Show that the average straight-line distance to a fixed point on the surface of a sphere of radius a (averaged over the whole surface of the sphere) is [Suggestion: Take the sphere centered at the origin, and choose the “north pole" as the fixed point.]

Show that the average straight-line distance to a fixed point on the surface of a sphere of radius a (averaged over the whole surface of the sphere) is [Suggestion: Take the sphere centered at the origin, and choose the “north pole" as the fixed point.]

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter11: Addition And Subtraction Of Decimal Fractions

Section: Chapter Questions

Problem 18A: Refer to the plate shown in Figure 117 and determine the following distances. All dimensions are in...

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Question

Show that the average straight-line distance to a fixed point on the surface of a sphere of radius a
(averaged over the whole surface of the sphere) is 4. [Suggestion: Take the sphere centered at the origin,
and choose the “north pole" as the fixed point.]

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