We know the equation, #F = (Gm_1m_2)/r^2#, where
#G = # Gravitational Constant
#m_1# #&# #m_2 = # Masses of 2 bodies repectively
#r = # The distance between the 2 bodies
#F = #It is the force acting on the bodies
We can rewrite the equation as #F = (GMm)/R^2# with respect to Earth, where
#M = #Mass of the Earth
#m =#mass of the object on Earth
#R = #Distance from the center of the Earth to the object
We know that #F = m/a#. So substituting this value for #F#, the Equation becomes #=># #m/a = (GMm)/R^2#
#1/a = (GMm)/(R^2m)#
#1/a = (GMcancelcolor(red)m)/(R^2cancelcolor(red)m)#
#1/a = (GM)/R^2#
#1 = (GMa)/R^2#
#R^2 = GMa#
#G# #&# #M# are constants, That means
#R^2 prop a#
#a prop R^2#
#a# means acceleration due to gravity. That is #a = g#
That means,
#g prop R^2#
From this, we can understand that acceleration due to gravity #(g)#
is directly proportional to the distance, that means when the distance from the center of the Earth and the object increases, #g# also increases and when the distance from the center of the Earth and the object decreases, #g# also decreases.
Distance from the center of the Earth to the poles is maximum, so #g# is maximum at the poles. When the object is at the center of the Earth, the distance between the center of the Earth and the Object will be #zero#, so #g# will also become #zero#.
