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.
