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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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.

Gia Schaefer · Accepted Answer

This is a first introduction to the issue of the relative changes in physics.Consider the motion of objects near the Earth&#039;s surface. Call the nominal radius of the Earth   R  ≈  6400   km, and the height of the object   hNow 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 &quot;Yeah, but it&#039;s down by two orders of magnitude, so we can neglect it&quot;.

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

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