3. We will investigate the shape of Saturn (the 6th planet iii our solar system)

Question

3. We will investigate the shape of Saturn (the 6th planet iii our solar system). Saturn has a low density and rotates very quickly which causes the planet to have a flatten shape. It is the most oblate planet in our solar system. The equatorial radius is 60, 268 kilometers and its polar radius is 54, 364 kilometers. (a) The ellipse cross section of the planet is x^2/60268^2 + y^2/54364^2 = 1. Find the volume of Saturn. (b) If the rotation of Saturn slowed down (unlikely) and caused the shape to become spherical what would the radius of the sphere he? (Assume that Saturn did not loose nor gain volume)

Explanation / Answer

a)volume of oblate ellipsoid v=(4/3)a2b

a=60268,b=54364

v=(4/3)(60268)2(54364) =827129617817030.7km3

b)volume of sphere =v=(4/3)a3

(4/3)a3 =827129617817030.7

==>a3 =827129617817030.7/(4/3)

==>a3=197462650879936

==>a=58232 km

radius =58232 km

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