Posted by Mandy on Thursday, October 11, 2007 at 8:54pm.
b. Neptune takes about 5.2 x 10^9 seconds to go around the sun. What is the average radius of Neptune's ath around the sun?
c. The time it takes a planet to go around the sun is called a year. Compare Neptune's year with Earth's year. Which planet has the longer year? How much longer is it.?
b-Since the planet;s period is defined by P = 2Pisqrt(r^3/µ), where r == the planets orbital radius and µ = the gravitational constant of the sun, solving for r yields r = (µP^2/4Pi^2)^(1/3).
Thus,
r = [4.68772x10^21(5.2x10^9)/4Pi^2]^1/3 = 2,794,059,276 miles.
c-Substitute the Earth's mean radius, 92,960,242 miles, and Neptunes mean radius, just calculated, into the expression for period given above, to get the comparison of orbital periods.
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