SOLUTION: 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 i

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Question 1025920: 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
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?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
T= period of a planet
d= distance from that planet to the sun
Kepler’s Third Law of planetary motion states that
T%5E2=k%2Ad%5E3
Let us measure T values in Earth-years,
and let us use the subscripts E for Earth and N for Neptune.
For Neptune,
T%5BN%5D%5E2=k%2Ad%5BN%5D%5E3 .
For Earth,
T%5BE%5D%5E2=k%2Ad%5BE%5D%5E3 .
Dividing one equation by the other,
T%5BN%5D%5E2%2FT%5BE%5D%5E2=k%2Ad%5BN%5D%5E3%2F%28k%2Ad%5BE%5D%5E3%29
Since we are measuring T values in Earth-years
T%5BN%5D%5E2%2F1%5E2=d%5BN%5D%5E3%2Fd%5BE%5D%5E3
T%5BN%5D%5E2=%28d%5BN%5D%2Fd%5BE%5D%29%5E3
Since we are told that Neptune is approximately 30 times as far away from the sun as Earth,
we can use d%5BN%5D%2Fd%5BE%5D=30 .
So, T%5BN%5D%5E2=30%5E3
T%5BN%5D%5E2=27000
T%5BN%5D=sqrt%2827000%29
T%5BN%5D=about164
So, the period of Neptune is about highlight%28164%29 Earth-years.
NASA says Neptune has a period of 164.8 Earth-years,
and that its distance from the sun is 30.07 AU,
so the calculated value is as close as could be expected.