  Based on the Generalized Principle of Inertia, which states that: \emph{An
inanimate object moves freely, that is, with zero acceleration, in its own
spacetime, whose geometry is determined by all of the forces affecting it,} we
geometrize Newtonian dynamics for any conservative force. For an object moving
in a spherically symmetric force field, using a variational principle,
conservation of angular momentum and a classical limit, we construct a metric
with respect to which the object's worldline is a geodesic. For the
gravitational field of a static, spherically symmetric mass, this metric is the
Schwarzschild metric. The resulting dynamics reduces in the weak field, low
velocity limit to classical Newtonian dynamics and exactly reproduces the
classical tests of General Relativity. The metric of gravitoelectromagnetism is
extended to handle a gravitational field generated by several sources.
