direct variations

Question

Using Earth's time of 1 year and mean distance of 93million miles. Find the equation relating T and a. What the question is aaking? 93 milliona=1t?

Answer 1

You don't have the whole question. You are given data for the earth of T = 1 year and the average orbital radius, a = 93 million miles. You need to be given the period in earth years and orbital radius for another planet. Your analysis would involve comparing the ratios:

a_P/a_E = (T_P/T_E) ⁿ and solving for n using n = ln(a_P/a_E)/(ln(T_P/T_E))

You will get n = 2/3 due to Kepler's 3rd Law.

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