The modified "d" calculation doesn't produce the same values as the previous equation if you take out the sqrt, so the effect has to be different.
Code:
dist = sqrt(v)
d = G_FORCE / (dist*dist*dist) = G_FORCE  / (sqrt(v) * sqrt(v) * sqrt(v))
power:
Code:
d^2 = G_FORCE*G_FORCE / (v * v * v)
d = sqrt(d^2)