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ABSTRACT: Lunar laser ranging (LLR) has made major contributions to our understanding
of the Moon's internal structure and the dynamics of the Earth-Moon system.
Because of the recent improvements of the ground-based laser ranging
facilities, the present LLR measurement accuracy is limited by the
retro-reflectors currently on the lunar surface, which are arrays of small
corner-cubes. Because of lunar librations, the surfaces of these arrays do not,
in general, point directly at the Earth. This effect results in a spread of
arrival times, because each cube that comprises the retroreflector is at a
slightly different distance from the Earth, leading to the reduced ranging
accuracy. Thus, a single, wide aperture corner-cube could have a clear
advantage. In addition, after nearly four decades of successful operations the
retro-reflectors arrays currently on the Moon started to show performance
degradation; as a result, they yield still useful, but much weaker return
signals. Thus, fresh and bright instruments on the lunar surface are needed to
continue precision LLR measurements. We have developed a new retro-reflector
design to enable advanced LLR operations. It is based on a single, hollow
corner cube with a large aperture for which preliminary thermal, mechanical,
and optical design and analysis have been performed. The new instrument will be
able to reach an Earth-Moon range precision of 1-mm in a single pulse while
being subjected to significant thermal variations present on the lunar surface,
and will have low mass to allow robotic deployment. Here we report on our
design results and instrument development effort.
10/2012;
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ABSTRACT: 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.
03/2012;
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ABSTRACT: Since it's initiation by the Apollo 11 astronauts in 1969, LLR has
strongly contributed to our understanding of the Moon's internal
structure and the dynamics of the Earth-Moon system. The data provide
for unique, multi-disciplinary results in the areas of lunar science,
gravitational physics, Earth sciences, geodesy and geodynamics, solar
system ephemerides, and terrestrial and celestial reference frames.
However, the current distribution of the retroreflectors is not optimal,
other weaknesses exist. A geographic distribution of new instruments on
the lunar surface wider than the current distribution would be a great
benefit; the accuracy of the lunar science parameters would increase
several times. We are developing the next-generation of the LLR
experiment. This work includes development of new retroreflector arrays
and laser transponders to be deployed on the lunar surface by a series
of proposed missions to the moon. The new laser instruments will enable
strong advancements in LLR-derived science. Anticipated science impact
includes lunar science, gravitational physics, geophysics, and geodesy.
Thus, properties of the lunar interior, including tidal properties,
liquid core and solid inner core can be determined from lunar rotation,
orientation, and tidal response. Anticipated improvements in Earth
geophysics and geodesy would include the positions and rates for the
Earth stations, Earth rotation, precession rate, nutation, and tidal
influences on the orbit. Strong improvements are also expected in
several tests of general relativity. We address the science return
enabled by the new laser retroreflectors. We also discuss deployment of
pulsed laser transponders with future landers on Mars/Phobos. The
development of active laser techniques would extend the accuracies
characteristic of passive laser tracking to interplanetary distances.
Highly-accurate time-series of the round-trip travel times of laser
pulses between an observatory on the Earth and an optical transponder on
Mars/Phobos could lead to major advances in science investigations of
Mars/Phobos. Technology is available to conduct such measurements with
a picosecond timing precision which could translate into mm-level
accuracies achieved in ranging between the Earth and Mars/Phobos. The
resulting Mars Laser Ranging (MLR) would provide new opportunities for
robust advances in the tests of relativistic gravity and the properties
of Martian interior, including liquid core, could be determined from
Martian rotation, orientation, tidal response. Alternatively, Phobos
laser Ranging (PLR) would benefit the study of Phobos and the Martian
system. Given the current technology readiness level, PLR could be
started in 2011 for launch in 2016 for 3 years of science operations. We
discuss the PLR's science objectives, instrument, and mission design. We
also present the details of science simulations performed to support the
mission's primary objectives. The work described here was carried out
at the Jet Propulsion Laboratory, California Institute of Technology
under a contract with the National Aeronautics and Space Administration.
04/2010; 12:1025.
