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) $\frac { x ^ { 2 } } { 3961 ^ { 2 } } + \frac { y ^ { 2 } } { 3957 ^ { 2 } } + \frac { z ^ { 2 } } { 3957 ^ { 2 } } = 1$

Question

Quizplus · Accepted Answer

The equation of an ellipsoid centered at the origin is given by $\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1$, where $a$, $b$, and $c$ are the radii along the x, y, and z axes, respectively. For an oblate ellipsoid representing a planet, the equatorial radius (for both x and y) is larger than the polar radius (z). Given the equatorial radius is 3961 miles and the polar radius is 3957 miles, the correct equation is $\frac{x^2}{3961^2} + \frac{y^2}{3961^2} + \frac{z^2}{3957^2} = 1$.

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

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