If you’ve been in bed at night, worrying that the planets in the Solar System will be bouncing across the galaxy, you can reassure your mind.
We have at least 100,000 years before that happens, according to new calculations.
In a new study, mathematicians Angel Zhivkov and Ivaylo Tounchev from Sofia University in Bulgaria presented an analytical test of the stability of the Solar System over the next 100 millennia, including the eight planets and Pluto.
Their calculations, yet to be reviewed in pairs, show that the orbits of these bodies will not vary significantly during this time.
This may seem strange; after all, the Solar System has been doing its thing for 4.5 billion years. But in fact, it is not easy to model and predict what it will continue to do in the future.
Of course, studies have been conducted to try to calculate the future of the Solar System, using advanced computing to model the movements of planets for millions or billions of years.
However, to cover such long periods, they leave out some of the smaller details.
Although the work of Zhivkov and Tounchev covers a much shorter period of time than other efforts, it increases the reliability of the results, they say.
This is because it takes into account deviations in initial conditions, such as the eccentricities and orbital inclinations of the planets, as well as the masses of all the bodies in the system.
The final fate of the Solar System is what has left scientists perplexed for a long time. It was Isaac Newton who proposed that mutual interactions between the planets would eventually lead the Solar System to chaos. Since then, the dynamic stability of our home planetary system has been very important to the brain mill.
This is because the more bodies there are in a dynamic system, the harder it will be to predict how they will behave. Two bodies, locked in mutual orbit, are relatively simple to describe and predict mathematically.
The more bodies you add, however, the more complicated the math becomes. This is because bodies begin to disrupt the orbits of others, adding an element of chaos to the system. This is known as the N-body problem.
Solutions can be derived for specific individual cases, but there is no formula that describes all N-body interactions. And the Solar System is really very complex, with not only eight planets and the Sun, but also asteroids, dwarf planets and other drifting pieces and bobs.
We can probably discount mostly really small things, like asteroids, but even so, that leaves a lot of bodies left in the system.
Zhivkov and Tounchev developed a numerical method that translates the orbital elements of the planets (and Pluto) into 54 ordinary first-order differential equations. The computer code, executed on a desktop computer, performed the calculations in 6,290,000 steps, and each step took about six days.
Calculations suggest that “[t]The configuration of the oscillating ellipses in which the planets move around the Sun will remain stable for at least 100,000 years in the sense that the major semi-axis of each planet varies within or less than one percent, ”the researchers write.
In other words, the Solar System will not yet mimic galactic billiards.
Even when conditions and initial masses were altered, the Solar System remained stable under team calculations, and researchers suggest that stability could ultimately be maintained for a million or even years. billion years, although a more powerful computer would be needed to do the calculations. .
Previous simulations found that the Solar System will take about 100 billion years to break and scatter along the Milky Way.
At that time, the Sun will be well dead, living its life beyond as a white dwarf, so it is unlikely that humanity will be able to see it, unless we have managed to find a safe haven elsewhere, very far. The probability of this, however, is questionable.
Anyways. Aside from existential fear, you can read the computer document on the arXiv prepress server.