Question 1025907
Kepler’s Third Law of planetary motion states that the square of the period T of a planet (the time taken for a complete revolution around the sun) is proportional to the cube of its average distance d from the sun.
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(a) Express Kepler’s Third Law as an equation. 
T^2 = k*d^3
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(b) Find the constant of proportionality. Note that the average distance the Earth is from the sun is 150 million kilometers, according to Wikipedia. You will also need some of your Earth knowledge. 
T^2 = k*(150x10^6)^3
k = T^2/(150x10^6)^3
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(c) Based on the idea of proportionality, if the average distance away from the sun was to double, would the period double also? If not, what is the percentage change?
Note: T = sqrt(k*d^3)
If d is doubled, T^2 = k*(2d)^3
T^2 would equal 8k*d^3
T would be 2sqrt(2)*sqrt(kd^3)
Percent change = 2sqrt(2) = 283%
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(d) Neptune is approximately 30 times as far away from the sun as Earth. Without using the specific number of kilometers, what is the period of Neptune? Does your answer correspond with the value from other sources?
I'll leave that to you.
Cheers,
Stan H.
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