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On a safe course

Simulation explains why the Earth did not collide with the Sun

nasaSun and Earth: new computer model avoids collisionnasa

The situation was confusing. Every time an astrophysicist carried out a computer simulation on the origin of the solar system over the last twenty years the result was invariably the same: the Earth should have disappeared a long time ago. Some 100,000 years after its genesis, even before it was completely formed, the planet should have gone into a suicidal spiral that would have made it collide with the Sun. According to the traditional models that try and explain the emergence of planetary systems the Earth is yet another heavenly body destined to bump into the mother star. Of course, nothing of this sort happened and there was never a fatal impact. But only recently have some researchers formulated an alternative theory capable of explaining why the planet was not swallowed up by the king star. “We’ve managed to carry out the first simulation in which the Earth does not ‘fall into’ the Sun”, says astrophysicist, Wladimir Lyra, a 29 year-old Brazilian who is doing post-doctoral studies at the American Museum of Natural History (AMNH) in New York. The researcher was responsible for loading data and carrying out the digital trial that, on computers, changed the Earth’s evolutionary history.

Like the other planets in our system the Earth emerged from the accumulation of dust and gas from the protoplanetary disk, a cloud that surrounded the Sun right after this star was formed some 4.6 billion years ago. Today there is almost a consensus among scientists that the planets in the solar system – and also the more than 500 extra-solar worlds so far discovered – did not originate in the same place in which they are currently found. They were born at one point on the disk and after a series of gravitational interactions with  gas and objects in the system, migrated to another region. There they found an equilibrium orbit around the Sun and settled down.

Over the last 20 years the computer models used by various groups of astrophysicists started from the principle that although the temperature across the whole disk varies (the closer to the Sun the hotter it becomes), any thermal fluctuation undergone by the gas at a particular point was instantly irradiated outwards. In practice, this is the equivalent to saying that any eventual excess heat at a specific place was transferred out into space and the temperature at each point on the disk was always constant. The consequences of this way of thinking, which is used without problems when studying galaxies, were catastrophic in simulations about the evolution of the solar system: not just the Earth, but all the planets hit the Sun. “When we introduced local temperature fluctuations to the disk the planets began to migrate to more distant orbits from the Sun”, says Lyra, who was the first author of an article published in the June 10, 2010 edition of Astrophysical Journal Letters (ApJL), giving the results of the new simulations.

According to the researchers the new model predicts the total evaporation of the protoplanetary cloud after 5 million years and is capable of explaining the migration of planets with masses up to 40 times bigger than that of the Earth. “During its evolution process the disk loses gas and has such low density that it no longer manages to move planets, which therefore end up entering into their new orbit”, explains astrophysicist, Mordecai-Mark Mac Low, coordinator of the work of the Brazilian at the AMNH and co-author of the study.

ESOIllustration shows young star with a gas disk from which the planets formESO

The central ideas that allowed the computer simulation to be loaded with data derive largely from recent work by another young generation astrophysicist. Since 2006, Dutchman Sijme-Jan Paardekooper, 31, who is today doing post-doctoral studies in the Department of Applied Mathematics and Theoretical Physics at Cambridge University, England, has been publishing studies on the possible effects arising from temperature variations in the gas of a protoplanetary disk. “We’re always looking for the simplest theoretical model for explaining a physical phenomenon”, says Paardekooper, who also signed the ApJL article.

The key question is to understand how the trajectory of planet embryos can change course in a situation because of thermal changes at specific points in the gas cloud. Before this it needs to be borne in mind that the final orbit of a planet that is forming is determined by a series of variables, above all gravitational interactions with the other components of the system (the mother star, other planets and the gas disk). “Some factors favor the occurrence of a migration towards the Sun and others away from it”, comments Paardekooper. Didactically, the explanation that follows deals with the central mechanism that, according to simulations of Lyra and his colleagues, removed the Earth from a collision path with the Sun.

In a protoplanetary disk the gravitational force of a planet modifies the original orbit of the gas that surrounds it. In response to this phenomenon the planet also alters its orbit, but in the opposite direction to that in which the gas moved. So far this is nothing new; it was all predicted by Isaac Newton’s law of action and reaction.  This is where the great leap forward comes in.  According to the new simulations, when the researchers incorporated occasional local temperature variations to the protoplanetary disc they noticed that the gas became denser in the zones closest to the Sun  and was able to shift the Earth to a safe orbit.