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ABSTRACT: Phobos Laser Ranging (PLR) is a concept for a space mission designed to
advance tests of relativistic gravity in the solar system. PLR's primary
objective is to measure the curvature of space around the Sun, represented by
the Eddington parameter $\gamma$, with an accuracy of two parts in $10^7$,
thereby improving today's best result by two orders of magnitude. Other mission
goals include measurements of the time-rate-of-change of the gravitational
constant, $G$ and of the gravitational inverse square law at 1.5 AU
distances--with up to two orders-of-magnitude improvement for each. The science
parameters will be estimated using laser ranging measurements of the distance
between an Earth station and an active laser transponder on Phobos capable of
reaching mm-level range resolution. A transponder on Phobos sending 0.25 mJ, 10
ps pulses at 1 kHz, and receiving asynchronous 1 kHz pulses from earth via a 12
cm aperture will permit links that even at maximum range will exceed a photon
per second. A total measurement precision of 50 ps demands a few hundred
photons to average to 1 mm (3.3 ps) range precision. Existing satellite laser
ranging (SLR) facilities--with appropriate augmentation--may be able to
participate in PLR. Since Phobos' orbital period is about 8 hours, each
observatory is guaranteed visibility of the Phobos instrument every Earth day.
Given the current technology readiness level, PLR could be started in 2011 for
launch in 2016 for 3 years of science operations. We discuss the PLR's science
objectives, instrument, and mission design. We also present the details of
science simulations performed to support the mission's primary objectives.
03/2010;
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Slava G. Turyshev,
Murphy, Jr., Thomas W,
Eric G. Adelberger,
James Battat,
Douglas Currie,
William M. Folkner,
Jens Gundlach,
Stephen M. Merkowitz,
Kenneth L. Nordtvedt,
Robert D. Reasenberg,
Irwin I. Shapiro,
Michael Shao,
Christopher W. Stubbs,
Massimo Tinto, James G. Williams,
Nan Yu
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ABSTRACT: The recent discovery of "dark energy" has challenged Einstein's general
theory of relativity as a complete model for our macroscopic universe. From a
theoretical view, the challenge is even stronger: general relativity clearly
does not extend to the very small, where quantum mechanics holds sway.
Fundamental physics models thus require some major revisions. We must explore
deeper to both constrain and inspire this needed new physics. In the realm of
the solar-system, we can effectively probe for small deviations from the
predictions of general relativity: Technology now offers a wide range of
opportunities to pursue experiments with accuracies orders of magnitude better
than yet achieved. We describe both the relevant theoretical backgrounds and
the opportunities for far more accurate solar system experiments.
03/2009;
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ABSTRACT: A decreasing gravitational constant, G, coupled with angular momentum conservation is expected to increrase a planetary semimajor axis, a, as \dot a/a=-\dot G/G. Analysis of lunar laser ranging data strongly limits such temporal variations and constrains a local (~1 AU) scale expansion of the solar system as \dot a/a=-\dot G/G =-(4\pm9)\times10^{-13} yr^{-1}, including that due to cosmological effects.
01/2007;
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ABSTRACT: Existing capabilities in laser ranging, optical interferometry and metrology, in combination with precision frequency standards, atom-based quantum sensors, and drag-free technologies, are critical for the space-based tests of fundamental physics; as a result, of the recent progress in these disciplines, the entire area is poised for major advances. Thus, accurate ranging to the Moon and Mars will provide significant improvements in several gravity tests, namely the equivalence principle, geodetic precession, PPN parameters $\beta$ and $\gamma$, and possible variation of the gravitational constant $G$. Other tests will become possible with development of an optical architecture that would allow proceeding from meter to centimeter to millimeter range accuracies on interplanetary distances. Motivated by anticipated accuracy gains, we discuss the recent renaissance in lunar laser ranging and consider future relativistic gravity experiments with precision laser ranging over interplanetary distances.
12/2006;
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ABSTRACT: Lunar laser ranging (LLR) is used to conduct high-precision measurements of ranges between an observatory on Earth and a laser retro-reflector on the lunar surface. Over the years, LLR has benefited from a number of improvements both in observing technology and data modeling, which led to the current accuracy of post-fit residuals of ~2 cm. Today LLR is a primary technique to study the dynamics of the Earth-Moon system and is especially important for gravitational physics, geodesy and studies of the lunar interior. LLR is used to perform high-accuracy tests of the equivalence principle, to search for a time-variation in the gravitational constant, and to test predictions of various alternative theories of gravity. On the geodesy front, LLR contributes to the determination of Earth orientation parameters, such as nutation, precession (including relativistic precession), polar motion, and UT1, i.e. especially to the long-term variation of these effects. LLR contributes to the realization of both the terrestrial and selenocentric reference frames. The realization of a dynamically defined inertial reference frame, in contrast to the kinematically realized frame of VLBI, offers new possibilities for mutual cross-checking and confirmation. Finally, LLR also investigates the processes related to the Moon's interior dynamics. Here, we review the LLR technique focusing on its impact on relativity and give an outlook to further applications, e.g. in geodesy. We present results of our dedicated studies to investigate the sensitivity of LLR data with respect to the relativistic quantities. We discuss the current observational situation and the level of LLR modeling implemented to date. We also address improvements needed to fully utilize the scientific potential of LLR.
