  We propose a Lorentz-covariant theory of gravity, and explain its theoretical
origins in the problem of time in Newtonian physics. In this retarded
gravitation theory (RGT), the gravitational force depends upon both retarded
position and velocity, and the equations of motion are time-asymmetric retarded
functional differential equations. We explicitly solve these equations, under
simplifying assumptions, for various NASA spacecraft. This shows that the
differences from Newtonian gravity, though tiny within the solar system, are
just appropriate to explain the flyby anomaly as a v/c effect due to earth's
rotation. The differences can, however, be large in the case of a spiral
galaxy, and we show that the combined velocity drag from a large number of
co-rotating stars enormously speeds up a test particle. Thus, the non-Newtonian
behaviour of rotation curves in a spiral galaxy may be explained as being due
to velocity drag rather than dark matter. RGT can also be tested in the
laboratory. It necessitates a reappraisal of current laboratory methods of
determining the Newtonian gravitational constant G. Since RGT makes no
speculative assumptions, its refutation would have serious implications across
physics.
