# physics

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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 -

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
and probably also in your textbook.

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