You can relax if you've been lying in bed at night worrying that the planets of the Solar System may start bouncing out into the cosmos.

New estimates show that we have at least 100,000 years until that occurs.

Researchers from the University of Sofia in Bulgaria, mathematicians Angel Zhivkov and Ivaylo Tounchev, present an analytical justification for the stability of the Solar System throughout the ensuing 100 millennia, including all eight planets and Pluto.

Their calculations, which have not yet undergone peer review, indicate that there won't be much of a change in the orbits of these bodies over that period.

That might sound unusual considering that the Solar System has been operating for over 4.5 billion years. However, it's quite difficult to estimate and foresee what it will do in the future.

Of course, research has been done to attempt to predict the future of the Solar System, modeling the movements of the planets over millions or billions of years using cutting-edge computation.

However, they omit some of the finer points in order to span such extensive timeframes.

Despite covering a considerably less time span than earlier studies, Zhivkov and Tounchev claim that their study boosts the dependability of the results. This is due to the fact that it takes into consideration variations from the original circumstances, such as the eccentricities and inclinations of the planets' orbits as well as the masses of all the components in the system.

Scientists have been baffled by the Solar System's ultimate fate for a very long time. The idea that the planets' interactions with one another might eventually result in the Solar System becoming chaotic was first put out by Isaac Newton. Since then, the long-standing dynamical stability of our own planetary system has served as food for thought.

This is due to the fact that it is increasingly difficult to anticipate the behavior of additional bodies in a dynamical system. Two entities locked in mutual orbit may be mathematically described and predicted with reasonable ease.

However, the equations grow increasingly challenging as you add additional bodies. Because the bodies begin to disturb one another's orbits, the system becomes more chaotic. The N-body issue is what's known as this.

There is no one formula that perfectly captures all N-body interactions, although solutions may be developed for particular unique circumstances. Along with the Sun, eight planets, asteroids, dwarf planets, and other stray objects, the Solar System is incredibly complicated.

Even while we can probably mainly ignore very tiny objects like asteroids, there are still a lot of bodies in the system.

In order to convert the orbital components of the planets (including Pluto) into 54 first-order ordinary differential equations, Zhivkov and Tounchev developed a numerical approach. The computations were then carried out over 6,290,000 steps using computer code running on a desktop computer, with each step taking around six days to complete.

The researchers claim that the calculations indicate "[t]he configuration of the osculating ellipses on which the planets move around the Sun will remain stable at least 100,000 years in the sense that the semi-major axis of each planet varies within or less than one percent".

To put it another way, it's not yet time for the Solar System to resemble cosmic pool.

The team's calculations showed that the Solar System remained stable regardless of the initial conditions and mass variations, and they speculate that stability may ultimately be preserved for a million or even a billion years, though a more powerful computer would be required to perform the calculations.

It will take the Solar System around 100 billion years to disintegrate and disperse over the Milky Way, according to previous calculations.

Unless we've managed to find safe harbor somewhere else, far away, mankind is unlikely to be around to witness it at that point since the Sun would have fully died and be living its afterlife as a white dwarf. But there's some doubt about how likely that is.

Anyway. Existential dread aside, you can read the team's paper on preprint server arXiv.