Forever Bound To Retrace The Same Trajectory

The present arrangement of planets in the Solar System holds clues to its formation. Kepler believed that the relative distance of the planets, which he inferred from their motion against the constellations, was set according to a divine order, obeying strict geometric rules. Kepler’s geometric universe was heliocentric, with the Sun staying still and the planets revolving around it, following the model set out a few decades earlier by the Polish astronomer Nicolaus Copernicus. Some 2000 years before Kepler, Pythagoras of Samos described the properties of the regular polyhedra. For centuries these mystical notions constituted the foundation of astronomy and mathematics. The universe appeared to be a beautiful orrery, with the planet’s orbits interlocking as tiles in a puzzle. And yet, some of the tiles did not quite fall into place. Kepler’s geometric construction of the Solar System. Planets are associated with spheres with radii equal to their mean distance from the Sun. The issue was that Mars did not move at a regular and constant pace across the sky. The crucial discovery of Kepler’s painstaking analytic work was that the planets revolve around the Sun on ellipses instead of circles. The validity of this conclusion, purely based on empirical observations, was demonstrated mathematically in 1687 by Isaac Newton’s theory of gravitation.

With Every Wish

Our understanding of the planets’ orbits and motion has greatly improved since the time of Kepler and Newton, but the geometric nature of the Solar System still reverberates in current theories. But gone is the sense of celestial order and immutability. Most astronomers believe that the current architecture of the Solar System has likely changed dramatically since its formation, and that the planets’ orbits went through a chaotic evolution leading to, as we shall see, massive collisions. Consequently, our ability to reconstruct the development of the Earth and other terrestrial planets requires us to retrace their past. For this, we need to know to what extent the current planetary arrangement is representative of the early Solar System. This is because planets, in addition to interacting gravitationally with the Sun, also exert mutual attraction. In a series of seminal treatises, they showed that the addition of the gravitational attraction between planets does not significantly alter their paths nor the overall stability of the Solar System because of the large distance between adjacent planets. So planets could have orbited the Sun close to their observed orbits since the beginning of time. But the devil is in the details. As more and more asteroids were discovered between Mars and Jupiter, subtle but important properties about the architecture of the Solar System emerged. Kuiper proposed that the main properties of the primordial protoplanetary disk could be estimated by mentally reversing accretion. In a seminal paper published in 1956, he imagined spreading out the mass of planets into rings with radial thicknesses comparable with their inferred feeding zones.3

Are You Listening?

Earth’s orbital plane, known as the ecliptic, defines an imaginary reference plane. The resulting mass distribution, which decays beyond Venus, is considered to mimic the original mass distribution of gas and dust in the protoplanetary disk. If we now add in the mass of all the main belt asteroids, the corresponding disk density between Mars and Jupiter is about ten thousand times lower than that expected based on nearby planets. There seems to be a sudden change here in the way mass is distributed with distance from the Sun. The missing mass in the asteroid belt underscores a clear transition between the inner rocky planets and the outer gaseous planets. Larger rocky and gaseous planets define a smooth decay of the gas density with increasing distance from the Sun. Asteroids also have a peculiar orbital distribution. While planets from Mercury to Neptune revolve around the Sun in nearly coplanar orbits within about 7º off the ecliptic plane, asteroids have a much wider distribution of inclinations up to 30–40º, leading them to periodically wander off the ecliptic plane. This is a telltale sign that the asteroids’ orbits have been stirred, but when and by what? We shall return to this issue below. More oddities emerged in the outer Solar System. This does not fit with the idea of Neptune’s clearing off its feeding zone. Researchers argue that Pluto was captured in its current orbit by Neptune at a later time, after their formation, while Neptune moved outward in the protoplanetary disk.

Brilliant Disguise

This theory, if correct, has important consequences, as it implies that planets may wander around, or migrate. The possibility that Neptune, and perhaps other planets, may have migrated, has huge implications. It opens up endless opportunities for imagining different configurations of the planets. Our Solar System is just one outcome among countless other possible configurations. So what causes planets to migrate? Scientists have found various drivers. The underlying cause of migration lies in the variability of a planet’s distance from the Sun. In the simplicity of Kepler’s Solar System, planets have elliptical orbits, and they are forever bound to retrace the same trajectory at each revolution. But migration implies that a planet may break off this perpetually repeating path. This, however, may have not been the case in the early Solar System. Jupiter and Saturn are the most massive planets in the Solar System, and they are primarily constituted by gas. As such, their accretion must have happened before the protoplanetary gaseous disk dissipated. They grew in size by attracting gas from nearby regions of the disk. The gravitational pull of the planets on the gas, and vice versa, produces quite a tug of war. As gas flows on to growing planets, enlarging them, they perturb the mass distribution in the disk, which becomes asymmetric. This produces subtle perturbations on the planets’ motion. A nascent planet responds to these forces by migrating, typically inward. This migration eventually halts before planets crash into the Sun or other parent star, simply because the gas dissipates, or because other perturbations kick in to stabilize the inward migration. Asteroids would have been thoroughly destabilized by the resulting strong gravitational perturbations. This process may explain why some asteroids have highly inclined orbits. At the same time, destabilized asteroids ended up on very elongated orbits, bringing them closer to the Sun.