One of Kepler's three laws of planetary motion states that the square of the period, P, of a body orbiting the sun is proportional to the cube of its average distance, d, from the sun. The Earth has a period of 365 days and its distance from the sun is approximately 93,000,000 miles.

a.) Find P as a function of d.
b.) The planet Venus has an average distance from the sun of 67,000,000 miles. How many earth days are in a Venus year -- in other words, what is the period of the planet Venus?

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  1. P^2 = kd^3
    That means that
    P^2/d^3 = k, a constant
    So, you want to find d such that
    P^2/67 = 365^2/93
    You can ignore all those zeroes, as they cancel out

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