The equation for #g# on Earth is given by:
#g_E=(GM_E)/r^2#, where:
- #g_E# = acceleration due to free fall on Earth (#ms^-2#)
- #G# = gravitational constant (#~6.67*10^-11Nm^2kg^-2#)
- #M_E# = mass of the object (#~5.972*10^24kg#)
- #r# = distance between the centre of gravities of the two objects (#m#)
Since #G# and #M_E# are constants #gpropto1/r^2#
#r# is possible to change even without you moving since many things like magma flow through the Earth which have very tiny changes in the position of the centre of gravity that will slightly change #r#.
Let's say you were 7000km away from the centre of gravity from the Earth:
#g=((6.67*10^-11)(5.972*10^24))/(7*10^6)^2=8.129ms^-2#
Now 5000km:
#g=((6.67*10^-11)(5.972*10^24))/(5*10^6)^2=15.93ms^-2#
#r# is usually 6371km
#g=((6.67*10^-11)(5.972*10^24))/(6371*10^3)^2=9.813646787ms^-2#
But if #r# was to get 1m less due to movements in the Earth's mantle (for example):
#g=((6.67*10^-11)(5.972*10^24))/((6371*10^3)+1)^2=9.813643707ms^-2#
A 1m change has a slightly small change in the value for #g#
Also, #r# could change if the ground was to become raised or lowered,movements of liquids like magma can raise and lower the ground, changing the distance between the person and the centre of gravity for the Earth (assuming that hasn't changed). If the ground was to sink by #1m# then #g# will become:
#g=((6.67*10^-11)(5.972*10^24))/((6371*10^3)-1)^2=9.813649868ms^-2# as you can see, #g# has increased by a very small amount, but not enough to have any noticeable effect on us.
