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Halley's Comet

# Halley's Comet - THE ORBIT OF HALLEYS COMET THANHTRINH...

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THE ORBIT OF HALLEY’S COMET THANH TRINH MTH 253

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I. Introduction: To analyze the orbit of Halley’s Comet is using Kepler’s first two laws of planetary motion. Why do we have to analyze only Halley’s Comet? Comets, like all planets, orbit the Sun in elliptic orbits, but Halley’s orbits are very eccentric (the major axis is much larger than the miner axis). Edmond Halley, the famous English astronomer and mathematician, predicted that the comets seen in 1531, 1607, and 1682 in 1705 are all the same comet and would return in 1758 by using Newton’s newly formulated laws of motion. The comet did, indeed return as predicted and was later named in his honor. Coincidently, in 1609, Johannes Kepler discovered that planets and comets orbit the Sun in elliptic orbits and that their orbital velocity is not constant but varies. Briefly Kepler’s biography, Johannes Kepler was a brilliant mathematician who lived in the last sixteenth and early seventeenth century, a contemporary of Tycho Brahe, Galileo, and Queen Elizabeth I. In order to gain access to the best measurements of planetary motions in the world, he became Tycho Brahe’s assistant, and his job is to analyze. The following Kepler’s first two laws: 1- Kepler’s first law is about shape of the orbit and it said “ The planets move in ellipses, with the Sun at one focus .”
2- Kepler’s second law is about motion around the orbit “ The line joining the Sun to a planet sweeps out areas in equal time. From first two laws, Kepler developed the equation called Kepler’s Equations, which are the exact implicit and the approximate explicit equations for E (eccentric anomaly). II. Main Presentation: A- Kepler’s first two laws: 1. The planets orbit the Sun in elliptic orbits with the Sun at one of the focal points. 2. The line joining the Sun to a planet sweeps out equal areas in equal time. Basically, Kepler’s first law is about all the planets orbit the Sun elliptically. An elliptical orbit is characterized by two parameters. The first parameter is called semi- major axis , and represented by the letter a . Also, it is the average distance of the planet from the Sun. The second parameter that characterizes an elliptical orbit is called the

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