We analyze the trajectories of three geostationary satellites forming the GEOstationary GRAvitational Wave Interferometer (GEOGRAWI)~cite{tinto}, a space-based laser interferometer mission aiming to detect and study gravitational radiation in the ($1
0^{-4} - 10$) Hz band. The combined effects of the gravity fields of the Earth, the Sun and the Moon make the three satellites deviate from their nominally stationary, equatorial and equilateral configuration. Since changes in the satellites relative distances and orientations could negatively affect the precision of the laser heterodyne measurements, we have derived the time-dependence of the inter-satellite distances and velocities, the variations of the polar angles made by the constellations three arms with respect to a chosen reference frame, and the time changes of the triangles enclosed angles. We find that, during the time between two consecutive station-keeping maneuvers (about two weeks), the relative variations of the inter-satellite distances do not exceed a value of $0.05$ percent, while the relative velocities between pairs of satellites remain smaller than about $0.7 {rm m/s}$. In addition, we find the angles made by the arms of the triangle with the equatorial plane to be periodic functions of time whose amplitudes grow linearly with time; the maximum variations experienced by these angles as well as by those within the triangle remain smaller than $3$ arc-minutes, while the East-West angular variations of the three arms remain smaller than about $15$ arc-minutes during the two-weeks period. The relatively small variations of these orbit parameters result into a set of system functional and performance requirements that are less stringent than those characterizing an interplanetary mission.
We discuss two geosynchronous gravitational wave mission concepts, which we generically name gLISA. One relies on the science instrument hosting program onboard geostationary commercial satellites, while the other takes advantage of recent developmen
ts in the aerospace industry that result in dramatic satellite and launching vehicle cost reductions for a dedicated geosynchronous mission. To achieve the required level of disturbance free-fall onboard these large and heavy platforms we propose a two-stage drag-free system, which incorporates the Modular Gravitational Reference Sensor (MGRS) (developed at Stanford University) and does not rely on the use of micro-Newton thrusters. Although both mission concepts are characterized by different technical and programmatic challenges, individually they could be flown and operated at a cost significantly lower than those of previously envisioned gravitational wave missions. We estimate both mission concepts to cost less than 500M US$ each, and in the year 2015 we will perform at JPL a detailed selecting mission cost analysis.
We propose a data processing technique that allows searches for a stochastic background of gravitational radiation with data from a single detector. Our technique exploits the difference between the coherence time of the gravitational wave (GW) signa
l and that of the instrumental noise affecting the measurements. By estimating the auto-correlation function of the data at an off-set time that is longer than the coherence time of the noise {underbar {but}} shorter than the coherence time of the GW signal, we can effectively enhance the power signal-to-noise ratio (SNR) by the square-root of the integration time. The resulting SNR is comparable in magnitude to that achievable by cross-correlating the data from two co-located and co-aligned detectors whose noises are uncorrelated. Our method is general and it can be applied to data from ground- and space-based detectors, as well as from pulsar timing experiments.
Recent advances in space-qualified atomic clocks (low-mass, low power-consumption, frequency stability comparable to that of ground-based clocks) can enable interplanetary spacecraft radio science experiments at unprecedented Doppler sensitivities. T
he addition of an on-board digital receiver would allow the up- and down-link Doppler frequencies to be measured separately. Such separate, high-quality measurements allow optimal data combinations that suppress the currently-leading noise sources: phase scintillation noise from the Earths atmosphere and Doppler noise caused by mechanical vibrations of the ground antenna. Here we provide a general expression for the optimal combination of ground and on-board Doppler data and compute the sensitivity such a system would have to low-frequency gravitational waves (GWs). Assuming a plasma scintillation noise calibration comparable to that already demonstrated with the multi-link CASSINI radio system, the space-clock/digital-receiver instrumentation enhancements would give GW strain sensitivity of $2.0 times 10^{-17}$ for randomly polarized, monochromatic GW signals over a two-decade ($sim0.0001-0.01$ Hz) region of the low-frequency band. This is about an order of magnitude better than currently achieved with traditional two-way coherent Doppler experiments. The utility of optimally combining simultaneous up- and down-link observations is not limited to GW searches. The Doppler tracking technique discussed here could be performed at minimal incremental cost to also improve other radio science experiments (i.e. tests of relativistic gravity, planetary and satellite gravity field measurements, atmospheric and ring occultations) on future interplanetary missions.
We previously showed how the measurements of some eighteen time series of relative frequency or phase shifts could be combined (1) to cancel the phase noise of the lasers, (2) to cancel the Doppler fluctuations due to non-inertial motions of the six
optical benches, and (3) to remove the phase noise of the onboard reference oscillators required to track the photodetector fringes, all the while preserving signals from passinggravitational waves. Here we analyze the effect of the additional noise due to the optical modulators used for removing the phase fluctuations of the onboard reference oscillators. We use a recently measured noise spectrum of an individual modulator to quantify the contribution of modulator noise to the first and second-generation Time-Delay Interferometric (TDI) combinations as a function of the modulation frequency. We show that modulator noise can be made smaller than the expected proof-mass acceleration and optical-path noises if the modulation frequencies are larger than $approx 682$ MHz in the case of the unequal-arm Michelson TDI combination $X_1$, $approx 1.08$ GHz for the Sagnac TDI combination $alpha_1$, and $approx 706$ MHz for the symmetrical Sagnac TDI combination $zeta_1$. These modulation frequencies are substantially smaller than previously estimated and may lead to less stringent requirements on the LISAs oscillator noise calibration subsystem.
