SOLUTION: When I use the formula T^2/R^3 (Kepler's third law). The only variable given in the problem is the variable for R (which is 0.723 Astronomical Units). When I replace the R with t

Question 144808: When I use the formula T^2/R^3 (Kepler's third law). The only variable given in the problem is the variable for R (which is 0.723 Astronomical Units). When I replace the R with that factor. How can I solve the equation. I tried setting it equal to 0 but that is going to make the answer 0. In case you cannot find the problem, I am indicating it here:
#108) If the average radius of the orbit of Venus is 0.723 AU, then how many years does it take for Venuis to complete one orbit of the sun? Use the information in Exercise 107
FOR REFERENCE #107)Kepler's third law.
According to Kepler's third law of planetary motion, the ration T^2/R^3 has the same value for every planet in our solar system. R is the average radius of the orbit of the planet measured in astronomical units (AU), and T is the number of years it takes for one complete orbit of the sun.
Found 2 solutions by Earlsdon, MathLover1:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Kepler's third law of planetary motion is:
where: T = time of orbital period (years) and R= the average orbital radius (semi-major axis).
You want to solve for T for the planet Venus and you are give that R = 0.723 AU.
Take the square root of both sides.
Substitute R = 0.723
Use your calculator to get:
Years.

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

Kepler's Third Law:

Given:
Astronomical Units
�� stands for one complete orbit of the sun

Earth years
��which is Earth days
Or approximately
Earth years��which is Earth days

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