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The Gömböc helps to decode interstellar asteroid's mysterious shape

December 18th 2017.

The recently discovered interstellar asteroid 'Oumuamua is currently traversing our Solar System.  The hugely elongated shape (length ~400 m, width ~ 40 m) of the first-ever observed interstellar object is so bizarre that it made scientists (including Harvard's Avi Loeb) wonder whether it may actually be a spaceship.  

Now a Hungarian team from the ELTE Gothard Astrophysical Observatory and the MTA-BME Morphodynamics Research group proposed a simple theory connecting 'Oumuamua's the origin and its shape. The research note published by the American Astronomical Society claims that the bizarre shape could be simply the result of an abrasion process, which lasted over hundreds of millions of years.

Vladimir Igorevich Arnol'd, one of the greatest mathematicians of the 20th century (after whom the minor planet 10031 Vladarnolda has been named), conjectured in 1995 the existence of a homogeneous shape which has just one stable and one unstable static balance points and thus behaves like a weeble when placed on a horizontal surface.  Ten years later two Hungarian engineers created the first such shape, dubbed "Gömböc" was created. The Gömböc became famous in its own right and led to a surprising series of discoveries, including a mathematical theory explaining the evolution of shapes under abrasion. " Our theory predicts that the number of static balance points tends to be reduced in this process, so, in this sense all abraded objects approach the Gömböc. However, they get stuck in the pen-ultimate stage of this process and these "imperfect Gömböcs" are the shapes often observed in Nature" - said Gabor Domokos, director of the Morphodynamics Research Group of the Hungarian Academy of Sciences at the Budapest University of Technology and Economics.

Depending on whether the number of stable or unstable points reaches the pen-ultimate value of 2, we can distinguish between stable and unstable "imperfect Gömböc" shapes. The best known example of the former are well-abraded beach pebbles which tend to be flat and thus they exhibit exactly two stable balance points (but possibly more unstable balance points). 

While pebbles collide with like-sized objects in the abrasion process, asteroids collide with micrometeorites several orders of magnitudes smaller compared to their own size. It is not surprising that the geometric outcome of the process is very different, what is surprising though is that it also results in "imperfect Gömböc" shapes, albeit with the much less common unstable version. Such shapes are not flat but thin and this is exactly how astronomers describe 'Oumuamua. Very thin objects have exactly two unstable balance points (at the tips) but possibly more stable balance points.

The reserch note by Gábor Domokos, András Sipos, Péter Várkonyi and Gyula M. Szabó claims that if an asteroid is abraded for a sufficiently long time by micrometeorites then its shape will be hugely elongated and thin, and this final geometry is practically independent of the asteroid's initial shape.

Asteroids in the Solar System rarely (if ever) reach this final stage of abrasion because the chance of larger collisions is not negligible. Such a large collision is likely to break a thin object and then the abrasion process is rebooted from the geometric point of view. 'Oumuamua, on the other hand, has travelled for several hundred million years in the interstellar space where the chances of major collisions are much smaller than in the Solar System, so it had plenty of time and opportunity to evolve its shape towards the now observed thin, elongated geometry.

The result was discussed on the cover page of  BBC  and also on Newsweek.




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