Physics
posted by Harry .
How many years would it take the planet to orbit the sun. How do you calculate. All I have is, that the planet is 97 times farther from sun than earth or 97 Astronomical units
Using Kepler's Law you find that the anser is 97^(1.5) years. You can estimate this without using a calculator:
97^(1.5) = (1003)^(1.5) =
[100*(1  3/100)]^(1.5) =
100^(1.5)*(13/100)^(1.5)=
1000*[11.5*3/100 + (1.5)*(0.5)/2 (3/100)^2 + term of order (3/100)^3] =
1000  45 + 27/80 + term of order 1/100
27/80 is about 1/3, so the answer is
955.3 years.
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