2008 (IPP)
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Item Time-delay interferometry and the relativistic treatment of LISA optical links(2008-08-20) Dhurandhar, SanjeevLISA is a joint spae mission of the ESA and NASA for deteting low frequeny gravitational radiation in the band 10−5 −1 Hz. In order to attain the requisite sensitivity for LISA, the laser frequeny noise must be suppressed below the other seondary noises su h asthe optial path noise, a eleration noise et. This is ahieved beause of the redundan y in the data, more spe i ally, by ombining six appropriately time-delayed data streams ontain ingfrational Doppler shifts - time delay interferometry (TDI). The orbits of the spa eraft are omputed in the gravitational eld of the Sun and Earth in the Newtonian framework, while the optial links are treated fully general relativisti ally and thus, e ets suh as the Sagna, Shapiro delay, et. are automatially in orporated. We show that in the model of LISA that we onsider here, there are symmetries inherent in the physis, whih may be used e e tively to suppress the residual laser frequen y noise and simplify the algebrai approa h to TDI.Item Optimising LISA orbits: The projectile solution(2008-09-11) Dhurandhar, Sanjeev; Nayak, K. R.; Vinet, J-Y.LISA is a joint spae mission of the NASA and the ESA for deteting low frequeny gravitational waves (GW) in the band 10−5 − 0.1 Hz. The proposed mission will use oherent laser beams whih will be exhanged between three idential spae raft forming a giant (almost) equilateral triangle of side 5×106 kilometres. The plane of the triangle will makean angle of ∼ 60◦ with the plane of the elipti. The spaeraft onstituting LISA will be freely oating in the ambient gravitational eld of the Sun and other elestial bodies. To ahieve the requisite sensitivity, the spaeraft formation should remain stable, one requirement being, the distanes between spaeraft should remain as onstant as possible - that is the exing of the arms should be minimal. In this paper we present a solution - the projetile solution - whih onstrains the exing of the arms to below 5.5 metres/se in a three year mission period. This solution is obtained in the eld of the Sun and Earth only, whih prinipally a et the motion of the spaeaft, espeially the exing of LISA's arms.Item General relativistic treatment of LISA optical links(2008-05) Dhurandhar, Sanjeev; Vinet, J-Y.; Nayak, K. R.LISA is a joint spae mission of the NASA and the ESA for deteting low frequeny gravitational waves in the band 10−5 − 1 Hz. In order to attain the requisite sensitivity for LISA, the laser frequeny noise must be suppressed below the other seondary noises suh as the optial path noise, a eleration noise et. This is ahieved by ombining time-delayed data for whih preise knowledge of time-delays is required. The gravitational eld, mainly that of the Sun and the motion of LISA a e t the time-delays and the opti al links. Further, the e e t of the gravitational eld of the Earth on the orbits of spaeraft is inluded. This leads to additional exing over and above that of the Sun. We have written anumerial ode whih omputes the optial links, that is, the time-delays with great auray∼ 10−2 metres - more than what is required for time delay interferometry (TDI) - for most of the orbit and with su ient auray 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 optial links is fully general relativisti and the numerial ode takes into aount e ets suh as the Sagna, Shapiro delay, et. We show that with the deemed parameters in the design of LISA, there are symmetries inherent in the on guration of LISA and in the physi s, whih may be used e etively to suppress the residual laser noise in the modi ed rst generation TDI. We demonstrate our results for some important TDI variables.