Posted by **Mandy** on Thursday, October 11, 2007 at 8:54pm.

The average radius r in meters of a planet's path around the sun is given by the formula r=[(3.35 x 10^18)t^2]^1/3, where t is the time in seconds that it takes the planet to go around the sun.

a. Rewrite the equation using the root symbol.

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.?

- Math -
**tchrwill**, Friday, October 12, 2007 at 3:02pm
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.

- robkget gphfidcj -
**robkget gphfidcj**, Sunday, December 28, 2008 at 8:34am
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