SOLUTION: Kepler's Third Law of planetary motion states that the square of the period T of a planet (the time it takes for the planet to make a complete revolution around the sun) is directl

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Misc -> SOLUTION: Kepler's Third Law of planetary motion states that the square of the period T of a planet (the time it takes for the planet to make a complete revolution around the sun) is directl      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 32194This question is from textbook College Algebra
: Kepler's Third Law of planetary motion states that the square of the period T of a planet (the time it takes for the planet to make a complete revolution around the sun) is directly proportional to the cube of its average distance d from the sun.
a.) Express Kepler's Third Law as an equation.
b.) Find the constant of proportionality by using the fact that for our planet the period is about 365 days and the average distance is about 93 million miles.
c.) The planet Neptune is about 2.79 x 10^9 mi from the sun. Find the period of Neptune.
The equation I got is T^2/d^3, but for b and c I'm confused about the units.
Thank you all so very much!This question is from textbook College Algebra

Answer by stanbon(57377) About Me  (Show Source):
You can put this solution on YOUR website!
a) T^2=kd^3
b)365^2=k(9.3E7)^3
k=[365^2]/[9.3E7)^3
k=1.656...E-19
c)T^2=[365^2/9.3E7^3][2.79E9]^3
T^2=7.8106E37
T=8.838E18 days per revolution