In 1705, Edmund Halley (1656–1742), an English astronomer, claimed that the comet sighting...

In 1705, Edmund Halley (1656–1742), an English astronomer, claimed that the comet sightings of 1531, 1607, and 1682 were all the same comet and that, after some rough calculations accounting for the influence of the larger planets, this comet would return again in 1758. Halley did not live to see the comet’s return, but it did return late in 1758 and reached perihelion in March 1759. In honor of his prediction, this comet was named “Halley.”

Each elliptical orbit of Halley is slightly different, but the average value of the semimajor axis a is about 17.95 AU*. Using this value, along with the fact that its orbital eccentricity is 0.967 (the orbit is drawn to scale, but the Sun is shown to be 36 times bigger than it should be), determine

(a) the orbital period in years of Halley’s comet, and

(b) its distance, in AU, from the Sun at perihelion P and at aphelion A. Look up the orbits of the planets of our solar system on the Web. What planetary orbits is Halley near to at perihelion and aphelion?

Use 1.989×1030 kg for the mass of the Sun.

Figure P5.99