Solution Found!
Show that the angle a between a plumb line and the
Chapter 9, Problem 9.13(choose chapter or problem)
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.
Questions & Answers
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.