Earth was not supposed to exist! This is because the orbits of the inner planets in the Solar System (Mercury, Venus, Earth, and Mars) are chaotic, and theoretical models show that they should collide and disrupt each other. But that didn’t happen.
A recent study published on May 3rd in Physical Review X finally provides an explanation.
Through in-depth analysis of planetary motion models, researchers have discovered that the motion of the inner planet group is constrained by certain parameters that act as binding threads, preventing the system from descending into chaos. In addition to providing a mathematical solution to the harmony of the Solar System, the findings from this study can also help scientists gain a better understanding of the orbits of exoplanets around other stars.
Unpredictable planets
Planets constantly exert gravitational forces on each other, creating continuous fluctuations in their orbits. The outer planets in the Solar System are much larger in size and mass, which means they are less affected by these small oscillations (the gravitational force they exert on each other is too small compared to their own orbital motion) and thus can maintain stable orbits more easily.
However, the problem of orbital dynamics within the planet group is still too complex to be accurately resolved. In the late 19th century, mathematician Jules Henri Poincaré proved that it is impossible to solve equations for the motion of three interacting bodies, commonly known as the “three-body problem.” The result is that the uncertainty in the initial positions and velocities of the planets increases over time. In other words, the distances between the inner planets change slowly over time, in one scenario they can shorten and collide with each other, while in the opposite scenario they gradually move farther apart.
The time it takes for two orbits with initially similar conditions to diverge significantly is characterized by a specific value known as the Lyapunov time of the chaotic system. In 1989, Jacques Laskar, an astronomer at the French National Scientific Research Center and the Paris Observatory, and co-author of the recent study, calculated the Lyapunov time for the orbits of the inner planet group in the Solar System to be only 5 million years.
“That basically means that every 10 million years, you lose one digit,” said Laskar. “For example, if the initial uncertainty is 15 meters, then after 10 million years, it will be 150 meters; after 100 million years, there will be an additional 9 digits added to it, making the uncertainty 150 million kilometers, which is the distance from Earth to the Sun. Essentially, you no longer know where the planet will be at that time.”
Although 100 million years may seem long, the Solar System itself has existed for over 4.5 billion years. This absence of dramatic events such as planet collisions or a planet being ejected from these chaotic motions has long puzzled scientists.
Laskar decided to approach this problem in a different way: by simulating the orbits of the planets for the next 5 billion years to see how they would turn out. He found that there is only a 1% chance of a planet collision occurring. Using the same approach, he calculated that on average, it would take 30 billion years for a collision to happen.
Dominance amidst chaos Using mathematics, Laskar and his colleagues were able to identify for the first time the “symmetry” or “conserved quantities” in the gravitational interactions that form what they call the “real barrier to the chaotic motion of the planets.”
These additional quantities remain nearly constant and directly hinder some chaotic motions, but they do not completely stop them. It is through this mechanism that they provide stability within the Solar System.
In another study, Laskar and his team are investigating clues about whether the number of planets in the Solar System has ever been different from what we currently observe. While everything seems stable now, whether that has always been the case for billions of years before the evolution of life remains a question that needs to be answered.