Laser Interferometer Space Antenna LISA represents the next frontier in gravitationalwave GW astronomy targeting the detection of millihertz gravitational signals Central to LISAs operation is the nanosecondprecision estimation of the light travel times LTTs between its constituent spacecraft Precise LTT estimates are critical for suppressing dominant laser noise with timedelay interferometry TDI and ensuring the required sensitivity to GW signals The baseline method is to modulate a pseudorandom noise PRN code on the laser beams exchanged between the spacecraft Timedelay interferometric ranging TDIR was proposed as a simpler alternative LTT estimation method TDIR LTT estimates are chosen to minimize the TDI residual noise over the full LISA frequency band TDIR can be used in case of PRN failure or to calibrate the biases of the PRN method In this study we introduce modulationassisted TDIR MATDIR an enhanced variant of TDIR that significantly improves LTT estimation precision and resilience MATDIR achieves this by modulating the laser phase at specific frequencies close to 1Hz thereby artificially elevating the laser phase content relative to secondary unsuppressed noises This modulation strategy not only enhances the signaltonoise ratio for TDIR but also mitigates the impact of GW signals and instrumental artifacts enabling more reliable LTT estimates with reduced integration times We develop the theoretical framework of MATDIR incorporating the full constellation of three spacecraft laser locking and multiple Michelson TDI combinations Analytical predictions confirmed by numerical simulations indicate that MATDIR can achieve LTT estimates comparable to the 1mrms at fs 4 Hz of the PRNbased baseline method We therefore suggest that the possibility to modulate lasers is added to the laser system requirements of LISA

The Gravitational Reference Advanced Technology Test In Space (GRATTIS) mission will demonstrate the end-to-end functionality and sensitivity performance of the Simplified Gravitational Reference Sensor (S-GRS), an ultra-precise inertial sensor for future Earth geodesy missions. These sensors are used to measure or compensate for all non-gravitational accelerations of the host spacecraft so that they can be removed in the data analysis to recover spacecraft motion due to Earth's gravity field, the main science observable. The S-GRS concept is a simplified version of the flight-proven LISA Pathfinder GRS. It consists of a free-falling cubic test mass inside an electrode housing that senses the position and orientation of the test mass and electrostatically applies forces and torques to it to keep it centered at a nanometer-level. The improved performance of the S-GRS is enabled by removing the small grounding wire used in the GRACE accelerometers, which limits its performance, and replacing it with a UV LED-based charge management system, increasing the mass of the sensor's TM, and increasing the gap between the TM and its electrode housing. GRATTIS will fly two identical S-GRS mounted next to one another at the center of mass of a 160 kg ESPA-class commercial microsatellite with a planned launch in 2027. The six-axis acceleration measurement capability of the S-GRS allows precision measurement of the spacecraft drag-induced translational acceleration, as well as the residual angular acceleration of the nominally inertially-pointed bus. By combining the outputs of each sensor and with the known relative position of the two TMs, we can recover the acceleration sensitivity (noise floor) of the S-GRS.

The current status of the LRI instrument will be presented. Topics will include a look at in-orbit LRI data following a firmware update in September 2022.

We found a calculation error affecting the scaling of results presented in Figure 7 of our article "Absolute frequency readout derived from ULE cavity for next generation geodesy missions" [Opt. Express2926014 (2021)10.1364/OE.434483] . The corrected Figure 7 is published here.

The intersatellite range measurements between the Gravity Recovery and Climate Experiment Follow‐On (GRACE‐FO) satellite pair enable mapping time variations in Earth's gravity field. The Laser Ranging Interferometer (LRI) and Microwave Instrument (MWI) provide independent range measurements. We compare gravity fields derived from the two instruments. The LRI captures time‐variable gravity field signals up to 21 mHz (165 km half‐wavelength) globally, while MWI reaches frequencies up to 15 mHz (230 km). Time‐variable mass variations free from annual cycles and trends are sensed up to 15 mHz (LRI) and 11 mHz (320 km) (MWI). Both instruments are shown to be excellent tools for detection and monitoring of sub‐monthly geophysical signals. Along‐track global maps of sub‐monthly signals are expected to shed light on the high‐frequency behavior of a large number of geophysical processes.

