Why does gravity decrease as we go down into the Earth?We all know that gravity decreases as the distance between the two increases. Hence F = G M m r 2 .Hence the acceleration due to gravity g = F m = G M r 2 increases as r decreases. Then why does it decrease as we go deep into the earth?

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Why does gravity decrease as we go down into the Earth?We all know that gravity decreases as the distance between the two increases. Hence  F  =  G            M      m              r      2        .Hence the acceleration due to gravity  g  =      F    m    =  G      M          r      2      increases as   r decreases. Then why does it decrease as we go deep into the earth?

Russell Knox · Accepted Answer

It&#039;s actually not entirely true that the strength of the Earth&#039;s gravitational field decreases as a function of depth. It is true for certain regions in the Earth, but it&#039;s untrue for others because of the non-trivial dependence of the Earth&#039;s density on depth.To see what&#039;s going on, assume that the Earth is a sphere whose density is spherically symmetric.Now consider a mass   m at some radius   r from the center of the Earth. Using Newton&#039;s Law of Gravitation, one can show that that given the spherical symmetry, the gravitational attraction on   m of all mass with radii greater than   r exert no net force on it. It follows that only the mass with radii less than or equal to   r contribute to the gravitational force on   m, which, by the Law of Gravitation is                    F        (        r        )        =        G                              M            (            r            )            m                                r            2                              where   M  (  r  ) is the mass of stuff at radii less than or equal to   r. Notice, then, that   F  (  r  ) will be an increasing function of   r (and will decrease as   r  →  0), provided   M  (  r  )      /        r    2   is an increasing function of   rNow, If the Earth were uniformly dense with density       ρ    0  , then the mass within a radius   r would be                    M        (        r        )        =                  4          3                π                  r          3                          ρ          0                    namely just the density times the volume of a sphere of radius   r, and in this case the strength of the gravitational field as a function of radius would be                    g        (        r        )        =                              F            (            r            )                    m                =        G                  1                      r            2                                    4          3                π                  r          3                          ρ          0                =                  (                      4            3                    π          g                      ρ            0                    )                r            However, the Earth&#039;s density is not constant, and instead has some non-trivial dependence on   r.

Why does gravity decrease as we go down into the Earth? We all know that gravity decreases as the distance between the two increases. Hence F = G (Mm)/(r^2).Hence the acceleration due to gravity g =F/m= G M/r^2 increases as r decreases. Then why does it decrease as we go deep into the earth?

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