10/2005;
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ABSTRACT: Lunar Laser Ranging (LLR), which has been carried out for more than 35 years, is used to determine many parameters within the Earth-Moon system. This includes coordinates of terrestrial ranging stations and that of lunar retro-reflectors, as well as lunar orbit, gravity field, and its tidal acceleration. LLR data analysis also performs a number of gravitational physics experiments such as test of the equivalence principle, search for time variation of the gravitational constant, and determines value of several metric gravity parameters. These gravitational physics parameters cause both secular and periodic effects on the lunar orbit that are detectable with LLR. Furthermore, LLR contributes to the determination of Earth orientation parameters (EOP) such as nutation, precession (including relativistic precession), polar motion, and UT1. The corresponding LLR EOP series is three decades long. LLR can be used for the realization of both the terrestrial and selenocentric reference frames. The realization of a dynamically defined inertial reference frame, in contrast to the kinematically realized frame of VLBI, offers new possibilities for mutual cross-checking and confirmation. Finally, LLR also investigates the processes related to the Moon's interior dynamics. Here, we review the LLR technique focusing on its impact on Geodesy and Relativity. We discuss the modern observational accuracy and the level of existing LLR modeling. We present the near-term objectives and emphasize improvements needed to fully utilize the scientific potential of LLR. Comment: 7 pages, 7 figures, 2 tables. Talk given at `Dynamic Planet 2005: Monitoring and Understanding a Dynamic Planet with Geodetic and Oceanographic Tools,'' a Joint Assembly of International Associations: IAG, IAPSO and IABO, Cairns, Australia, 22-26 August 2005
09/2005;
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ABSTRACT: A primary objective of the Lunar Laser Ranging (LLR) experiment is to provide precise observations of the lunar orbit that contribute to a wide range of science investigations. Time series of the highly accurate measurements of the distance between the Earth and Moon provide unique information used to 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. Current LLR solutions give $(-1.0 \pm 1.4) \times 10^{-13}$ for any possible inequality in the ratios of the gravitational and inertial masses for the Earth and Moon, $\Delta(M_G/M_I)$. This result, in combination with laboratory experiments on the weak equivalence principle, yields a strong equivalence principle (SEP) test of $\Delta(M_G/M_I)_{\tt SEP} = (-2.0 \pm 2.0) \times 10^{-13}$. Such an accurate result allows other tests of gravitational theories. The result of the SEP test translates into a value for the corresponding SEP violation parameter $\eta$ of $(4.4 \pm 4.5)\times10^{-4}$, where $\eta = 4\beta -\gamma -3$ and both $\gamma$ and $\beta$ are parametrized post-Newtonian (PPN) parameters. The PPN parameter $\beta$ is determined to be $\beta - 1 = (1.2 \pm 1.1) \times 10^{-4}$. Focusing on the tests of the EP, we discuss the existing data, and characterize the modeling and data analysis techniques. The robustness of the LLR solutions is demonstrated with several different approaches that are presented in the text. We emphasize that near-term improvements in the LLR ranging accuracy will further advance the research of relativistic gravity in the solar system, and, most notably, will continue to provide highly accurate tests of the Equivalence Principle. Comment: 50 pages, 18 figures, 4 tables
07/2005;
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ABSTRACT: Analyses of laser ranges to the Moon provide increasingly stringent limits on any violation of the equivalence principle (EP); they also enable several very accurate tests of relativistic gravity. These analyses give an EP test of Delta(MG/MI)EP=(-1.0+/-1.4) x 10(-13). This result yields a strong equivalence principle (SEP) test of Delta(MG/MI)SEP=(-2.0+/-2.0) x 10(-13). Also, the corresponding SEP violation parameter eta is (4.4+/-4.5) x 10(-4), where eta=4beta-gamma-3 and both beta and gamma are post-Newtonian parameters. Using the Cassini gamma, the eta result yields beta-1=(1.2+/-1.1) x 10(-4). The geodetic precession test, expressed as a relative deviation from general relativity, is Kgp=-0.0019+/-0.0064. The search for a time variation in the gravitational constant results in G /G=(4+/-9) x 10(-13) yr(-1); consequently there is no evidence for local (approximately 1 AU) scale expansion of the solar system.
