SOLUTION: Hi I need help with 3 word problems. I don't even know where to begin. This is from my textbook. According to Kepler's third law of planetary motion, the average radius R of the

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Question 187404: Hi I need help with 3 word problems. I don't even know where to begin. This is from my textbook.
According to Kepler's third law of planetary motion, the average radius R of the orbit of a planet around the sun is determined R=T^2/3, where T is the number of years for one orbit and R is measured in astronomical units.
a. It takes Mars 1,881 years to make one orbit of the sun. What is the average radius in AUs of the orbit of Mars?
b.The average radius of the orbit of Saturn is 9.05 AU. How many number of years does it take for Saturn to make one orbit of the sun?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Remember that a fractional exponent means raise to the power of the numerator and take the root of the denominator



Alternatively you could say:



Same thing. Now all you need to do is substitute the given value for T and start punching buttons on the calculator:



For the other problem, you need to solve:



for T by cubing both sides, and then taking the square root:



Now, just plug in the given value for R and get to work with your calculator.

John