Chris D.

asked • 03/26/18

It takes Neptune 165 years to orbit the Sun Find its distance from the Sun in AU

How to solve the problem?

1 Expert Answer

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Arturo O. answered • 03/26/18

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Use Kepler's 3rd law.
 
T = period of orbit
a = average distance from Sun
 
T2/a3 = constant for all planets in our solar system
 
For the Earth,
 
T2/a3 = (1y)2/(1 AU)3
 
For Neptune,
 
T2/a3 = (165 y)2 / a3
 
T2/a3 must be the same for the Earth and Neptune, so
 
(165 y)2 / a3 = (1y)2 / (1 AU)3
 
a = (165)2/3 AU ≅ 30.1 AU 
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