  Well-known to specialists but little-known to the wider audience is that
Newtonian gravity can be understood as geodesic motion in space-time, where
time is absolute and space is Euclidean. Newtonian cosmology formulated by
Heckmann agrees implicitly with Cartan's formulation of Newtonian mechanics as
geodesic motion in space-time, but does not unfold the underlying geometric
picture. I present the transformation theory of Newtonian mechanics and gravity
developed by Cartan and Heckmann, and show via coordinate transformations that
Heckmann's Newtonian cosmological model has a center, so that the cosmological
principle cannot hold globally.
  It is possible to confuse the relativity principle with a position of
relativism. Mach's principle has much to do with the latter and nothing to do
with the former. Both general relativity and nonlinear dynamics inform us that
most coordinate systems ae defined locally by differential equations that are
globally nonintegrable: global extensions of local coordinates usually do not
exist. I explain how defining inertial frames locally by free fall
short-circuits Mach's philosophic objectios to Newtonian dynamics.
