SOLUTION: According to Kepler’s third law of planetary motion, the ratio 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 m

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Question 149808: According to Kepler’s third law of planetary motion, the ratio 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 and T is the number of years it takes for one complete orbit of the sun.
If the average radius of the orbit of Venus is 0.723 AU, then how many years does it take for Venus to complete one orbit of the sun? Use the information above to solve this problem.

Found 2 solutions by vleith, nerdybill:
Answer by vleith(2517) About Me  (Show Source):
You can put this solution on YOUR website!
You need to set up a ratio. For Earth we know that T = 1 and R = 1. So the ratio is 1^2/1^3 = 1 for Earth.
Now we need to use the information provided to find out about Venus
1+=+T%5E2%2FR%5E3
1+=+T%5E2%2F0.723%5E3
0.723%5E3+=+T%5E2
0.378+=+T%5E2
sqrt%280.378%29+=+T
0.615+=+T+
So Venus takes a trip around the sun every 0.615 years = ~224 days. She's zippin' right along

Answer by nerdybill(5404) About Me  (Show Source):
You can put this solution on YOUR website!
The key is to know that T^2/R^3 has the value 1 for all planets in the Solar System.
.
Knowing this we can now have the following relationship:
1 = T^2/0.723^3
.
Solving for T:
1 = T^2/0.723^3
0.723^3 = T^2
sqrt(0.723^3) = T
0.615 years = T