Is acceleration due to gravity constant? I was taught in school that acceleration due to gravity i

Matilda Webb 2022-05-10 Answered
Is acceleration due to gravity constant?
I was taught in school that acceleration due to gravity is constant. But recently, when I checked Physics textbook, I noted that
F = G m 1 m 2 r 2 .
So, as the body falls down, r must be changing, so should acceleration due to gravity.
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Answers (1)

Gia Schaefer
Answered 2022-05-11 Author has 16 answers
This is a first introduction to the issue of the relative changes in physics.
Consider the motion of objects near the Earth's surface. Call the nominal radius of the Earth R 6400  km, and the height of the object h
Now the acceleration due to gravity at h is
g = F g m = G M e m ( R + h ) 2 m = G M e ( R + h ) 2
and lets manipulate this a little
g = G M e ( R + h ) 2 = G M e R 2 ( 1 + h / R ) 2 G M e R 2 ( 1 2 h R ) .
The last approximation there is dropping higher order terms in h R which will shortly be seen to be justified.
So, ask yourself how big is h R for the situations you encounter in your life. A few meters or a few tens of meters at most, right? So h R is of order 10 5 or smaller over human scales or 10 3 even over the whole height range that we use including airplane elevations.
So, for almost all calculation that you want to make the variation of g negligible.
Physicists get a lot of millage out of these kinds of considerations to the point that you there is a fair amount of shorthand devoted to discussing fractional changes. People say things like "Yeah, but it's down by two orders of magnitude, so we can neglect it".
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