“Why the Inner Solar System Shouldn’t Exist: New Research Explains Stability”

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As well as providing a mathematical explanation for the alignments found in solar systems, this new research insight could help scientists understand the trajectories of exoplanets around other stars.

Planets are unpredictable

Planets are constantly tugging on one another’s gravity, and that slight pull keeps making tiny adjustments to the planet’s orbit. The outer planets (Jupiter and so on), which are much larger, are more resistant to minor tugs and so maintain relatively stable orbits.

The problem of inner planet trajectories, however, is still too complex for scientists to solve with precision. In the late 19th century, the mathematician Henri Poincare proved that it was mathematically impossible to solve the equations governing the motion of three or more interacting objects (often known as the triple body problem).

As a result, the uncertainty regarding the details of the planet’s initial position and velocity continues to grow over time. In other words: It is possible to take two scenarios where the distances between Mercury, Venus, Mars and Earth differ only slightly. In one scenario, the planets will collide with each other and in another, they will deflect each other.

The time required for two paths with nearly the same initial conditions to deviate by a certain amount is called the Lyapunov time of a chaotic system.

In 1989, Jacques Laskar, astronomer and research director at the National Scientific Research Center and Paris Observatory and co-author of the new study, calculated the Lyapunov time characteristic of the orbits of the inner solar system planets. He found Lyapunov only needed 5 million years.

“That means you’re basically losing a digit every 10 million years,” Warriors told Live Science.

So, for example, the initial uncertainty of the planet’s position is 15 meters, 10 million years later this uncertainty becomes 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,” Warriors said.

100 million years may sound long, but our solar system is over 4.5 billion years old. The absence of dramatic events like planetary collisions or planets being knocked out of all that chaotic motion has long puzzled scientists.

Laskar then looked at the problem in a different way. It simulates the trajectory of the inner planet over the next 5 billion years, stepping from one moment to the next. He found the probability of a planetary collision was only 1 percent. Using the same approach, he calculated, it would take an average of about 30 billion years for one of the planets to collide.

Survival in Chaos

Delving into the math, Laskar and his colleagues claim to have identified a so-called symmetry or ‘retained quantity’ in gravitational interactions. “Symmetry creates a practical barrier in the chaos of planetary wanderings,” claims the Warriors.

The quantity that appears remains almost constant and hinders the movement of certain chaos, but does not prevent total chaos. Laskar gave an example, like a raised lip of a dinner plate, will prevent food from falling off the plate, but not completely prevent it from falling. “We can thank this number for the stability of our solar system,” he said.

Professor of Planetary Science at the University of Arizona, Renu Malhotra highlights how subtle or ingenious the mechanisms identified in this study are. “It is interesting that the orbits of the planets of our solar system show very weak chaos,” he said.

In another work, Laskar and colleagues are looking for clues as to whether the number of planets in the solar system was once different from what we see today. Even so, all the stability claimed in the study is still in question.

For one thing, did the retained sums always occur over billions of years, before life evolved? Source: LiveScience