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The Discovery of the Asteroid Belt

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The shield of the Science, Mathematics and Engineering faculty of the h2g2 University.
Near Earth Objects | The Discovery of the Asteroid Belt
Comets as Harbingers of Doom | Evidence of Meteorite Impacts
Asteroids and Meteorites - Mankind's Fate?

Before the discovery of the Asteroid Belt, many astronomers and mathematicians wondered why it is that the planets are arranged in the orbits that we see today. Foremost amongst their questions was: 'Why is there such a large gap between Mars and Jupiter?' There were many theories put forward in an attempt to explain this anomaly, but the first one that contemplated the existence of the Asteroid Belt was proposed by Thomas Wright in the mid-18th Century; he thought that it might contain a planet that had been smashed apart by a comet.

In his book of 1702, however, it was the astronomer David Gregory that noted the relationship between the planets' orbits and a simple mathematical number sequence. When this text was translated from its original Latin in 1715, it was taken as the basis of works by two German astronomers at the time, most notably Johann Titius and Johann Bode, who made it into what is today known as the Bode-Titius Law. What they discovered was this:

  • Take the simple mathematical series 0, 3, 6, 12, 24, 48, 96, 192. Notice that each number (apart from the 0 and 3) is double the previous one.

  • Now, add 4 to each number so that you get the series 4, 7, 10, 16, 28, 52, 100, 196.

  • Now divide each of those numbers by 10 to get the series 0.4, 0.7, 1.0, 1.6, 2.8, 5.2, 10.0, 19.6.

  • If, as the astronomers of the time were, you are familiar with the planets' average distances from the Sun, you'll notice that if you take Earth's orbit to be 1.0 (this is known as the Astronomical Unit, or AU), all the other numbers in this series correspond to each of the planet's orbital distances remarkably well.

This was a fascinating discovery because it could be used as a basic guide to predict where any other hitherto undiscovered planets might be in the Solar System. The table below shows how accurate this number series is for each of the planets known at the time (with the distance from the Sun being shown in AU):

PlanetCalculated DistanceActual Distance
Mercury0.40.39
Venus0.70.72
Earth1.01.00
Mars1.61.52
?2.8?
Jupiter5.25.20
Saturn10.09.54
Uranus19.619.19

That's a pretty good correlation for such a simple mathematical series!

Now, you'll notice that there is a 'rogue' number in there that doesn't seem to have a planet associated with it - between Mars and Jupiter at a distance of 2.8AU. No one had ever seen a planet that fitted this distance, so where was it? Obviously, the first thought was that this mathematical series theory was just a happy coincidence for the existing planets, except for this one mystery one. The other thought - which turned out to be the correct one - was that there was the remains of a planet, or at least something with the equivalent mass, sitting at that distance from the Sun. So, if it really was there, then what was it?

Unbeknownst to him, Titius had discovered the location of the Asteroid Belt, a cloud of rocks, some the size of a peanut, some the size of the UK, that were orbiting the Sun in a large ring. Collectively, they make up for the mass of another planet, although it's still not clear whether they are a planet that has been destroyed (perhaps after being hit by something itself, as Wright originally suggested), a malformed planet that never coalesced properly, or whether it has always been just a bunch of individual rocks, the leftovers from the formation of other planets. The existence of the Asteroid Belt also filled in that annoyingly large gap between the orbits of Mars and Jupiter that Titius' number theory predicted should hold another planet.

This theory is often wrongly attributed to Bode (and often cited as Bode's Law), but it was Titius that first discovered the number series for the planets, and Bode (two years later in 1778) that turned it into a related mathematical theorem that could be applied to any orbiting bodies, even moons around planets themselves1.

As Bode said: 'I cannot believe that the Founder of the universe left this space empty,' and he therefore proposed that an undiscovered planet lay at that distance from the Sun... but of course they weren't going to find it because it was all in tiny pieces.

It wasn't until a carefully orchestrated effort by a couple of dozen European astronomers around the very beginning of the 19th Century found the first asteroid, that had earlier been thought to be a wandering comet. The actual observation was recorded over three weeks by the Italian astronomer Piazzi, who named the body Ceres Ferdinandea - Ceres for the patron goddess of Sicily, and Ferdinandea for Piazzi's royal patron. A distance calculation showed it to be at a distance of 2.77AU, a remarkable correspondence to the 2.8AU predicted by the Bode-Titus number sequence. Now they knew what to look for, as well as where to look, astronomers soon discovered many more asteroids, and now we know of thousands of them. Ceres is still the largest ever discovered at roughly 915km in diameter, with the next largest being Pallas (523km), Vesta (501km) and Juno (244km).

Interestingly, it was the Bode-Titius Law that helped locate the next planet out as well - Neptune - in 1846.

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1The mathematical law is: Pn = P0An, where n is the number of the planet (starting with Mercury = 1), Pn is the period of orbit of the nth planet, P0 is the period of the Sun's rotation, and A is the semi-major axis of the nth planet's orbit. This means that if you plot a graph of planet number (n) against the logarithm of the period of orbit, you will get a straight line, indicating the mathematical relationship (and, rather niftily, giving you the rotational period of the Sun at n=0).

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