  Galaxies and galaxy clusters have rotational velocities apparently too fast
to allow them to be gravitationally bound by their visible matter. This has
been attributed to the presence of invisible (dark) matter, but so far this has
not been directly detected. Here, it is shown that a new model that modifies
inertial mass by assuming it is caused by Unruh radiation, which is subject to
a Hubble-scale (Theta) Casimir effect predicts the rotational velocity (v) to
be: v^4=2GMc^2/Theta (the Tully-Fisher relation) where G is the gravitational
constant, M is the baryonic mass and c is the speed of light. The model
predicts the outer rotational velocity of dwarf and disk galaxies, and galaxy
clusters, within error bars, without dark matter or adjustable parameters, and
makes a prediction that local accelerations should remain above 2c^2/Theta at a
galaxy's edge.
