  In 2008 a group of NASA scientists reported an anomalous change in the speed
of six spacecraft flybys of the Earth. The reported speed change for the NEAR
spacecraft flyby is 13.46+-0.01 mm/s. It is known that general relativity
theory reduces to classical time-retarded electromagnetic field theory in the
linearized approximation. This report shows that time-retarded field theory
applied to the Earth's transverse gravitational field gives rise to a small
change in the speed of a spacecraft during a flyby. The speed change depends on
the time dependence of the transverse gravitational field, which generates an
induction field that is proportional to the time derivative of the transverse
gravitational field. If the corresponding speed for the induction field is set
equal to (4.130+-0.003) times the Earth's equatorial rotational surface speed,
and the speed of the Earth's gravitational field is set equal to (1.060+-0.001)
times the vacuum speed of light, the calculated value for the speed change for
the NEAR flyby agrees exactly with the observed value. Similar results are
found for the remaining five flybys.
