# Halley’s Comet

English astronomer Edmund Halley examined reports of a comet approaching near to Earth in 1531, 1607 and 1682 and from this he made an accurate calculation for its return.  Chinese astronomers recorded this observation as early as 239 BC.  Ancient astronomers saw the appearance of any comet as an isolated event and it wasn’t until 1695 that Halley suspected this was same comet returning over and over again. Astrologers regarded comets as being a sign of great disaster or a symbol of evil power which brought forth natural disasters, human-related disorders, slaughter or some significant change.

Halley saw the comet in 1682 when he was 26 years old, but since he died in 1742 he did not live long enough to see it return again in 1759.  Halley used advanced mathematics to figure out the return of this comet, he did not just subtract years to come up with the return being every 75 years or 76 years.  The math behind this prediction involves perturbation theory and three-body motion.  Comets move according to Newton’s laws of motion and gravity, but the gravitational influence of each planet that the comet passes by during its entire course needs to be considered.  Simple math would reveal that the comet had returned in a seventy-six year period from 1531 to 1607, and a seventy-five year period from 1607 to 1682, but this did not include perturbational effects which might be accelerating or retarding the return of the comet.  Since we have been studding this comet, its return has varied between 74.4 and 79.2 years.  Over time we have gotten much better at making the prediction for the return of Halley’s Comet and in 1986, it was off by less than five hours.

In simple two-body math the comet forms an elliptical orbit around the Sun.  Three body math is needed to describe the orientation of the ellipse in space relative to some coordinate system, and a fourth quantity is required if one wishes to define the location of a body in that elliptical orbit.  Alexis Clairaut, a French astronomer and mathematician working with the aid of Madame Lepaute another French astronomer, accomplished the cumbersome calculations and found that the combined effect of Jupiter and Saturn would delay the return of the comet for another 618 days and they predicted that it would not be observable until before April in 1759.  The return of the comet to its perihelion (the point in the comet’s orbit when it is nearest the Sun) in March 1759 was a triumph for the science of Newtonian laws, and it added validity for solution methods to three-body problems.

It is theoretically possible to view Halley’s Comet throughout its entire 74 to 79 year-orbit, although seeing it with your naked eye at night, when it’s actively emitting dust and gas, and it is close to the Earth will last only for several weeks.  The last time it was here was in 1986, and it is projected to return in 2061.