Gravity Newtonian

The expression for gravity:

$g=-G.\cfrac { 1 }{ { (-a(x+{ r }_{ o })+{ a }_{ 0 }) }^{ 2 } } =-\cfrac { G }{ { a }^{ 2 } } \cfrac { 1 }{ { (x+\cfrac { { { ar }_{ o }-a }_{ o } }{ a } ) }^{ 2 } } =-\cfrac { G }{ { a }^{ 2 } } \cfrac { 1 }{ { (x+{ r }_{ e }) }^{ 2 } }$

can be further simplified, it is basically $g=\cfrac { 1 }{ { x }^{ 2 } }$ scaled by $-G$ along g axis, scaled along x axis by factor  ${ a }$  and translated along x axis by ${ a }_{ 0 }$ and since  $g=\cfrac { 1 }{ { x }^{ 2 } }$  is symmetrical about x=0, we have

$g=-{ G }_{ 0 }.\cfrac { 1 }{ { (x+{ r }_{ e }) }^{ 2 } }$

which is a more familiar form of the expression.