A Missing Planet?

In the late 1700s some astronomers started to suspect there was a missing planet. How could such an idea arise? Certainly the ancient astronomers would not think of such a thing, the Sun, Moon, and five planets made 7 objects that moved against the background of fixed stars. Seven was considered a perfect number so there was no such thing as a missing planet. That would be a bit like us today worrying about a missing sun. Also when the Solar System was viewed as made of cycles and epicycles, relative distances really didn't matter that much, only periods of revolution. Such models gave no hint at a missing planet.

Copernicus was the first to develop a good map of the Solar System in the mid 1500s. He actually derived the relative size of the orbits of the planets based on astronomical measurements of their positions. Later, Johannes Kepler believed the Copernican system and using accurate planetary positions measured by Tycho Brahe worked out an accurate map of the orbits in the early 1600s. Kepler viewed Earth as another planet, moving under the same laws as the rest of the planets. The relative sizes of the orbits were now known, but not the actual scale. However, relative sizes are enough to show the overall pattern. The spacing between the orbits of Mars and the next planet, Jupiter seemed larger than expected. Kepler was aware of the extra space and considered that an unkown planet might be there, but nothing came of it at the time.

Titius-Bode Law

Note the timing in the following events. In 1766 Johann Titius mentioned a pattern in the arrangement of the orbits out to Saturn. In 1778 J.E. Bode gave a simple mathematical expression for the arrangement and also predicted a new planet in the gap between Mars and Jupiter. The gap could also be considered as evidence against the relationship, now known as Bode's Law or Titius-Bode Law. However, in 1781 William Herschel discovered the planet Uranus beyond Saturn, and its orbit fit Bode's Law, strengthening the belief that a planet should exist in the gap. In 1801 the missing planet was found. Or so it was first thought, more on this later.
Orbits of the planets out to Uranus
A snapshot from a modern planetarium program (Starry Night) shows the orbits of the 7 innermost planets. The sun is the black spot at the center of the image, the orbits of the seven planets from the sun out are: Mercury (red), Venus (gray), Earth (green), Mars (orange), Jupiter (red), Saturn (orange), and Uranus (gray).

The gap between Mars and Jupiter is more apparent if the the actual orbit size is plotted against planet number as shown at right. On top of that is plotted the orbit sizes predicted by Bode's Law. The Semimajor axis is 1/2 the long axis of the elliptical orbit. AU mean Astronomical Unit, intended to be 1 for the Earth's semimajor axis.

Note that Bode's Law predicts an orbit between Mars and Jupiter, where no planet was known to exist.

Before leaving Bode's Law it should be stated that it doesn't work well for the later planets, Neptune and Pluto, and is not an actual law such as Kepler's Laws of planetary motion. There has been speculation on why it fits as well as it does.

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