Surprising theory by the designers of the Gömböc whose previous hypothesis was proven during the modelling of the recently discovered interstellar asteroid.
“Since its publication, our paper has become the most frequently read article in the Research Notes of the AAS, the American Astronomical Society”, we were told by Gábor Domokos, professor of the Department of Mechanics, Materials and Structures of the Faculty of Architecture and head of the MTA-BME Morphodynamics Research Group. Together with his colleagues András Árpád Sipos (deputy dean for research and associate professor at the Department of Mechanics, Materials and Structures of the Faculty of Architecture and researcher of the MTA-BME Morphodynamics Research Group), Gyula M. Szabó (director of the ELTE Gothard Astrophysical Observatory) and Péter Várkonyi (associate professor of the Department of Mechanics, Materials and Structures of the Faculty of Architecture) he wrote a paper eight years ago which was published in the The Astrophysical Journal Letters, describing a theory which could now explain the origin of the recently discovered asteroid called Oumuamua (meaning:“a messenger from afar arriving first”) and the abrasion history that shaped its surface over hundreds of millions of years.
Várkonyi Péter, Gábor Domokos, András Árpád Sipos
The designers of the Gömböc (Editor's note: the first known convex homogeneous body with one stable and one unstable, that is two, points of equilibrium.) issued a statement following the discovery of the new interstellar object, which has been published recently in the journal of the American Astronomical Society. The short statement refers to the mathematical model, put forward eight years ago in order to explain the shape evolution of asteroids. It proposes that the current strange cigar-like shape of the interstellar asteroid, which initially was thought to have been an extra-terrestrial spaceship by many and was discovered by the Pan-STARRS system located on Maui, is of natural origin. “The interstellar object is a spectacular illustration of the shape evolution predicted by our equation”, said BME’s professor and researcher. This was also covered by the international press: in Newsweek and the Science and Environment section of the BBC.
The elongated, cigar-shaped asteroid entered our solar system from interstellar space. Scientists so far did not have the opportunity to study such astronomical objects. The photometry revealed that its length is approx. 400 metres, while its width and height cannot be more than 40 metres. Its original shape, exact history and material composition are yet unknown, but scientists from the MTA-BME Morphodynamics Research Group and the ELTE Gothard Astrophysical Observatory explain its shape with the model used for designing the Gömböc. “Gömböc, which has one stable and one unstable point of equilibrium helped us to discover the mathematical models, according to which all abraded objects ‘approach’ the Gömböc shape, which means that the number of static balance points are reduced. Most of the objects, however, get stuck in the penultimate stage of this process and eventually finish their existence as ‘imperfect Gömböcs’. These objects have two types: depending on whether the number of stable or unstable points reaches the penultimate value of 2, we can distinguish between stable and unstable ‘imperfect Gömböc’ shapes”, explained Gábor Domokos in an interview to bme.hu, bringing beach pebbles as the example of the former and adding that the unstable version is much less common in nature.
According to the researcher, the shape of interstellar objects – unlike in the Earth’s atmosphere – is determined by its collisions with micrometeorites. “These conditions may lead to such irregular shapes as that of Oumuamua. Such elongated objects have exactly two unstable balance points (one more than the Gömböc), but possibly more stable balance points.” BME’s professor and his colleagues claim that in natural conditions, if an interstellar object is abraded for a sufficiently long time by micrometeorites, its shape will be flat or elongated, similarly to Oumuamua, and this final geometry is practically independent of the asteroid's initial shape. Unlike the asteroid discovered by the Hawaii observatory, objects orbiting within our solar system frequently collide with smaller or larger pieces of stone in spite of the less dense environment. During these collisions they are very likely to break or even be destroyed. The object discovered last autumn has been probably travelling for several hundred million years in interstellar space where the chances of major collisions are much smaller and the amount of broken fragments is much less compared to the Solar System.
Using the mathematical models developed after the discovery of Gömböc, the scientists also looked at other objects to analyse the correlation between the shape of the object and the number of its balance points and to see whether these can be used to explain the changes in the shape of these objects. “We presented a small Gömböc with the serial number 001 to Vladimir Igorevich Arnold on his 70th birthday, as a proof of the Gömböc which was first conjectured by the Russian mathematician. This is when the professor pointed out to us that mathematical equations related to the Gömböc could be used to explain other phenomena in the shape evolution of other objects. Among other things, this also inspired us to further develop our model”, said Gábor Domokos on the subsequent experiments.
The Gömböc helped the Hungarian scientists answer several cosmic questions: for example they worked with NASA to analyse the stones in the images taken by the Curiosity Mars rover to prove that at one point the Red Planet was criss-crossed by large rivers. Researchers at the University of Pennsylvania GRASP Lab used the Gömböc shape as the design for their pico-drones. BME’s researchers are currently collaborating with several foreign research groups. There are several thousand Gömböc pieces in over 50 countries. The individual, numbered pieces are on display in such renowned institutions as Princeton University or Windsor Castle. (Editor note: To read to online publication on the Gömböc visit the following link.)
The world’s largest Gömböc was erected in Budapest’s Corvin Promenade in the middle of December. It is almost 4.5 metres high, weighs over 4 tonnes, and is made of stainless steel, with a bead blasted chrome steel shell.
Photo: Zoltán Adrián Zoltán / Futureal
The 40,000-litre-volume statue commemorates the Hungarian invention that has become a world sensation. The largest version of the object so far, a symbol of serious research and mathematical genius, was 2.5 metres high and it was exhibited in the Hungarian pavilion at the 2010 Shanghai Expo. The newly unveiled Gömböc statue was built by Direct Line Kft. under the artistic supervision of József Zalavári, associate professor at the Department of Machine and Product Design of the Faculty of Mechanical Engineering.
BME’s scientist thinks that he and his colleagues are attempting to explore and partly explain a fascinating range of questions within the natural sciences. The right models already exist within mathematics, but their interpretation is not an easy task. “The study of shape evolution is one of the most beautiful and most difficult branches within mathematics. It will take time for us to become familiar with this specialist field.” Gábor Domokos believes that this research area has immense potential. He welcomed the establishment of the MTA-BME Morphodynamics Research Group last summer, which is a testament to the Academy’s support for this subject. He hopes that BME can become the national or even the regional international centre for research on shape evolution.
“We are committed to long-term research projects. For this we need to understand the language of mathematicians, physicists or practicing geologists from the various BME faculties and disciplines, and we also need their coordinated involvement”, stressed the inventor, who believes that this group of young BME researchers can bridge the gap between theoretical and applied sciences. “We all believe that mathematics, and within that geometry, is the language of the natural processes of morphogenesis. We hope that this approach can help us better understand the shapes and forms of inanimate nature”, he added.
TZS - GI
Photo source: NASA, MTI