I am currently working through a physics book (Spacetime Physics by Edwin Taylor) and I have come across this question and I don't know how to solve it:"Take the differential of this equation for g to obtain an approximate algebraic expression for Δg, the change in g, for a small change Δr in height."How do I sovle this question? Demonstrate this 2-millimeter increase in separation.The following outline may be useful. Take the gravi-tational acceleration at the surface of Earth to be go9.8 meters/second² and the radius of Earth to be r6.37 X 106 meters. More generally, the gravitationalacceleration g of a particle of mass m a distance r fromthe center of Earth (mass M) is given by the expression8FmGMp²70/2GM2p² p28010p²

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Answered: Take the differential of this equation…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter11: Gravity, Planetary Orbits, And The Hydrogen Atom

Section: Chapter Questions

Problem 47P: Let gM represent the difference in the gravitational fields produced by the Moon at the points on...

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I am currently working through a physics book (Spacetime Physics by Edwin Taylor) and I have come across this question and I don't know how to solve it:

"Take the differential of this equation for g to obtain an approximate algebraic expression for Δg, the change in g, for a small change Δr in height."

How do I sovle this question?

Demonstrate this 2-millimeter increase in separation.
The following outline may be useful. Take the gravi-
tational acceleration at the surface of Earth to be go
9.8 meters/second² and the radius of Earth to be r
6.37 X 106 meters. More generally, the gravitational
acceleration g of a particle of mass m a distance r from
the center of Earth (mass M) is given by the expression
8
F
m
GM
p²
70/2
GM2
p² p2
8010
p²

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