ps5_nov2011

ps5_nov2011 - planets, and estimate how much their orbits...

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Problem set 5 Ge/Ay 133 Due November 10 More MMSN Scattering of planetesimals in the outer solar system caused the orbits of Saturn, Uranus, and Neptune to expand. Using adiabatic theory, one can show that the eccentricies of the KBOs grow as they are pushed outward so that the Fnal eccentricity is related to the initial eccentricity and begining and ending semimajor axes of Neptune as: e 2 KBOfnal (1 / 3) ln ( a Neptune fnal /a Neptune initial ) + e 2 KBOinitial . a. How much did Neptune’s orbit have to expand to account for Plutinos with eccentricities as high as 0.34? b. Using conservation of angular momentum, estimate to order of magnitude precision the amount of mass that Neptune needs to have scattered inward to account for this motion. c. Make a hand waving argument about the movement of the other giant
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Unformatted text preview: planets, and estimate how much their orbits expanded or contracted. d. Assuming the starting orbital positions you calculated above, make a plot of the surface density in this minimum mass solar nebula. Be sure to use the original masses of the planets (as calculated in Problem Set 2). e. Discuss timescales for the formation of Uranus and Neptune in your new minimum mass solar nebula. Are there still problems? f. If you extrapolate your new MMSN, how much mass resides in the 10 AU region beyond Neptune. How does this compare to the mass of the present-day Kuiper belt? How does this compare with the mass that you calculated that Neptune need have scattered? Comments? 1...
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This note was uploaded on 01/03/2012 for the course GEL 133 taught by Professor List during the Fall '10 term at Caltech.

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