Homework Help: physics

Posted by Anonymous on Monday, November 23, 2009 at 9:41am.

Mercury is an average distance of 5.79 x 107 km from the Sun. Estimate the length of the Mercurian year given that the Earth is 1.50 108 km from the Sun on the average.

An explanation of how to do this would be great, thanks.

physics - drwls, Monday, November 23, 2009 at 9:48am
Use Kepler's third law. There is a particuarly simple form of it
P^2 = a^3
if you measure the period (P) in years and the distance (a) in astronomical units (a.u.). The earth's distance from the sun is 1 au. Mercury's is 5.79*10^7/1.50*10^8 = 0.386 au

You will find the formula at
http://www.windows.ucar.edu/tour/link=/the_universe/uts/kepler3.html&edu=high
and probably also in your textbook.

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