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Register a new userModeling and Analysis of the APOLLO Lunar Laser Ranging Data
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The Earth-Moon-Sun system has traditionally provided the best laboratory for testing the strong equivalence principle. For a decade, the Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) has been producing the worlds best lunar laser ranging data. At present, a single observing session of about an hour yields a distance measurement with uncertainty of about 2~mm, an order of magnitude advance over the best pre-APOLLO lunar laser ranging data. However, these superb data have not yet yielded scientific results commensurate with their accuracy, number, and temporal distribution. There are two reasons for this. First, even in the relatively clean environment of the Earth-Moon system, a large number of effects modify the measured distance importantly and thus need to be included in the analysis model. The second reason is more complicated. The traditional problem with the analysis of solar-system metric data is that the physical model must be truncated to avoid extra parameters that would increase the condition number of the estimator. Even in a typical APOLLO analysis that does not include parameters of gravity physics, the condition number is very high: $8 times 10^{10}$.
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A next-generation lunar laser ranging apparatus using the 3.5 m telescope at the Apache Point Observatory in southern New Mexico has begun science operation. APOLLO (the Apache Point Observatory Lunar Laser-ranging Operation) has achieved one-millimeter range precision to the moon which should lead to approximately one-order-of-magnitude improvements in the precision of several tests of fundamental properties of gravity. We briefly motivate the scientific goals, and then give a detailed discussion of the APOLLO instrumentation.
The Lunar Laser Ranging (LLR) experiment has accumulated 50 years of range data of improving accuracy from ground stations to the laser retroreflector arrays (LRAs) on the lunar surface. The upcoming decade offers several opportunities to break new ground in data precision through the deployment of the next generation of single corner-cube lunar retroreflectors and active laser transponders. This is likely to expand the LLR station network. Lunar dynamical models and analysis tools have the potential to improve and fully exploit the long temporal baseline and precision allowed by millimetric LLR data. Some of the model limitations are outlined for future efforts. Differential observation techniques will help mitigate some of the primary limiting factors and reach unprecedented accuracy. Such observations and techniques may enable the detection of several subtle signatures required to understand the dynamics of the Earth-Moon system and the deep lunar interior. LLR model improvements would impact multi-disciplinary fields that include lunar and planetary science, Earth science, fundamental physics, celestial mechanics and ephemerides.
Arm-locking is a technique for stabilizing the frequency of a laser in an inter-spacecraft interferometer by using the spacecraft separation as the frequency reference. A candidate technique for future space-based gravitational wave detectors such as the Laser Interferometer Space Antenna (LISA), arm-locking has been extensive studied in this context through analytic models, time-domain simulations, and hardware-in-the-loop laboratory demonstrations. In this paper we show the Laser Ranging Interferometer instrument flying aboard the upcoming Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) mission provides an appropriate platform for an on-orbit demonstration of the arm-locking technique. We describe an arm-locking controller design for the GRACE-FO system and a series of time-domain simulations that demonstrate its feasibility. We conclude that it is possible to achieve laser frequency noise suppression of roughly two orders of magnitude around a Fourier frequency of 1Hz with conservative margins on the systems stability. We further demonstrate that `pulling of the master laser frequency due to fluctuating Doppler shifts and lock acquisition transients is less than $100,$MHz over several GRACE-FO orbits. These findings motivate further study of the implementation of such a demonstration.
The Lunar Laser Ranging (LLR) experiment provides precise observations of the lunar orbit that contribute to a wide range of science investigations. In particular, time series of highly accurate measurements of the distance between the Earth and Moon provide unique information that determine whether, in accordance with the Equivalence Principle (EP), both of these celestial bodies are falling towards the Sun at the same rate, despite their different masses, compositions, and gravitational self-energies. Analyses of precise laser ranges to the Moon continue to provide increasingly stringent limits on any violation of the EP. Current LLR solutions give (-0.8 +/- 1.3) x 10^{-13} for any possible inequality in the ratios of the gravitational and inertial masses for the Earth and Moon, (m_G/m_I)_E - (m_G/m_I)_M. Such an accurate result allows other tests of gravitational theories. Focusing on the tests of the EP, we discuss the existing data and data analysis techniques. The robustness of the LLR solutions is demonstrated with several different approaches to solutions. Additional high accuracy ranges and improvements in the LLR data analysis model will further advance the research of relativistic gravity in the solar system, and will continue to provide highly accurate tests of the Equivalence Principle.
The Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) began millimeter-precision ranging to the Moon in 2006. Until now, a comprehensive validation of APOLLO system range accuracy has not been possible because of centimeter-scale deficiencies in computational models of the Earth-Moon range, and because APOLLO lacked an internal timing calibration system. Here, we report on the development of a system that enables in-situ calibration of the timing response of the APOLLO apparatus, simultaneous with lunar range measurements. The system was installed in August 2016. Preliminary results show that the APOLLO system can provide lunar range measurements with millimeter accuracy.
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