Discovery of Planets by Numbers

In 1768, Bode published his law giving the distances of the planets from the Sun in terms of the distance of Earth.

Consider the series

0, 1, 2, 4, 8, 16, 32, 64, 128, 256, …..

Multiply by 3,

0, 3, 6, 12, 24, 48, 96, 192, 384, 768, …..

Add 4 to each term,

4, 7, 10, 16, 28, 52, 100, 196, 388, 772, …..

Divide by 10,

0.4, 0.7, 1.0, 1.6, 2.8, 5.2, 10, 19.6, 38.8, 77.2, …

Each term represents the distance of a planet from the Sun in our Solar family.

Mercury 0.39 a.u.,

Venus 0.72 a.u.,

Earth 1 a.u.,

Mars 1.52 a.u.,

-------,

Jupiter 5.2 a.u.,

Saturn 9.54 a.u.,

Uranus 19.2 a.u.,

Neptune 30.1 a.u.,

……

where 1 astronomical unit (a.u.) = Distance between the Sun and Earth.

When the law was formulated in 1768, Uranus, Neptune and Pluto had not been discovered.

Discovery of Uranus in 1781 confirmed this law.

Bode urged a search for a fifth planet. Ceres, the largest object in the asteroid belt, was found at Bode's predicted position in 1801. A group of small objects following the laws of Kepler was found at that distance. These small objects moving between the orbits of Mars and Jupiter are called minor planets or Asteroids.

Neptune was discovered in 1846. Pluto was discovered in 1930. However, the law does not hold good for Neptune and Pluto, for their distances from Sun are 30.1 and 39.5 a.u.s which are very different from the distances 38.8 and 77.2 as given by the law.

Numbers are like children; love them enough and they’ll tell you secrets.