  The flyby anomalies are unexplained velocity increases of 3.9, 13.5, 0.1 and
1.8 mm/s observed near closest approach during the Earth flybys of the Galileo,
NEAR, Cassini and Rosetta spacecraft. Here, these flybys are modelled using a
theory that assumes that inertia is caused by a form of Unruh radiation,
modified by a Hubble-scale Casimir effect. This theory predicts that when the
craft's accelerations relative to the galactic centre approached zero near
closest approach, their inertial masses reduced for about 10^-7 s causing
Earthward jumps of 2.6, 1.2, 1.4 and 1.9 mm/s respectively, and, to conserve
angular momentum, increases in orbital velocity of a few mm/s that, except
NEAR's, were quite close to those observed. However, these results were
extremely sensitive to the Hubble constant used. As an experimental test of
these ideas, it is proposed that metamaterials could be used to bend Unruh
radiation around objects, possibly reducing their inertial mass.
