Proposals to enhance satellite-based gravitational field recovery

The Gravitational Recovery And Climate Experiment Follow-On (GRACE-FO) mission provides incredibly accurate measurements of changes in the Earth's gravitational field; important for climate scientists, oceanographers and geologists. In our paper, we propose new techniques to enhance such missions.
Published in Physics

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Why do we care about measuring changes in the Earth's gravitational field?

There are a huge number of reasons to track changes in Earth's gravity. Measuring changes in the Earth's gravitational field can provide information about water movement across the Earth, important for predicting droughts and flooding. Changes in the Earth's gravitational field also provides information about earthquakes and movement below the Earth's surface after an earthquake. Finally, such measurements are important for measuring climate change, providing information about changes in ice mass and sea levels.

How do we measure changes in the Earth's gravitational field?

The GRACE-FO mission consists of two satellites which orbit the Earth on similar trajectories. By using a microwave ranging system, the separation between the two satellites can be measured over time. The changes in this satellite separation at different positions can be used to infer changes in the gravitational field of the Earth at that position. For example, if one satellite passes over a region where the gravitational field is very strong, e.g. when flying over Mount Everest or Slieve Donard, then this satellite will experience a stronger gravitational attraction, accelerating it and changing the satellite separation. By reverse engineering this process, from measuring changes in the satellite separation we can learn about changes in the gravitational field.

What are the noise sources in such a measurement?

When measuring the satellite separation, some noise is introduced, which ultimately corrupts the gravitational field recovery. If we could remove this noise, we could make more accurate measurements of the Earth's gravitational field. In our paper we considered three sources of noise and proposed techniques to reduce each of them in turn. The GRACE-FO mission uses a laser ranging interferometer as well as the microwave ranging system. By measuring changes in the phase of the laser as the satellites move, changes in the satellite separation can be inferred. However, the phase of the laser will drift naturally over time, even if the satellite separation isn't changing. This adds noise to the measurement of the satellite separation. The GRACE-FO mission also requires an accelerometer on-board each satellite to remove non-gravitational accelerations, such as drag or solar radiation pressure. Imperfections in the accelerometer will also add noise to our measurement. Finally, quantum noise, caused by unavoidable fluctuations in the number of photons arriving at each satellite will also add noise. By proposing techniques to remove these noises, we hope that future satellite-based geodesy missions can be improved. 

How can we remove this noise?

Our main result focuses on the removal of the laser phase noise. By introducing a third satellite, we can make two satellite separation measurements, between the middle satellite and the leading satellite and between the middle satellite and the trailing satellite. We were able to show that careful post-processing of this measured data would allow for the removal of the laser phase noise. The reason for this is that the laser phase noise is now common to both satellites and so can be cancelled out. This can allow several orders of magnitude improvement in the signal-to-noise ratio of the measured signal. We were also able to show that by switching to a six satellite configuration, the accelerometer noise can be removed. Finally, we considered using squeezed light, a uniquely quantum mechanical technology, to reduce the quantum noise. However, we found that squeezed light does not improve the signal-to-noise ratio in the appropriate regime for satellite geodesy. 

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