  In an effort to eliminate laser phase noise in laser interferometer
spaceborne gravitational wave detectors, several combinations of signals have
been found that allow the laser noise to be canceled out while gravitational
wave signals remain. This process is called time delay interferometry (TDI). In
the papers that defined the TDI variables, their performance was evaluated in
the limit that the gravitational wave detector is fixed in space. However, the
performance depends on certain symmetries in the armlengths that are available
if the detector is fixed in space, but that will be broken in the actual
rotating and flexing configuration produced by the LISA orbits. In this paper
we investigate the performance of these TDI variables for the real LISA orbits.
First, addressing the effects of rotation, we verify Daniel Shaddock's result
that the Sagnac variables will not cancel out the laser phase noise, and we
also find the same result for the symmetric Sagnac variable. The loss of the
latter variable would be particularly unfortunate since this variable also
cancels out gravitational wave signal, allowing instrument noise in the
detector to be isolated and measured. Fortunately, we have found a set of more
complicated TDI variables, which we call Delta-Sagnac variables, one of which
accomplishes the same goal as the symmetric Sagnac variable to good accuracy.
Finally, however, as we investigate the effects of the flexing of the detector
arms due to non-circular orbital motion, we show that all variables, including
the interferometer variables, which survive the rotation-induced loss of
direction symmetry, will not completely cancel laser phase noise when the
armlengths are changing with time. This unavoidable problem will place a
stringent requirement on laser stability of 5 Hz per root Hz.
