If the average radius of the orbit of Venus is 0.723 AU, then how many years doe

Question

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? 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 (AU), and T is the number of years it takes for one complete orbit of the sun. Jupiter orbits the sun in 11.86 years with an average radius of 5.2 AU, whereas Saturn orbits the sun in 29.46 years.

Explanation / Answer

The specific answer is 224.7 days (.6156 years) - but that's just looking it up. To calculate it, think of this as an algebra word problem. An AU (astronomical unit) is the distance from the Earth to the Sun, so Earth = 1AU. That means that .723 AU is essentially 3/4 (.75) the distance from the Sun to the Earth, thus Venus is 3/4 (.75) the distance from the Sun as Earth. The ratio you are speaking of equals 1 (1 year squared divided by 1 AU cubed is still 1). So if t^2/r^3=1, then t^2/(.723^3)=1, t=[squareroot:(.723^3)]=.6147 years (close enough to the .6156 year value given when I looked it up). *if you don't understand my t=sqrrt part, t=.723^(3/2), if you type that exactly the same way into your calculator ".723^(3/2)" that is the same as cubing (.723), then taking the square root.

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