What is the orbital radius (in AU) of Neptune if its period is 163.78 Earth years?

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07-05-2022
Biology

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What is the orbital radius (in AU) of Neptune if its period is 163.78 Earth years?

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Atoro8150 Atoro8150 · Answer 1 · 2022-05-07T18:47:50+02:00

Step-by-step explanation
Solution:

Step 1:
Use the Kepler's third Law
P2 = a3 where:
P = measurement in earth years
a = distance in units of AU

Step 2
Substitute the value
(Since we are looking for the orbital radius, we will use the formula a3 = P2)
a3 = P2
a3 = (163.78)2
a3 = 26,823.8884

Step 3
Get the cube root of your answer in step 2 to get the appropriate value "a"
cube root of 26,823.8884 = 29.9 AU