  Certain measurements in celestial mechanics necessitate having the origin O
of a Cartesian coordinate system (CCS) coincide with a point mass. For the two
and three body problems we show mathematical inadequacies in Newton's celestial
mechanics equations (NCME) when the origin of a coordinate system coincides
with a point mass. A certain system of equations of relative differences
implied by NCME is free of these inadequacies and is invariant with respect to
any CCS translation. A new constant of motion is derived for the relative
system. It shows that the universe of relative differences of the $N$-body
problem is ``restless''.
