Because of the Forces Caused by Its Rotation, a Planet $( z = 0 )$

question 57

Multiple Choice

Because of the forces caused by its rotation, a planet is actually an oblate ellipsoid rather than a sphere. The equatorial radius is 3961 miles and the polar radius is 3957 miles. Find an equation of the ellipsoid. Assume that the center of a planet is at the origin and the xy- trace $( z = 0 )$ corresponds to the equator.

• A) \(\frac { x ^ { 2 } } { 3961 ^ { 2 } } + \frac { y ^ { 2 } } { 3961 ^ { 2 } } - \frac { z ^ { 2 } } { 3957 ^ { 2 } } = 1\)
• B) \(\frac { x ^ { 2 } } { 3961 ^ { 2 } } + \frac { y ^ { 2 } } { 3957 ^ { 2 } } + \frac { z ^ { 2 } } { 3961 ^ { 2 } } = 1\)
• C) \(\frac { x ^ { 2 } } { 3961 ^ { 2 } } + \frac { y ^ { 2 } } { 3961 ^ { 2 } } + \frac { z ^ { 2 } } { 3957 ^ { 2 } } = 1\)
• D) \(\frac { x ^ { 2 } } { 3961 ^ { 2 } } - \frac { y ^ { 2 } } { 3961 ^ { 2 } } - \frac { z ^ { 2 } } { 3957 ^ { 2 } } = 1\)
• E) \(\frac { x ^ { 2 } } { 3961 ^ { 2 } } + \frac { y ^ { 2 } } { 3957 ^ { 2 } } + \frac { z ^ { 2 } } { 3957 ^ { 2 } } = 1\)

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