Chang'e 3 booster. At that time, I stated that by contrast the Chang'e 2 booster, 2010-050B, appears steady.

I can now say that is not true: 2010-050B is tumbling too. And very rapidly, which is why I didn't notice it earlier.

My earlier imaging sessions were done while 2010-050B was at well over one Lunar distance (beyond 400 000 km), towards its apogee. On July 18th I imaged it from MPC Q65 Warrumbungle while it was only a few hours from its perigee, at a distance of 280 000 km (about three quarter of a Lunar Distance), moving at 47" per minute. The result is a much longer trail on the image than in earlier imaging sessions.

Rather than being a trail, suddenly the trail is resolved in a series of dots: typically three (and in one image two) per 30 second exposure. See the image in the top of this post. The reason this was not visible during earlier imaging sessions, was that the trail was so short (a  few arcsecs) when imaging the object at larger distance, that the dots merge into one trail.

The 3 dots per image, and once two dots, indicate a flash period of ~15 seconds, testifying to a rapid tumble. This is close to the period determined by Peter Birthwhistle (MPC J95 Great Shefford) in 2010 shortly after the launch.

I also imaged 2013-070B that night, at a distance of about 479 000 km (1.25 Lunar Distances). This object is tumbling much slower than 2010-050B: the brightness variation in the animated GIF below fits nicely with the 7m 05s flash period determined from June 26 and July 5.

The orbits of 2010-050B and 2013-070B are changing extremely fast, in a chaotic way, notably as a result of Lunar perturbations. As you can see in the table that is part of my SeeSat-List post here, the apogee of the 2010-050B orbit for example changed from about 550 000 km to about 446 000 km between May 7 and July 18. The perigee changed from about 350 000 km to about 280 000 km, i.e. from about 1 Lunar Distance to about 0.73 Lunar Distance, during that same period. The orbital period was shortened by almost 10 days.

While the apogee and perigee distances are currently decreasing for this object, a new Lunar perturbation might make them increase again in the future. The orbital inclination also widely varies over time. Such changes are very sudden, especially in connection to close Lunar encounters. These objects are on a true Rollercoaster ride through the Earth-Moon system.

As it turns out, this kind of chaotic orbit is very difficult to model, even over relatively short time scales. Attempts using GMAT show that very small variations in the determined orbit yield very different outcomes within only a few years. Variations in the order of a few hundred meters (!) in apogee and perigee will already do it, i.e. variations well within the uncertainties in the determined orbital parameters.

GMAT-simulated chaotic orbital evolution of 2010-050B over a 1.5 year period. Grey is the Moon orbit, red is 2010-050B orbit, blue grid is earth equatorial plane. In reality, the orbital evolution might be different as small variations in initial conditions (see text) yield large differences after 1.5 years.

So we have to observe these objects to see how their orbits evolve in the future. And this is what I will do: keep following them, over the coming years.

Basically, three eventual future fates are possible for these objects: one is eventual ejection into a Heliocentric orbit (so it will leave the Earth-Moon system); two is an eventual Earth impact (i.e. a decay in the Earth atmosphere); and three is an impact on the moon.