# Math

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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 -

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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