SOLUTION: DIRECT VARIATION: Kepler's third law states that in the solar system, the square of the period of the planet varies directly as the cube of its mean distance from the Sun; the m

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Question 1104508: DIRECT VARIATION:
Kepler's third law states that in the solar system, the square of the period of the planet varies directly as the cube of its mean distance from the Sun; the mean distance of the Earth from the sun being 92.9 million km and its period is one year. Find the period of Venus whose mean distance from the Sun is 67.2 million km.
Found 3 solutions by josgarithmetic, ikleyn, Alan3354:
Answer by josgarithmetic(39628) About Me  (Show Source):
Answer by ikleyn(52866) About Me  (Show Source):
You can put this solution on YOUR website!
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According to the Kepler's law, you have this proportion

T%5Bv%5D%5E2%2FT%5Be%5D%5E2 = D%5Be%5D%5E3%2FD%5Bv%5D%5E3,


where T is the period, D is the mean distance, the index "e" relates to the Earth, while the index "v" relates to Venus.


You can use ANY consistent units for the distance; I will use  millions of kilometers  to avoid unnecessary degrees of 10.


So, my proportion is

T%5Bv%5D%5E2%2F1%5E2 = 67.2%5E2%2F392.9%5E3,


which implies

T%5Bv%5D%5E2 = %2867.2%2F92.9%29%5E3 = 0.38,


T%5Bv%5D = sqrt%280.38%29 = 0.62.


Answer.  The period for Venus is 0.62 of an year,  or  225 days.


Check.  The Internet sources say  224.7 days.


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Kepler's third law states that in the solar system, the square of the period of the planet varies directly as the cube of its mean distance from the Sun; the mean distance of the Earth from the sun being 92.9 million km and its period is one year. Find the period of Venus whose mean distance from the Sun is 67.2 million km.
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The distances are in miles, not kilometers.