Classical Gravity in Planck Units: Looking at a old equation from a new angle

A few months ago I did a bit of thinking about gravity from a different angle.  I asked the question... How would the equations of classical General Relativity look if Planck Units were used.  Let me make it clear I am not not talking about the Planck Scale.. just the use of it's units at the classical scale.  Of course anywhere near Planck Scale Quantum effects dominate.  I have already written a book about that.  "Quantum Space-Time Dynamics"
by Hontas Farmer .         This came to me after writing the book and finalizing it.  Consider the following. 

The Planck Units are defined using three universal physical constants.....the reduced Planck constant ħ, the speed of light c, and the gravitational constant G.  If ħ=c=1  then they become  Planck Length = √G,  Planck time= √G, and Planck mass = 1/√G. 

For this blog posting just consider Newton's law of gravity.  Which appears as part of general relativity in the weak field limit, and Schwarzchild geometry, such as in the solar system. (Basically any place but near a massive black hole.)

The potential of Newtonian gravity .  V=-GM/r  is supposed to have units of energy.  But if the Planck units are used. 
V= - G(1/√G)/√G  = -√G/√G=1  !  Or the dimensions disappear!   This is not supposed to happen unless all three base units are set equal to one all quantities should retain their units in the new system of measurement.   So I propose the following modification to classical gravity when planck units are used.

V=-GM/(√G r).

When this is done and planck units are plugged in V=-(G/√G)/G= -√G/G=-1/√G  The correct unit of measure for potential energy.  Now I know it is not a trivial matter to modify such a well tested law of nature.  However the concern I raise is such a simple and fundamental point of science it cannot be totally ignored. 

Old NID
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