Earth probably shouldn’t exist.
This is because the orbits of the planets in the inner solar system (Mercury, Venus, Earth, and Mars) are chaotic, and models have suggested that these inner planets should have crashed into each other by now. And yet that has not happened.
New research published May 3 in the journal Physical exam X (opens in a new tab) can finally explain why.
Through a deep plunge into the planetary motion models, the researchers discovered that the movements of the inner planets are constrained by certain parameters that act as a tether that inhibits the chaos of the system. In addition to providing a mathematical explanation for the apparent harmony in our solar system, the insights from the new study may help scientists understand the trajectories of exoplanets surrounding other stars.
unpredictable planets
The planets constantly exert a mutual gravitational pull on each other, and these little tugs constantly make minor adjustments to the orbits of the planets. The outer planets, which are much larger, are more resistant to small jerks and therefore maintain comparatively stable orbits.
However, the problem of the internal trajectories of the planets is still too complicated to solve exactly. In the late 19th century, the mathematician Henri Poincaré demonstrated that it is mathematically impossible to solve the equations governing the motion of three or more interacting objects, often known as “three body problem.” As a result, the uncertainties in the details of the initial positions and velocities of the planets increase with time. In other words: it is possible to take two scenarios in which the distances between Mercury, Venus, Mars and Earth differ by the smallest quantity, and in one the planets collide with each other and in another they separate.
The time it takes two trajectories with nearly identical initial conditions to diverge by a specified amount is known as the Lyapunov time of the chaotic system. In 1989, jacques lascar (opens in a new tab)astronomer and director of research at the National Center for Scientific Research and the Paris Observatory and co-author of the new study, calculated Lyapunov’s characteristic time (opens in a new tab)for the planetary orbits of the inner solar system it was only 5 million years.
“Basically, it means you lose a digit every 10 million years,” Laskar told Live Science. Thus, for example, if the initial uncertainty in the position of a planet is 15 meters, 10 million years later this uncertainty would be 150 meters; after 100 million years, another 9 digits are lost, giving an uncertainty of 150 million kilometers, equivalent to the distance between the Earth and the sun. “Basically, you have no idea where the planet is,” Laskar said.
While 100 million years may seem like a long time, the solar system itself is more than 4.5 billion years old, and the lack of dramatic events, such as a planetary collision or the ejection of a planet from all this chaotic motion, baffled scientists for years. a long time.
Laskar then looked at the problem in a different way: by simulating the planet’s internal trajectories over the next 5 billion years, moving from one moment to the next. He found only a 1% chance of a planetary collision. Using the same approach, he calculated that it would take, on average, about 30 billion years for any of the planets to collide.
restraining the chaos
Delving deeper into the mathematics, Laskar and his colleagues identified for the first time “symmetries” or “conserved quantities” in gravitational interactions that create a “practical barrier in the chaotic wandering of the planets,” Laskar said.
These emergent amounts remain nearly constant and inhibit certain chaotic movements but do not completely prevent them, just as the raised rim of a plate will inhibit food from falling off the plate but not completely prevent it. We can thank these numbers for the apparent stability of our solar system.
Renu Malhotra (opens in a new tab), a professor of planetary sciences at the University of Arizona who was not involved in the study, noted how subtle the mechanisms identified in the study are. Malhotra told Live Science that it is interesting that “the planetary orbits of our solar system show exceptionally weak chaos.”
In other work, Laskar and his colleagues are looking for clues as to whether the number of planets in the solar system once differed from what we see today. Despite all the stability evident today, it remains an open question whether that has always been the case in the billions of years before life evolved.