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Show that the angle a between a plumb line and the

Chapter 9, Problem 9.13

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QUESTION:

Show that the angle a between a plumb line and the direction of the earth's center is well approximated by tan a = (R,Q2 sin 26)/(2g), where g is the observed free-fall acceleration and we assume the earth is perfectly spherically symmetric. Estimate the maximum and minimum values of the magnitude of a.

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QUESTION:

Show that the angle a between a plumb line and the direction of the earth's center is well approximated by tan a = (R,Q2 sin 26)/(2g), where g is the observed free-fall acceleration and we assume the earth is perfectly spherically symmetric. Estimate the maximum and minimum values of the magnitude of a.

ANSWER:

Step 1 of 3

The radial and tangential components of g are given by (9.45) and (9.47) as

        and

where I use “radial” to mean the direction of the center of the earth.

 

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