Because of the forces caused by its rotation,a planet is actually an oblate ellipsoid rather than a sphere.The equatorial radius is 3967 miles and the polar radius is 3951 miles.Find an equation of the ellipsoid.Assume that the center of a planet is at the origin and the xy- trace corresponds to the equator.

Question

Because of the forces caused by its rotation,a planet is actually an oblate ellipsoid rather than a sphere.The equatorial radius is 3967 miles and the polar radius is 3951 miles.Find an equation of the ellipsoid.Assume that the center of a planet is at the origin and the xy- trace  corresponds to the equator. ​

Quizplus · Accepted Answer

The equation of an ellipsoid centered at the origin is given by:

(x^2/a^2) + (y^2/b^2) + (z^2/c^2) = 1

where a, b, and c are the lengths of the semi-axes along the x, y, and z directions, respectively.

In this case, the equatorial radius (a) is 3967 miles and the polar radius (b) is 3951 miles. The z-axis corresponds to the polar axis, which has the same length as the semi-axis in the direction of the polar radius, so c = b = 3951 miles.

Therefore, the equation of the ellipsoid is:

(x^2/3967^2) + (y^2/3967^2) + (z^2/3951^2) = 1

Simplifying and converting to decimal form, we get:

0.00006308x^2 + 0.00006308y^2 + 0.00006544z^2 = 1

which corresponds to choice C.

Because of the Forces Caused by Its Rotation,a Planet Is