Trojan lands
Before the study on why the Earth did not migrate into the Sun, Lyra produced another computer simulation with protoplanetary disks that also aroused a great deal of interest. In a study published as the cover article in one of the January 2009 editions of the scientific journal, Astronomy & Astrophysics, the Brazilian and three other authors disclosed calculations and equations that indicate the possibility of there being rocky worlds with a mass similar to that of the Earth, hidden right “on the shoulders” of huge and gassy exoplanets. These are Trojan Earths. Objects that follow the same orbit as a much larger heavenly body, but without ever crashing into this privileged traveling companion, are called Trojans. They are located in two regions at the so-called Lagrangian points on the orbit, 60 degrees before and 60 degrees after the place in which the biggest object is found. The points are so called because they were proposed by the Italian-French mathematician and astronomer, Joseph Louis Lagrange (1736-1813).

There is no lack of heavenly objects that bear the adjective Trojan. The gaseous giant, Jupiter, orbits the Sun in the company of two groups of celestial rocks located at the Lagrangian points, the Trojan asteroids (from whose name came the inspiration for naming the phenomenon) and the Greek asteroids. Saturn, Mars and Neptune are also escorted by Trojan objects. But a Trojan planet has never been found, not even outside the solar system, where exoplanets have been discovered orbiting more than 420 stars. “Wladimir’s simulations show that we need the following ingredients for there to be Trojan Earths: giant gaseous planets, like Jupiter, have to form quickly in a proptoplanetary disk full of pebbles and boulders”, says Danish astrophysicist, Anders Johansen, 34, from Lund University, Sweden, one of the co-authors of the study with Lyra. “As we concentrate on the Lagrangian points the solids give rise to such a dense body that they form planets similar to ours.”

At least this was the result of the computer model run by the Brazilian. In the simulation the pebbles that joined together to generate virtual Trojan Earths were between 1 centimeter and 1 meter across. “We began the experiment with smaller objects”, says Lyra. “In this way we managed to resolve the hydrodynamics of the gas, the strength of the drag in the particles and their joint gravitational attraction”. The scientists know that minute dust grains easily join together in protoplanetray disks, but maintaining the process becomes uncertain as the solid bodies get bigger. Even so, if the calculations of the astrophysicists are correct the possibility of there being Trojan Earths in the neighborhood of major gassy exoplanets is real. All that is needed is for man to have the means of detecting them.

NASA / JPL-CALTECHBacchus instead of HD 128311 b
Astrophysicist proposes adopting names from Greco-Roman mythology for the known exoplanets

They are not planet names. They are automobile registration plate numbers. This is how Wladimir Lyra defines the terminology used to refer to the more than 500 exoplanets, uninhabited worlds located outside the solar system and discovered since October 1995. So far, the rule has been to call them by the name of the star around which they orbit, plus a letter (b, c, d and so on). Three planets, for example, orbit a star in the Virgo constellation, the pulsar PSR 1257+12. In scientific literature they are known as PSR 1257+12 b, PSR 1257+12 c and PSR 1257+12 d. Lyra is suggesting giving them names from the Greco-Roman mythology associated with the star’s constellation. The trio of planets would then be called Sisyphus, Ixion and Tantalus.

This is no joke. The Brazilian has written a formal proposal with the names for more than 400 exoplanets, which he submitted to the International Astronomical Union (IAU), the body that deals with this subject. The idea was not accepted. They said that scientists use the mass of letters and numbers to refer to the planets without any problem. “They forget that astrophysicists also used to belong to the general public”, says Lyra. “When I was 6 years old I was fascinated by the idea that there were other worlds like Earth and I spent days learning the names of satellites by heart, like the moon”. Lyra has still not given up the proposal and is going to re-present it to the IAU.

Scientific articles
LYRA, W. et al. Orbital migration of low-mass planets in evolutionary radiative models: Avoiding catastrophic infall. Astrophysical Journal Letters. v. 715, n. 2, p. L68-L73. 1º jun. 2010.
LYRA, W. et al. Standing on the shoulders of giants – Trojan Earths and vortex trapping in low-mass selfgravitating protoplanetary disks of gas and solids. Astronomy & Astrophysics. v. 493, n. 3, p. 1.125-39. jan. 2009.