SOLUTION: hey guys this is a two part problem not doing so great on I could use your help please. 115. Kepler’s third law. According to Kepler’s third law of planetary motion, the ratio

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Question 182080: hey guys this is a two part problem not doing so great on I could use your help please.
115. Kepler’s third law. 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. Find the average radius of the orbit
of Saturn. (One AU is the distance from the earth to
the sun.)
116. Orbit of Venus. 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 in question115
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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115. Kepler’s third law. 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. Find the average radius of the orbit
of Saturn. (One AU is the distance from the earth to
the sun.)
:
t%5E2%2Fr%5E3 = 1
As you can see by the data given about Jupiter
11.86%5E2%2F5.2%5E3 = 140.6596%2F140.608 ~ 1
:
to find the r of Saturn:
1 = 29.46%5E2%2Fr%5E3
1 = 867.8916%2Fr%5E3
therefore
r^3 = 867.8916
r = 867.8916^(1/3)
r = 9.54 au is the radius of the orbit of Saturn

116. Orbit of Venus. 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 in question115
;
Find the yrs for Venus to complete 1 orbit
t%5E2%2F.723%5E3 = 1
t%5E2%2F.3779 = 1
t^2 = .3779
t = sqrt%28.3779%29
t = .6147 yrs or .6714 * 365 = 223.4 days