  In recent work we constructed completely general conservation laws for energy
and linear and angular momentum of extended systems in general relativity based
on the notion of a rigid quasilocal frame (RQF). We argued at a fundamental
level that these RQF conservation laws are superior to conservation laws based
on the local stress-energy-momentum tensor of matter because (1) they do not
rely on spacetime symmetries and (2) they properly account for both matter and
gravitational effects. Moreover, they provide simple, exact, operational
expressions for fluxes of gravitational energy and linear and angular momentum.
In this paper we derive the form of these laws in a general first
post-Newtonian (1PN) approximation, and then apply these approximate laws to
the problem of gravitational tidal interactions. We obtain formulas for tidal
heating and tidal torque that agree with the literature, but without resorting
to the use of pseudotensors. We describe the physical mechanism of these tidal
interactions not in the traditional terms of a Newtonian gravitational force,
but in terms of a much simpler and universal mechanism that is an exact,
quasilocal manifestation of the equivalence principle in general relativity. As
concrete examples, we look at the tidal heating of Jupiter's moon Io and
angular momentum transfer in the Earth-Moon system that causes a gradual
spin-down of the Earth and recession of the Moon. In both examples we find
agreement with observation.
