Buckle Up

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Summer arrives in style with blazing heat and glorious sunshine. Fashionistas everywhere browse through crowded wardrobes to pick out the most trendy outfit. Day after day, they boast a vivid rainbow of well-constructed attire and accessory combinations. However, there’s one person I know who leads a much more simplistic lifestyle. All they ever seem to wear is their belt…

I am, of course, referring to our very own Solar System’s asteroid belt. This is a ring of millions of rocky bodies that occupy the space between the orbits of Mars and Jupiter. Over half of its total mass is given by four main asteroids: Ceres, Vesta, Pallas, and Hygiea. The rest is mostly dust-sized material that is very thinly distributed.

So how did the asteroid belt come to be? For a long time, scientists believed that the layer of small rock fragments was a result of the destruction of a planet which had been bombarded and broken apart by high-energy comet impacts. This hypothesis became disregarded based on the amount of energy required to perform such demolition, and considering the total mass of the asteroid belt, which sums up to only about 4% the mass of the Earth’s moon.

In the primordial Solar System, most planets would have been formed out of large clouds of rock and dust that was gradually brought together into clumps due to the effects of gravitation. Clumps of a certain size are called planetesimals, which would be able to attract other particles towards itself with its sufficient gravitational influence. As the ‘planetary embryos’ collided with each other and accreted more mass, they began to make up as much mass as our present day Mars, forming planets. The four planets closest to the Sun are what make up the terrestrial region of our Solar System, and were formed in such a stable configuration. The gravitational influence of these newly-formed planets, combined with the perturbations of Jupiter, which was the first planet to be formed in the Solar System, caused primordial asteroids in the planet-nebula to be excited. Most of them were ejected out of the system, with only less than 1% surviving in the space between Mars and Jupiter.

At present day, we would expect objects within the asteroid belt to take orbits similar to most other planets in our solar system, an almost circular, coplanar one. What we tend to find, however, is that the distribution of asteroids in the belt take up the general shape of a ‘donut’ or torus, with the hole covering the terrestrial region of the Solar System. Despite the tiny overall mass, there is a very wide spread in the eccentricities and inclination of the orbits.

Contrary to what scientists originally believed, research has shown that this is not caused by the gravitational influence of other planets as they are now. The problem lies in the fact that the large bodies such as Jupiter and Saturn can only exert their influence in specific spots, and not across the whole asteroid belt. Orbital resonance is an effect in celestial mechanics which occurs when two orbiting bodies exert a periodic gravitational influence on each other at the same place in the orbit. This happens if their orbital periods, the time taken to complete one orbit around the Sun, are related by a ratio of two small integers. The repeated acceleration adds up over time and amplifies, acting like a gravitational slingshot. In the majority of cases, this will result in an unstable interaction as the smaller body gains so much orbital energy that it will be thrown into a higher orbit, losing the resonance. Therefore, if there are asteroids with orbits which resonate with the orbit of Jupiter, they will get thrown out of their orbit.

Over time, this effect has left bands of gaps in the asteroid belt, where material has been pushed out of occupying that space. There are known as Kirkwood gaps, the most prominent of which have the following orbital resonances with Jupiter – 3:1, 5:2, 7:3, 2:1, as shown in the graph below. AU stands for Astronomical Unit, and is a unit of length representing the distance between the Earth and the Sun.

kirkwood_gaps
Image: Professor Quibb

This effect does not explain, however, why the orbits of asteroid are so wild across the entire belt.

Recent studies, which involve numerical simulation of the orbits of bodies, have shown that currently, the most plausible explanation for this is due to the characteristics of the early orbits of Jupiter and Saturn. The only simulation which can be made to match the eccentric and tilted orbits of asteroids, the thin mass distribution of the asteroid belt, and the oddly small size of Mars, is one in which the orbits of Jupiter and Saturn were chaotic. This led to their orbital configurations jumping around unpredictably, expanding and contracting erratically, which, in turn, meant that their resonances with other bodies moved constantly, depending on the orbit of the gas giant at the time. This model is known as “The Grand Tack”, and shows Jupiter migrating inwards from 3.5 AU to 1.5 AU, where it’s movement is reversed through orbital resonance with Saturn and it finally arrives at its current orbit of 5.2 AU.

It seems like even the planets need to get away from the chaos of life once in awhile.

Harvey

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