Comet ISON is one of the more recent comets that was originallycalled the \"comet of the century\" but turned out to be lessspectacular than predicted, while in the mid-1990s, there were twoother very bright comets visible that made them real \"comets of thecentury\". Still, though, let's compare their orbits.

a) Here is the link to the ephemeris for ISON:http://scully.cfa.harvard.edu/cgi-bin/returnprepeph.cgi?d=c&o=CK12S010(Links to an external site.)Links to an external site. -- note thatq is the perihelion distance, and e is its eccentricity. Why don'tthey list a semi-major axis or period for its orbit? Can youdescribe what happened after its perihelion passage and how thatrelates to the values you gave previously?

b) Here is the link to the ephemeris for Hale-Bopp:http://www2.jpl.nasa.gov/comet/ephemjpl8.html (Links to an externalsite.)Links to an external site. -- note that q and e are providedfor it, too. Calculate its semi-major axis in AU.

c) Calculate the aphelion and perihelion velocities forHale-Bopp. Calculate the circular velocity for an object with acircular orbit with a radius equal to the aphelion distance ofHale-Bopp. How much would you have to change the velocity of anobject on a circular orbit at that distance to put it on an orbitlike Hale-Bopp's? What mechanisms do you know of that wouldpotentially be able to change an object's velocity by thatmuch?