  A relativistic theory is proposed to explain the anomalous accelerations of
Pioneer 10/11, Galileo and Ulysses spacecrafts. The theory points out at the
limitations of the weak field approximation and proposes a drift in the proper
time of the spacecraft outside the framework of general relativity. The theory
yields a very accurate and precise value for the anomalous acceleration. In
this theory the proper time of a body is associated with the gravitational
frequency shift of the constituent fundamental particles of the body. The
frequency shift changes the energy level of the body which gets reflected in
its relativistic mass and therefore in its motion. This change in energy level
causes the time like geodesics to deviate from that of the standard theoretical
models. We introduce proper time in the line element of a metric theory
according to a fixed set of rules laid down by general relativity for
introducing deviation in the flat Minkowski metric. The frequency shift for
bodies of different composition traversing different trajectories however, is
not the same and this gets reflected in its motion as an unmodeled anomalous
effect. This association of proper time with the gravitational frequency shift
of the body requires the flat Minkowski metric to deviate in different ways for
different two body systems. The solution to Pioneer anomaly given here yields
anomalous acceleration within the limits of observational accuracy.
Gravitational redshift of light, bending of light and perihelic precession of
planets are within the permissible limits. The theory shows that Einstein's
field equations do provide some clue to the Pioneer anomaly but the solution is
not very accurate. The theory can also explain the rotation curves of the
spiral galaxies.
