When one looks into the sky on a clear night, it is easy to forget that the stunning beauty of the night sky is full of mathematical equations.  Great mathematicians have spent hours observing and meticulously recording what they saw in the sky.  Then spent hours calculating what might later occur.  Then followed it by many more hours of observation to see if they were correct.  Sometimes things have been discovered because they were observed as different from the rest.  However, when Neptune was first seen as a planet on September 18, 1846 is was due to the mathematical calculations that predicted it would be there.

Many people had noticed that Uranus was straying from its predicted orbit.  There were many theories as to why this was.  Bouvard tried to update the published tables of Delambre with what he felt were more accurate tables, but soon even they turned out to be wrong.  George Biddelle Airy thought that the calculations were wrong because the inverse of a square law of gravitation must break down over large distances.  Others, however, such as John Couch Adams felt that there was another planet further away from the sun than Uranus, and that it was throwing off Uranus' orbit.  Airy did not agree with this, but Adams kept pursuing the posibility with research.  On October 1, 1845, Adams did something with math that was completely different then what math had been being used for.  He did a detailed study which calculated the mass of the "other planet".  Newtons theory of gravitation had never been used to predict the position of a body from observations of the effects of gravity on other bodies.  This made Adams all the more sure of the existence of another planet, and he went on to try to find it's location.

Urbain Jean Joseph Le Verrier was also of the school of thought that there was another planet beyond Uranus that was effecting the predicted path of Uranus' orbit.  LeVerrier and Adams were, however, unaware of each others work.  In June of 1846 LeVerrier published a work that showed other causes for Uranus' orbit being off its predicted path, including the ideas of Jupiter and Saturn effecting its course, and then went on to disprove all of them.  For him, this left only the possiblity of a new planet.

Adams had shown his work to Airy, who rejected his ideas and the two of them did not work together.  Later, however, when Airy saw the similarties between the work of LeVerrier and Adams, he worked with LeVerrier to find out more about this other planet that he felt he now had to pay attention to.  He didn't however mention the similarity in work of LeVerrier and Adams to either of them.

Airy told Herschel about the calculations for the new planet who inturn told Lassell.  LeVerrier told Galle about the calculations of the new planet's location and predicted orbit.  After making observations on the night of September 18, 1846, Galle confirmed that the new planet exists.  He was able to find it almost exactly where it had mathematically been shown to exist.  LeVerrier re-confimed it's existence on August 31 and October 1.

Later the work of both Adams and LeVerrier were acknowledged in there discovery of the new planet we now know as Neptune. They were able to go on and soon after mathematically discover Neptune's moon.  This is just one example of mathematics in planetary calculations.

Author: Maggie Cooper

References:
 http://www-groups.dcs.st.-andac.uk/~history/HistTopics/Neptune_and_Pluto.html