If you've been lying in bed all night worrying that the solar system will vanish throughout the galaxy, you may rest assured that your mind is at ease.
According to new estimates, we will have to wait at least 100,000 years before it happens.
Angel Zhivkov and Ivaylo Tounchev of the University of Sofia in Bulgaria present an analytical proof of the Solar System's stability over the next 100 millennia, including all eight planets and Pluto.
Their calculations,which are yet to be peer-reviewed, indicate that the orbits of these bodies will not significantly vary over a period of time.
After all, the Solar System has been here for 4.5 billion years or so already. However, it isn't easy to model and anticipate what it'll continue to do in the future.
Evidently, studies have been conducted to try to predict the future of the Solar System, by using advanced computing to model the motions of the planets over millions or billions of years.
However, in order to cover such long timescales, they leave out some of the more subtle details.
Although Zhivkov and Tounchev's work covers a shorter time period than other efforts, it increases the accuracy of the findings, they assert.
This is because it accounts for variations in initial conditions, such as the planets' orbital eccentricities and inclinations, as well as the masses of all the bodies in the system.
The ultimate fate of the Solar System has puzzled scientists for a long time. It was Isaac Newton who proposed that mutual interactions between the planets might eventually cause the Solar System to collapse. Since then, the long-term dynamical stability of our home planet has been grist for the brain.
Because the more bodies there are in a dynamical system, the harder it becomes to predict how they'll behave. Two bodies, locked in mutual orbit, are relatively simple to mathematically describe and predict.
The more bodies you add, the more complicated the mathematics becomes. This is because the bodies begin to perturb each other's orbits, causing more chaos to the system. This is known as the N-body problem.
Individual solutions may be devised, but there is no one uniform formula for all N-body interactions. The Solar System is also quite complex, with not just eight planets and the Sun, but also asteroids, dwarf planets, and other bits and bobs tumbling around.
We can probably scupper the really minor things, like asteroids, but even then, there are still a lot of bodies left in the system.
The computer code, run on a desktop computer, then performed the calculations over 6,290,000 steps, each step taking about six days.
The authors estimate that "[t]he configuration of the osculating ellipses on which the planets move around the Sun will remain stable for at least 100,000 years in the sense that the semi-major axis of each planet differs within or less than one percent".
In other words, the Solar System isn't going to emulate galactic billiards right now.
Although a more powerful processor might be required to perform the calculations, the Solar System remained stable under the team's methods.
Previous simulations have shown that the Solar System will take 100 billion years to breakdown and dissipate across the Milky Way.
The Sun will be fully and truly dead, living its afterlife as a white dwarf, so humanity is unlikely to be able to see it until we've found a safe haven elsewhere far away. The probability of that, however, is slim.
Regardless of your existential fears, you can view the team's paper on preprint server arXiv.