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ps4_oct2011 - Problem set 4 Ge/Ay 133 Due 03 November 2011...

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Problem set 4 Ge/Ay 133 Due 03 November 2011 1 Gaps and migration (a) Large planets open gaps in disks and then become tied to the evolution of the disk. Thus, if the disk is evolving on the viscous timescale, the planet will also migrate on the viscous timescale. Based on the viscous disk evolution timescale discussed in class, write an approximate expression for the speed of the migration for a giant planet which has formed a gap. (b) Assume that every planetary system forms planets at 5 AU and then these planets migrate inwards on the viscous timescale. Then, at some random time, the gas in the disk instantly disappears (halting migration). If this happens in a huge set of planetary systems, what dis- tribution of semi-major axes might you expect to observe in planetary systems? (You can try your own simulation, or else create a sketch of what you think it will look like.) (c) Compare this predicted distribution to that of extrasolar planets. Be sure to consider the (severe) biases in the discoveries of extrasolar planets. You can make your own up-to-date plot
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