We describe a Simplified Gravitational Reference Sensor (S-GRS), an ultra-precise inertial sensor for future Earth geodesy missions. These sensors are used to measure or compensate for all non-gravitational accelerations of the host spacecraft so that they can be removed in the data analysis to recover spacecraft motion due to Earth's gravity field, which is the main science observable. Low-low satellite-to-satellite tracking missions like GRACE-FO that utilize laser ranging interferometers are technologically limited by the acceleration noise performance of their electrostatic accelerometers, in addition to temporal aliasing associated with Earth's dynamic gravity field. The S-GRS is estimated to be at least 40 times more sensitive than the GRACE accelerometers and more than 500 times more sensitive if operated on a drag-compensated platform. The improved performance is enabled by increasing the mass of the sensor's test mass, increasing the gap between the test mass and its electrode housing, removing the small grounding wire used in the GRACE accelerometers and replacing them with a UV LED-based charge management system. This level of improvement allows future missions to fully take advantage of the sensitivity of the GRACE-FO laser Ranging Interferometer in the gravity recovery analysis. The S-GRS concept is a simplified version of the flight-proven LISA Pathfinder GRS. Our performance estimates are based on models vetted during the LISA Pathfinder flight and the expected Earth orbiting spacecraft environment based on flight data from GRACE-FO. The relatively low volume, mass, and a power consumption enables use of the S-GRS on ESPA-class microsatellites, reducing launch costs or enabling larger numbers of satellite pairs to be utilized to improve the temporal resolution of Earth gravity field maps.

This paper presents a novel method for laser frequency stabilisation in the Laser Interferometer Space Antenna (LISA) mission by locking a laser to two stable length references - the arms of the interferometer and an on-board optical cavity. The two references are digitally fused using carefully designed control systems, attempting minimal or no changes to the baseline LISA mission hardware. The interferometer arm(s) provides the most stable reference available in the LISA science band (0.1 mHz - 1 Hz), while the cavity sensor's wide-band and linear readout enables additional control system gain below and above the LISA band. The main technical issue with this dual sensor approach is the undesirable slow laser frequency pulling which couples into the control system with the imperfect knowledge of the Doppler shift of the light due to relative spacecraft motion along the LISA arm. This paper outlines requirements on the Doppler shift knowledge to maintain the cavity well within the resonance when activating the fused control system. Two Doppler shift estimation methods are presented that use the already on-board measurements, the inter-spacecraft interferometer link (the main science measurement), and the absolute inter-spacecraft laser ranging system. Both methods reach the required precision after a few thousand seconds of measurement integration. The paper demonstrates an approach to initialise and engage the proposed laser stabilization system, starting from free-running laser and ending with the dual sensor frequency control system. The results show that the technique lowers the residual laser frequency noise in the LISA science band by over 3 orders of magnitude, potentially allowing the requirements on Time-Delay-Interferometry (TDI) to be relaxed - possibly to the point where first-generation TDI may be sufficient.

The next generation of Gravity Recovery and Climate Experiment (GRACE)-like dual-satellite geodesy missions proposals will rely on inter-spacecraft laser interferometry as the primary instrument to recover geodesy signals. Laser frequency stability is one of the main limits of this measurement and is important at two distinct timescales: short timescales over 10-1000 seconds to measure the local gravity below the satellites, and at the month to year timescales, where the subsequent gravity measurements are compared to indicate loss or gain of mass (or water and ice) over that period. This paper demonstrates a simple phase modulation scheme to directly measure laser frequency change over long timescales by comparing an on-board Ultra-Stable Oscillator (USO) clocked frequency reference to the Free Spectral Range (FSR) of the on-board optical cavity. By recording the fractional frequency variations the scale correction factor may be computed for a laser locked to a known longitudinal mode of the optical cavity. The experimental results demonstrate a fractional absolute laser frequency stability at the 10 ppb level (10-8) at time scales greater than 10 000 seconds, likely sufficient for next generation mission requirements.

Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) was launched on May 22, 2018. It carries the Laser Ranging Interferometer (LRI) as a technology demonstrator that measures the inter-satellite range with nanometer precision using a laser-link between satellites. To maintain the laser-link between satellites, the LRI uses the beam steering method: a Fast Steering Mirror (FSM) is actuated to correct for misalignment between the incoming and outgoing laser beams. From the FSM commands, we can compute the inter-satellite pitch and yaw angles. These angles provide information about the spacecraft's relative orientation with respect to line-of-sight (LOS). We analyze LRI derived inter-satellite pointing angles for 2019 and 2020. Further, we present its comparison with the pointing angles derived from GRACE-FO SCA1B data, which represents the spacecraft attitude computed from star cameras and Inertial Measurement Unit (IMU) data using a Kalman filter. We discuss the correlations seen between the laser based attitude data and the spacecraft temperature variations. This analysis serves as the basis to explore the potential of this new attitude product obtained from the Differential Wavefront Sensing (DWS) control of a FSM.

