LISA is a joint space mission of the NASA and the ESA for detecting low
frequency gravitational waves in the band 10−5−1 Hz. In order to attain
the requisite sensitivity for LISA, the laser frequency noise must be
suppressed below the other secondary noises such as the optical path noise,
acceleration noise etc. This is achieved by combining time-delayed data for
which precise knowledge of time-delays is required. The gravitational field,
mainly that of the Sun and the motion of LISA affect the time-delays and the
optical links. Further, the effect of the gravitational field of the Earth on
the orbits of spacecraft is included. This leads to additional flexing over and
above that of the Sun. We have written a numerical code which computes the
optical links, that is, the time-delays with great accuracy ∼10−2
metres - more than what is required for time delay interferometry (TDI) - for
most of the orbit and with sufficient accuracy within ∼10 metres for an
integrated time window of about six days, when one of the arms tends to be
tangent to the orbit. Our analysis of the optical links is fully general
relativistic and the numerical code takes into account effects such as the
Sagnac, Shapiro delay, etc.. We show that with the deemed parameters in the
design of LISA, there are symmetries inherent in the configuration of LISA and
in the physics, which may be used effectively to suppress the residual laser
noise in the modified first generation TDI. We demonstrate our results for some
important TDI variables
