Where is the missing planet?

L-R: Asteroid Vesta photographed by the spacecraft Dawn. Asteroid Belt.

In 1766, a German physicist named Johan Titius found a simple mathematical rule to explain the arrangement of the planets in the Solar System. The rule was popularized by another German named Johann Bode and today it is known as the Titius-Bode Law. The law relates the average distance of a planet from the Sun in terms of the average Earth-Sun distance which is one astronomical unit (a.u.) or 93 million miles.
Consider the sequence of numbers 0, 3, 6, 12, 24, 48, 96, and so on. Each of the numbers, except the first two, is double its predecessor. Now add 4 to each number in the sequence and divide the sum by 10; we end up with the numbers 0.4, 0.7, 1.0, 1.6, 2.8, 5.2, and 10.0 which correspond closely to the observed planetary distances in astronomical units. How simple but remarkable the law is. The only problem is with the 2.8 a.u. where no planet was known to exist. The discovery of Uranus in 1781 and the recognition that its measured distance of 19.2 a.u. is close to the distance (19.6 a.u.) given by the next number (192) in the sequence aroused a great deal of interest in the "missing" planet between Mars and Jupiter.
Astronomers set out to find the missing planet and on the first night of 1801, a Sicilian monk Giuseppe Piazzi discovered an object 2.77 a.u. away from the Sun. He named it Ceres, after the patron goddess of Sicily. In early 1802, the Viennese physician Heinrich Olbers discovered another faint, star-like object much smaller than Ceres. He named it after the Greek goddess of wisdom Pallas. Between 1802 and 1807, two more small planet-like bodies, Juno and Vesta, were discovered between 2.3 and 2.8 a.u. The small size of these objects precluded them from being characterized as planets. Instead, they were called "minor planets" or asteroids (Greek for "star-like"). Just like the planets, they orbit around the Sun in the same direction.
Since Ceres or Pallas, the two largest asteroids, is not the missing planet, the question arose: Did the missing planet even exist? There are many views about the origin of the asteroids. Some astronomers speculated that perhaps they are objects left over from the giant cloud of gas and dust that condensed to create the Sun, planets, and moons some 4.6 billion years ago. Others suggested that they are the residuals of large planetary embryos that were destroyed in a massive collision long ago. The most natural explanation seems to be that there had once been a full-sized planet that somehow broke apart or exploded to produce a population of rocky matters orbiting between Mars and Jupiter that never successfully coalesced into a planet. The search was on to discover this population.
By mid-1800's several hundred more asteroids were discovered. As of today, there are over 500,000 of these vagabonds with known orbits about the Sun. The region of the solar system between the orbits of Mars and Jupiter where most of these nomads are is called the "asteroid belt" and the asteroids are called "belt asteroids." There are also asteroids outside of Jupiter's orbit. They are known as Trojan asteroids.
Some asteroids come perilously close to the Earth and are known as Earth-Crossing asteroids. They generally survive 10 million years or so before colliding with the Earth. In the past, the Earth has been hit many times by these asteroids. Depending on their size, such a collision can cause massive damage on local to global scales.
It is believed that sometime in the near future, the Earth will suffer a colossal cosmic impact. Will it be this year? Let us hope that the Mayans are messed up with their calendar or the asteroids miss us. How could a civilization that could not predict the demise of its own culture foretell our destruction? Even if the Mayans are right, we have until December to figure out how to alter their orbit or destroy them in space before we meet with the same fate as the dinosaurs.

The writer is a Professor of Department of Physics & Engineering Physics, Fordham University, New York.