Physical Review Letters 01/2005; 93(26 Pt 1):261101. · 7.37 Impact Factor
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ABSTRACT: Analysis of Lunar Laser Ranging (LLR) data provides science results: gravitational physics and ephemeris information from the orbit, lunar science from rotation and solid-body tides, and Earth science. Sensitive tests of gravitational physics include the Equivalence Principle, limits on the time variation of the gravitational constant G, and geodetic precession. The equivalence principle test is used for an accurate determination of the parametrized post-Newtonian (PPN) parameter \beta. Lunar ephemerides are a product of the LLR analysis used by current and future spacecraft missions. The analysis is sensitive to astronomical parameters such as orbit, masses and obliquity. The dissipation-caused semimajor axis rate is 37.9 mm/yr and the associated acceleration in orbital longitude is -25.7 ''/cent^2, dominated by tides on Earth with a 1% lunar contribution. Lunar rotational variation has sensitivity to interior structure, physical properties, and energy dissipation. The second-degree lunar Love numbers are detected; k_2 has an accuracy of 11%. Lunar tidal dissipation is strong and its Q has a weak dependence on tidal frequency. A fluid core of about 20% the Moon's radius is indicated by the dissipation data. Evidence for the oblateness of the lunar fluid-core/solid-mantle boundary is getting stronger. This would be independent evidence for a fluid lunar core. Moon-centered coordinates of four retroreflectors are determined. Station positions and motion, Earth rotation variations, nutation, and precession are determined from analyses. Extending the data span and improving range accuracy will yield improved and new scientific results. Adding either new retroreflectors or precise active transponders on the Moon would improve the accuracy of the science results.
12/2004;
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ABSTRACT: Current and future optical technologies will aid exploration of the Moon and Mars while advancing fundamental physics research in the solar system. Technologies and possible improvements in the laser-enabled tests of various physical phenomena are considered along with a space architecture that could be the cornerstone for robotic and human exploration of the solar system. In particular, accurate ranging to the Moon and Mars would not only lead to construction of a new space communication infrastructure enabling an improved navigational accuracy, but will also provide a significant improvement in several tests of gravitational theory: the equivalence principle, geodetic precession, PPN parameters $\beta$ and $\gamma$, and possible variation of the gravitational constant $G$. Other tests would become possible with an optical architecture that would allow proceeding from meter to centimeter to millimeter range accuracies on interplanetary distances. This paper discusses the current state and the future improvements in the tests of relativistic gravity with Lunar Laser Ranging (LLR). We also consider precision gravitational tests with the future laser ranging to Mars and discuss optical design of the proposed Laser Astrometric Test of Relativity (LATOR) mission. We emphasize that already existing capabilities can offer significant improvements not only in the tests of fundamental physics, but may also establish the infrastructure for space exploration in the near future. Looking to future exploration, what characteristics are desired for the next generation of ranging devices, what is the optimal architecture that would benefit both space exploration and fundamental physics, and what fundamental questions can be investigated? We try to answer these questions.
12/2004;
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ABSTRACT: This paper addresses the motivation, technology and recent results in the tests of the general theory of relativity in the solar system. We specifically discuss Lunar Laser Ranging (LLR), the only technique available to test the Strong Equivalence Principle (SEP) and presently the most accurate method to test for the constancy of the gravitational constant G. After almost 35 years since beginning of the experiment, LLR is poised to take a dramatic step forward by proceeding from cm to mm range accuracies enabled by the new Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) currently under development in New Mexico. This facility will enable tests of the Weak and Strong Equivalence Principles with a sensitivity approaching 10–14, translating to a test of the SEP violation parameter, [(G)\dot]/G\dot{G}/G, would be~0.1% the inverse age of the universe.
This paper also discusses a new fundamental physics experiment that will test relativistic gravity with an accuracy better than the effects of the second order in the gravitational field strength, G2. The Laser Astrometric Test Of Relativity (LATOR) will not only improve the value of the parameterized post-Newtonian (PPN) to unprecedented levels of accuracy of 1 part in 108, it will also be able to measure effects of the next post-Newtonian order (c–4) of light deflection resulting from gravitys intrinsic non-linearity, as well as measure a variety of other relativistic effects. LATOR will lead to very robust advances in the tests of fundamental physics: this mission could discover a violation or extension of general relativity, or reveal the presence of an additional long range interaction in the physical law. There are no analogs to the LATOR experiment; it is unique and is a natural culmination of solar system gravity experiments.
