Gravity field mapping using laser-coupled quantum accelerometers in space

Abstract

The emergence of quantum technologies, including cold atom-based accelerometers, offers an opportunity to improve the performances of space geodesy missions. In this context, CNES initiated an assessment study called GRICE (GRadiométrie à Interféromètres quantiques Corrélés pour l’Espace) in order to evaluate the contribution of cold atom technologies to space geodesy and to the end users of geodetic data. In this paper, we present mission scenario for gravity field mapping based on a long baseline gradiometer. The mission is based on a constellation of two satellites, flying at an altitude of 373 km, each equipped with a cold atom accelerometer with a sensitivity of $6 \times 10^{-10}\,\hbox {m}\,\hbox {s}^{-2}\,\tau ^{-1/2}$. A laser link measures the distance between the two satellites and couples these two instruments in order to produce a correlated differential acceleration measurement. The main parameters, determining the performances of the payload, have been investigated. We carried out a general study of satellite architecture and simulations of the mission performances in terms of restitution of the gravity field. The simulations show that this concept would give its best performance in terms of monthly gravity fields recovery under 1000 km resolution. In the resolution band between 1000 and 222 km, the improvement of the GRICE gradient approach over the traditional range-rate approach is globally in the order of 10 to 25%.

Appendix: Attitude control subsystem

The mission definition and constraints have a strong impact on the attitude control system (ACS) architecture. The nadir pointing shall be maintained within 4 mrad and $50~\mu \hbox {rad}/\hbox {s}$. This nonetheless ensures a correct alignment of the payloads of the two spacecraft with respect to one another, but it also minimizes the impact of air drag (and thus increases the mission lifetime). ACS shall also provide the estimated attitude to the instrument with a knowledge error lower than 0.1 mrad. Such requirements are not particularly stringent, but due to the low altitude of the orbit and the elongated shape of the spacecraft, the impact of orbit-related perturbations has to be carefully considered in the ACS design. Indeed, with such a long shape, the air drag and gravity gradient torques are strongly dependent of the pointing error. The spacecraft layout also plays an important part in the air drag torque: Any offset between the center of mass and the aerodynamic center increases the aerodynamic torque linearly. Moreover, in addition to the attitude control during the measurements sessions, ACS shall ensure a correct pointing during the orbit correction maneuvers and in case of failure. To reply to all these considerations, ACS is defined to provide three-axis stabilized Earth-pointing attitude control during all mission phases. Thus, ACS architecture is composed of a set of equipment and onboard software used within the control closed loop. Sensors are used to measure the attitude and actuators to correct it. Estimation and attitude control algorithms are implemented onboard to compute the estimated attitude and the control law. Three ACS modes are defined depending on the phase of the mission described below:

Mission mode This is the mode during which the mission is carried out. In this mode, the control loop uses measurements from a 3-head Star-Tracker (STR) and a 3-axis optical gyroscope to estimate the attitude. As the orbital plane is inertial, a 3-head STR is needed: The satellite-Sun angle varies along the mission (which induces successive dazzling of each panel of the satellite), and the heads are thus set on the lateral and upper panels to ensure at least one available STR. Both measurements are hybridized in a gyro-stellar filter to compute the attitude.

Concerning the actuators, in order to minimize the perturbations toward the payload, two options are considered to realize the commanded torques: a set of 4 reaction wheels in pyramidal configuration (to ensure the torque capacity and a redundancy in case of failure) or a cold gas propulsion subsystem (CGPS). The CGPS configuration is composed of $4 \times 2$ thrusters on the front and back sides of the satellite. Magnetotorquer bars (MTBs) are also used in both options: either to unload the wheels or to help the CGPS to compensate for the Earth’s magnetic torque.

Safehold mode This mode is enabled just after separation to stabilize the satellite (inertial acquisition) and in case of failure detection or attitude loss. The satellite remains in geocentric pointing to minimize air drag perturbations, but with relaxed pointing and stability performances. The attitude estimation uses a set of Sun sensors and magnetometers. Six Coarse Earth Sun Sensors (one head on each of the six sides of the satellite) are used to give omnidirectional and coarse attitude estimation. In addition, 2 fine Sun sensors located on the lateral sides are used to provide a precise attitude once the satellite is stabilized. Two magnetometers are used to estimate the angular rate. The 3-axis stabilization is performed by MTBs.

Orbit control mode During the orbit control maneuvers, the thrust direction has to be maintained along track to counter air drag effect. Consequently, the satellite has to remain in nadir pointing. The orbit control propulsion system is not suited to realize attitude control by off-modulation. ACS uses the same sensors and actuators as the mission mode (star tracker and gyroscope as sensors, and reaction wheels or CGPS as actuators), while the thrust is performed by electric propulsion. During this mode, no scientific measurements will be realized.

In this early phase of the project, particular attention is paid to the dimensioning of the actuators (MTBs, reaction wheels, CGPS). Indeed, the satellite layout is strongly dependent of the size and mass of the actuators. The dimensioning process consists in checking that the capacities of the chosen actuators are compliant with the main perturbations encountered for each mode.

In Safehold mode, MTBs have to deal with potential huge pointing errors and thus high aerodynamic and gravity gradient torques. Nevertheless, in Mission and Orbit Control modes, the main constraint is the unload duration of the reaction wheels that has to be lower than a quarter orbital period.

For the reaction wheels and the CGPS, the dimensioning constraint comes from the orbit control maneuvers. Indeed, the thrust torque is directly linked to the offset between the center of mass and the aerodynamic center of the platform: With a $300~\hbox {m}/\hbox {s}\ \Delta V$ budget over 5 years shared with maneuvers every 48 h, each 2h-spread tangential thrust generates a constant 2.5 mN m torque in the case of 50 mm offset (in pitch/yaw). Moreover, concerning the reaction wheels option, an unloading by MTBs during the maneuver is necessary to be compatible with the wheels’ angular momentum. Concerning the CGPS option, it is also important for the satellite layout to estimate the gas consumption during both modes: With the considered hypotheses (5-year mission, 50 mm offset, 55 s Isp, 1000 kg satellite mass), the foreseen gas consumption is 35 kg in Mission mode and 15 kg in Orbit Control mode. This consumption is a major factor in the trade-off between the two options.

The trade-off between reaction wheels and cold gas propulsion system is not completely done at this stage of the project. Both solutions are compatible with the mission needs. Reaction wheels are often used as main actuator in ACS, mainly because they do not need any propellant. They also provide the satellite attitude control system with a high torque capacity. However, they induce micro-vibrations which may be incompatible with atomic accelerometer measurements (the effect of micro-vibrations on the instrument has not been characterized yet). On the other hand, CGPS certainly induces a gas consumption which has to be taken into account in the satellite layout, but the feedback of high precision missions such as microscope (Delavault et al. 2019) or GAIA showed a very satisfactory level of performance well suited to GRICE needs. At this stage of the study, the CGPS is then the reference solution for the satellite layout.