2. A Comet Orbit (20 pts.): a) Go to the Wikipedia list of periodic comets (http://en.wikipedia.org/wiki/List of periodic comets) and choose one that includes the following information on its page: orbit period, semi- major axis, eccentricity, and inclination. Record this information in your homework.
Verify by calculation that the orbit period and semi-major axis follow Kepler’s Third Law. (Keep significant digits in mind.)
b) Use the semi-major axis and eccentricity to calculate the perihelion and aphelion distance. Name the pair of planets that the comet is between when it is at perihelion and at aphelion (if it remains inside Neptune’s orbit). The planet pairs may be different.
c) Draw a side view of Earth’s and the comet’s orbits (so that the orbits appear as lines through the Sun) properly showing how much the comet’s orbit is inclined compared to Earth’s orbit. Make sure i) the Sun is clearly marked, ii) Earth’s orbit and the perihelion and aphelion distances have the proper scale, and iii) the angle between the orbits is correct (a protractor would be helpful). You will probably want to make sure your comet’s orbit can fit on the paper first, then draw in Earth’s orbit to scale.
d) Graph an ellipse with the same eccentricity as your comet, or use an online tool like http://astro.unl.edu/classaction/animations/renaissance/ellipsedemo.html or http://astro.unl.edu/classaction/animations/renaissance/kepler.html (If you can find a better website for the purpose, give the web address.) Measure the semi-major axis a and the distance from the center to a focus c on a printout, record the numbers, and show that the eccentricity is correct. Draw a properly scaled version of Earth’s orbit on the printout as well (you can represent it as a circle).
e) What is the ratio of the comet’s speed at perihelion compared to when it is at aphelion? How does this explain why comets tend to become bright for just a short part of their entire orbits?