08/2004: pages 311-330;
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ABSTRACT: Accurate analysis of precision ranges to the Moon has provided several tests of gravitational theory including the Equivalence Principle, geodetic precession, parameterized post-Newtonian (PPN) parameters $\gamma$ and $\beta$, and the constancy of the gravitational constant {\it G}. Since the beginning of the experiment in 1969, the uncertainties of these tests have decreased considerably as data accuracies have improved and data time span has lengthened. We are exploring the modeling improvements necessary to proceed from cm to mm range accuracies enabled by the new Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) currently under development in New Mexico. This facility will be able to make a significant contribution to the solar system tests of fundamental and gravitational physics. In particular, the Weak and Strong Equivalence Principle tests would have a sensitivity approaching 10$^{-14}$, yielding sensitivity for the SEP violation parameter $\eta$ of $\sim 3\times 10^{-5}$, $v^2/c^2$ general relativistic effects would be tested to better than 0.1%, and measurements of the relative change in the gravitational constant, $\dot{G}/G$, would be $\sim0.1$% the inverse age of the universe. Having this expected accuracy in mind, we discusses the current techniques, methods and existing physical models used to process the LLR data. We also identify the challenges for modeling and data analysis that the LLR community faces today in order to take full advantage of the new APOLLO ranging station.
12/2003;
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ABSTRACT: Recent observations of Europa suggest that the Jovian satellite may have a liquid ocean underneath its icy surface. Geophysical models indicate that the tidal Love number k2 has a strong dependence on the presence or ab-sence of an ocean. The k2 dependence on the ice shell thick-ness is also significant. Measurements of the static and tidal gravity fields through their dynamic effects on the trajec-tory of a low Europan orbiter can be essential in the detec-tion of an ocean and inference of other internal structures. Covariance analyses have been carried out to assess accura-cies using simulated Doppler tracking data. With 15 days of tracking from 2 Earth stations, the uncertainties for k2, mantle libration amplitude and the epoch radial position of the spacecraft are expected to be 0.0004, 2.8 arcsec and 5.7 m, respectively. These tight constraints will strongly con-tribute to ocean detection and ice thickness determination when combined with altimeter measurements.
01/2001; 28(1):2245-2248.
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ABSTRACT: The lunar interior is hidden, but Lunar Laser Ranging (LLR) senses interior properties through physical librations and tides. The mean density of the Moon is like rock and the mean moment of inertia is only 1.6% less than a uniform body would have. Neither is compatible with a large dense core like the Earth's, though a small dense core is permitted. The solid-body tides are proportional to Love numbers that depend on interior structure and the radial dependence of elastic parameters and density. A small core, either solid or fluid, increases the Love numbers by a few percent, but uncertainty of deep elastic parameters also affects Love number computations. LLR sees three effects through the physical librations that indicate a fluid core. The strongest effect is from energy dissipation arising at the fluid-core/solid-mantle boundary (CMB). Since there is also dissipation from tides in the solid mantle, we separate tide and CMB dissipation by determining phase shifts in multiple periodic libration terms. The second indicator of a fluid core comes from the oblateness of the CMB which causes a torque as the fluid moves along the oblate surface. The third effect comes from the moment of inertia of the fluid core which affects the amplitude of a physical libration term. The fluid moment is difficult to detect, but it is now weakly seen and its determination should improve from future LLR data. LLR does not separate fluid core density and size, but if the fluid core has the density of iron then a radius of roughly 330-400 km is suggested. Lower density materials would have larger radii; Fe-FeS mixtures are attractive because they have lower freezing points. The dissipation analysis which gives CMB dissipation also gives tidal Q vs frequency. At one month Q is ~30, while Q is ~35 at one year. These low values may come from the lower mantle which is suspected to be a partial melt. How can the core and mantle parameter determinations be improved? Expanded modeling may improve fits and add parameters. Long LLR data spans are important, so future accurate ranges to the four retroreflector arrays are requested. Expanding the number and spread of lunar retroreflector sites, by finding the lost Lunokhod 1 rover or placing new retroreflectors on the Moon, would also benefit the extraction of scientific information from LLR data.
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ABSTRACT: Laser pulses fired at retroreflectors on the Moon provide very accurate ranges. Analysis yields information on Earth, Moon, and orbit. The highly accurate retroreflector positions have uncertainties less than a meter. Tides on the Moon show strong dissipation, with Q = 33 ± 4 at a month and a weak dependence on period. Lunar rotation depends on interior properties; a fluid core is indicated with radius ∼20% that of the Moon. Tests of relativistic gravity verify the equivalence principle to ±1.4 × 10−13, limit deviations from Einstein’s general relativity, and show no rate for the gravitational constant with uncertainty 9 × 10−13/year.
Advances in Space Research.
