SOLUTION: The average radius (R) of the orbit of a planet around the sun is determined by R = T⅔ , where T is the number of years for one orbit and R is measured in astronomical uni

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Question 1104560: The average radius (R) of the orbit of a planet around the sun is
determined by R = T⅔
, where T is the number of years for one orbit and
R is measured in astronomical units (AU).
a. If it takes Neptune 164.97 years to make one orbit of the sun,
then what is the average radius of the orbit of Neptune?
b. If the average radius of the orbit of Pluto is 39.53 AU, then
how many years does it take Pluto to complete one orbit of the
sun?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The average radius (R) of the orbit of a planet around the sun is determined by R = T^⅔, where T is the number of years for one orbit and R is measured in astronomical units (AU).
:
a. If it takes Neptune 164.97 years to make one orbit of the sun,
then what is the average radius of the orbit of Neptune?
R+=+164.97%5E%282%2F3%29
calculate
R = 30.079 AU
:
b. If the average radius of the orbit of Pluto is 39.53 AU, then
how many years does it take Pluto to complete one orbit of the sun?
let t = no. of years
t%5E%282%2F3%29 = 39.53
Using natural logs
ln%28t%5E%282%2F3%29%29 = ln(39.53)
the log equiv of exponents
2%2F3*ln(t) = ln(39.53)
2%2F3*ln(t) = 3.677056
ln(t) = 3.677056*3%2F2
ln(t)= 5.5156
find e%5Ex
t = 248.54 years to orbit the sun