Kenneth Nordtvedt

The Apache Point Observatory Lunar Laser-ranging Operation: Instrument Description and First Detections

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. The Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) has achieved 1m mrange precision to the moon, which should lead to ap- proximately 1 order-of-magnitude improvements in several tests of fundamental properties of gravity. We briefly outline the scientific goals, and then give a detailed discussion of the APOLLO instrumentation.

The Solar Test of the Equivalence Principle

The Earth, Mars, Sun, Jupiter system allows for a sensitive test of the strong equivalence principle (SEP) which is qualitatively different from that provided by Lunar Laser Ranging. Using analytic and numerical methods we demonstrate that Earth-Mars ranging can provide a useful estimate of the SEP parameter η. Two estimates of the predicted accuracy are derived and quoted, one based on conventional covariance analysis, and another (called “modified worst case” analysis) which assumes that systematic errors dominate the experiment. If future Mars missions provide ranging measurements with an accuracy of σ meters, after ten years of ranging the expected accuracy for the SEP parameter η will be of order (1 − 12) × 10 4 σ. These ranging measurements will also provide the most accurate determination of the mass of Jupiter, independent of the SEP effect test. Subject headings: celestial mechanics, stellar dynamics – gravitation – Earth – planets and satellites: Mars – dark matter

35 years of testing relativistic gravity: Where do we go from here?

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 - 1 4 , translating to a test of the SEP violation parameter, η, to a precision of ∼ 3 × 10 - 5 . In addition, the ν 2 /c 2 general relativistic effects would be tested to better than 0.1%, and measurements of the relative change in the gravitational constant, 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, oc G 2 . The Laser Astrometric Test Of Relativity (LATOR) will not only improve the value of the parameterized post-Newtonian (PPN) γ to unprecedented levels of accuracy of 1 part in 10 8 , 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.

The Apache Point Observatory Lunar Laser-ranging Operation (APOLLO): Two Years of Millimeter-Precision Measurements of the Earth-Moon Range1

Lunar Laser Ranging (LLR) is the only means available for testing Einstein’s Strong Equivalence Principle, on which general relativity rests. LLR also provides the strongest limits to date on variability of the gravitational constant, the best measurement of the de Sitter precession rate, and is relied upon to generate accurate astronomical ephemerides. LLR is poised to take a dramatic step forward, enabled both by detector technology and access to a large-aperture astronomical telescope. Using the 3.5 m telescope at the Apache Point Observatory, we will push LLR into a new regime of multiple photon returns with each pulse, enabling millimeter range precision to be achieved. In order to reap the benefits of this “strong” return, we will incorporate a technologically novel integrated array of avalanche photodiodes—capable of generating a temporal range profile while preserving two-dimensional spatial information. We will also employ a high precision gravimeter at the ranging site to measure local displacements of the earth’s crust to sub-millimeter precision. This approach of obtaining directly relevant measurements relating to the earth surface deformation is to be contrasted with the approach to date that relies strictly on models for this information.

Experimental design for the LATOR mission

This paper discusses experimental design for the Laser Astrometric Test Of Relativity (LATOR) mission. LATOR is designed to reach unprecedented accuracy of 1 part in 10^8 in measuring the curvature of the solar gravitational field as given by the value of the key Eddington post-Newtonian parameter \gamma. This mission will demonstrate the accuracy needed to measure effects of the next post-Newtonian order (~G^2) of light deflection resulting from gravitys intrinsic non-linearity. LATOR will provide the first precise measurement of the solar quadrupole moment parameter, J2, and will improve determination of a variety of relativistic effects including Lense-Thirring precession. The mission will benefit from the recent progress in the optical communication technologies -- the immediate and natural step above the standard radio-metric techniques. The key element of LATOR is a geometric redundancy provided by the laser ranging and long-baseline optical interferometry. We discuss the mission and optical designs, as well as the expected performance of this proposed mission. 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.

The Laser Astrometric Test of Relativity (LATOR) Mission

This paper discusses the motivation and general design elements of a new fundamental physics experiment that will test relativistic gravity at the accuracy better than the effects of the second order in the gravitational field strength, G 2 . The laser astrometric test of relativity (LATOR) mission uses laser interferometry between two micro-spacecraft whose lines of sight pass close by the Sun to accurately measure deflection of light in the solar gravity. The key element of the experimental design is a redundant geometry optical truss provided by a long-baseline (100 m) multi-channel stellar optical interferometer placed on the International Space Station (ISS). The spatial interferometer is used for measuring the angles between the two spacecraft and for orbit determination purposes. In Euclidean geometry, determination of a triangles three sides determines any angle therein; with gravity changing the optical lengths of sides passing close by the Sun and deflecting the light, the Euclidean relationships are overthrown. The geometric redundancy enables LATOR to measure the departure from Euclidean geometry caused by the solar gravity field to a very high accuracy. LATOR will not only improve the value of the parametrized post-Newtonian (PPN) parameter y to unprecedented levels of accuracy of 1 part in 10 8 , it will also reach the ability to measure effects of the next post-Newtonian order (G 2 ) of light deflection resulting from gravitys intrinsic nonlinearity. The solar quadrupole moment parameter, J 2 , will be measured with high precision, as well as a variety of other relativistic effects including Lense-Thirring precession. 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 analogues to the LATOR experiment; it is unique and is a natural culmination of solar system gravity experiments.

LATOR: ITS SCIENCE PRODUCT AND ORBITAL CONSIDERATIONS

In a LATOR mission to measure the non-Euclidean relationship between three sides and one angle of a light triangle near the Sun, the primary science parameter, to be measured to part-in-109 precision, is shown to include not only the key parametrized post-Newtonian (PPN) γ, but also the Suns additional mass parameter, MΓ, which appears in the spatial metric field potential. MΓ may deviate from the Suns well-measured gravitational mass due to post-Newtonian features of gravitational theory not previously measured in relativistic gravity observations. Under plausible assumptions, MΓ is a linear combination of the Suns gravitational and inertial masses. If LATORs two spacecraft lines of sight are kept close to equal and opposite relative to the Sun during the missions key measurements of the light triangle, it is found that the navigational requirements for the spacecraft positions are greatly relaxed, eliminating the need for on-board drag-free systems. Spacecraft orbits from the Earth to achieve the e...

Shooting the Moon: Laser Ranging Pushes Tests of Einstein's Gravity

Decades of lunar laser ranging have produced superlative tests of Einsteins general relativity. A new effort (APOLLO) seeks to extend these tests another order-of-magnitude via millimeter range accuracy between Earth and Moon.