Frequency-domain expressions are found for gradiometer and satellite-to-satellite tracking measurements of a point source on the surface of the Earth. The maximum signal-to-noise ratio as a function of noise in the measurement apparatus is computed, and from that the minimum detectable point mass is inferred. A point mass of magnitude M-3 = 100 Gt gives a signal-to-noise ratio of 3 when a GOCE-like gradiometer passes directly over the mass. On the satellite-to-satellite tracking mission GRACE-FO M-3 = 1.3 Gt for the microwave instrument and M-3 = 0.5 Gt for the laser ranging interferometer. The sensitivity of future GRACE-like missions with different orbital parameters and improved accelerometer sensitivity is explored, and the optimum spacecraft separation for detecting point-like sources is found. The future-mission benefit of improving the accelerometer sensitivity for measurement of nongravitational disturbances is shown by the resulting reduction of M-3, to as small as 7 Mt for 500 km orbital altitude and optimized satellite separation of 900 km. (C) 2020 Published by Elsevier Ltd on behalf of COSPAR.

A point mass on the surface of the Earth gives the highest frequency content for orbiting gravimetric measurements, with the maximum frequency for gradiometers or satellite-to-satellite tracking determined by orbital altitude. Frequency-domain expressions are found for orbiting gravimetric measurements of a point-like source on the surface of the Earth. The response of orbiting gradiometers such as GOCE and satelliteto-satellite tracking missions such as GRACE-FO are compared. The optimal signal-to-noise ratio as a function of noise in the measurement apparatus is computed, and from that the minimum detectable mass is inferred. The point mass magnitude that gives signal-to-noise ratio = 3 is for GOCE M3 = 200 Gton and for the laser ranging interferometer measurement on GRACE-FO M3 = 0.5 Gton. For the laser ranging interferometer measurement, the optimal filter for detecting point-like masses has a passband of 1 to 20 mHz, differing from the 0.3 to 20 mHz admittance filter of Ghobadi-Far et al. (2018), which is not specialized for detecting point-like masses. M3 for future GRACE-like missions with different orbital parameters and improved instrument sensitivity is explored, and the optimum spacecraft separation is found. c © 2020 COSPAR. Published by Elsevier Ltd All rights reserved.

The sensitivity of gravity-sensing low-low satellite-to-satellite ranging measurements in the style of GRACE is assessed as the minimum detectable point mass $M_3$ that gives signal-to-noise ratio = 3 as a function of orbital altitude, satellite separation, and instrument noise. We find for the laser ranging interferometer measurement on GRACE Follow-on $M_3= 470$ Mton. $M_3$ for a future mission with different orbital parameters and improved instrument sensitivity is explored.

Frequency-domain expressions are found for gradiometer and satellite-to-satellite tracking measurements of a point source on the surface of the Earth. The maximum signal-to-noise ratio as a function of noise in the measurement apparatus is computed, and from that the minimum detectable point mass is inferred. A point mass of magnitude M_3=100 Gt gives a signal-to-noise ratio of 3 when a GOCE-like gradiometer passes directly over the mass. On the satellite-to-satellite tracking mission GRACE-FO M_3=1.3 Gt for the microwave instrument and M_3=0.5 Gt for the laser ranging interferometer. The sensitivity of future GRACE-like missions with different orbital parameters and improved accelerometer sensitivity is explored, and the optimum spacecraft separation for detecting point-like sources is found. The future-mission benefit of improving the accelerometer sensitivity for measurement of non-gravitational disturbances is shown by the resulting reduction of M_3 to as small as 7 Mt for 500 km orbital altitude and optimized satellite separation of 900 km.

The first terrestrial gravitational wave interferometers have dramatically underscored the scientific value of observing the Universe through an entirely different window, and of folding this new channel of information with traditional astronomical data for a multimessenger view. The Laser Interferometer Space Antenna (LISA) will broaden the reach of gravitational wave astronomy by conducting the first survey of the millihertz gravitational wave sky, detecting tens of thousands of individual astrophysical sources ranging from white-dwarf binaries in our own galaxy to mergers of massive black holes at redshifts extending beyond the epoch of reionization. These observations will inform - and transform - our understanding of the end state of stellar evolution, massive black hole birth, and the co-evolution of galaxies and black holes through cosmic time. LISA also has the potential to detect gravitational wave emission from elusive astrophysical sources such as intermediate-mass black holes as well as exotic cosmological sources such as inflationary fields and cosmic string cusps.

The Laser Ranging Interferometer (LRI) instrument on the Gravity Recovery and Climate Experiment (GRACE) Follow-On mission has provided the first laser interferometric range measurements between remote spacecraft, separated by approximately 220 km. Autonomous controls that lock the laser frequency to a cavity reference and establish the 5 degrees of freedom two-way laser link between remote spacecraft succeeded on the first attempt. Active beam pointing based on differential wave front sensing compensates spacecraft attitude fluctuations. The LRI has operated continuously without breaks in phase tracking for more than 50 days, and has shown biased range measurements similar to the primary ranging instrument based on microwaves, but with much less noise at a level of 1  nm/sqrt[Hz] at Fourier frequencies above 100 mHz.

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