P. L. Bender

Lunar Laser Ranging: A Continuing Legacy of the Apollo Program

On 21 July 1969, during the first manned lunar mission, Apollo 11, the first retroreflector array was placed on the moon, enabling highly accurate measurements of the Earthmoon separation by means of laser ranging. Lunar laser ranging (LLR) turns the Earthmoon system into a laboratory for a broad range of investigations, including astronomy, lunar science, gravitational physics, geodesy, and geodynamics. Contributions from LLR include the three-orders-of-magnitude improvement in accuracy in the lunar ephemeris, a several-orders-of-magnitude improvement in the measurement of the variations in the moons rotation, and the verification of the principle of equivalence for massive bodies with unprecedented accuracy. Lunar laser ranging analysis has provided measurements of the Earths precession, the moons tidal acceleration, and lunar rotational dissipation. These scientific results, current technological developments, and prospects for the future are discussed here.

The Lunar Laser Ranging Experiment: Accurate ranges have given a large improvement in the lunar orbit and new selenophysical information

The lunar ranging measurements now being made at the McDonald Observatory have an accuracy of 1 nsec in round-trip travel time. This corresponds to 15 cm in the one-way distance. The use of lasers with pulse-lengths of less than 1 nsec is expected to give an accuracy of 2 to 3 cm in the next few years. A new station is under construction in Hawaii, and additional stations in other countries are either in operation or under development. It is hoped that these stations will form the basis for a worldwide network to determine polar motion and earth rotation on a regular basis, and will assist in providing information about movement of the tectonic plates making up the earths surface. Several mobile lunar ranging stations with telescopes having diameters of 1.0 m or less could, in the future, greatly extend the information obtainable about motions within and between the tectonic plates. The data obtained so far by the McDonald Observatory have been used to generate a new lunar ephemeris based on direct numerical integration of the equations of motion for the moon and planets. With this ephemeris, the range to the three Apollo retro-reflectors can be fit to an accuracy of 5 m by adjusting the differences in moments of inertia of the moon about its principal axes, the selenocentric coordinates of the reflectors, and the McDonald longitude. The accuracy of fitting the results is limited currently by errors of the order of an arc second in the angular orientation of the moon, as derived from the best available theory of how the moon rotates in response to the torques acting on it. Both a new calculation of the moons orientation as a function of time based on direct numerical integration of the torque equations and a new analytic theory of the moons orientation are expected to be available soon, and to improve considerably the accuracy of fitting the data. The accuracy already achieved routinely in lunar laser ranging represents a hundredfold improvement over any previously available knowledge of the distance to points on the lunar surface. Already, extremely complex structure has been observed in the lunar rotation and significant improvement has been achieved in our knowledge of lunar orbit. The selenocentric coordinates of the retroreflectors give improved reference points for use in lunar mapping, and new information on the lunar mass distribution has been obtained. Beyond the applications discussed in this article, however, the history of science shows many cases of previously unknown, phenomena discovered as a consequence of major improvements in the accuracy of measurements. It will be interesting to see whether this once again proves the case as we acquire an extended series of lunar distance observations with decimetric and then centimetric accuracy.

Gravitational radiation from the Galaxy

The spectral flux of gravitational radiation incident on earth from the Galactic W UMa binaries, unevolved binaries, cataclysmic binaries, neutron star binaries, black hole-neutron star binaries, and close white dwarf binary (CWDB) systems is calculated. The peak values for the strain amplitude hv produced by the binaries are: log hv = -17.0/sq rt Hz at log v = -4.40 Hz for W UMas; log hv = -16.5/sq rt Hz at log v = -5.50 Hz for unevolved binaries; log hv = -18.2/sq rt Hz at log v = -5.15 Hz for neutron star binaries; log hv = -17.0/sq rt Hz at log v = -4.7 Hz for black hole-neutron star binaries; log hv = -18.0 /sq rt Hz at log v = -4.10 Hz for cataclysmic binaries, and log hv = -27.0/sq rt Hz at log v = -4.0 Hz for CWDBs. The gravitational flux at ultralow frequencies is emitted mainly by unevolved binaries. The integrated flux incident on earth is about 2.4 x 10 to the -9th ergs/sq cm/s. 74 refs.

Using the Global Positioning System (GPS) for geodetic positioning

The development of relatively inexpensive satellite receivers in the early 1970s has resulted in cost-effective applications of satellites for a variety of geodetic surveying needs. Currently achievable accuracies range from 10 to 20 centimeters. The NAVSTAR Global Positioning System, now under development by the Department of Defense, incorporates advanced technology which has the potential capability of revolutionizing satellite geodesy.Several concepts for utilizing GPS signals are briefly reviewed, and another concept, called the reconstructed carrier phase method, is described in some detail. This concept is being pursued by the Defense Mapping Agency, National Oceanic and Atmospheric Administration, and the U.S. Geological Survey. These agencies have numerous requirements for accurate positioning. Several prototype receivers are planned to be available for testing in mid-1982. These receivers should be highly portable, consume little power, and obtain base line accuracies of several centimeters in several hours of observation time. However, water vapor radiometers will be needed in order to achieve the full accuracy. Initial simulation results utilizing the reconstructed carrier phase method are included.

LISA: laser interferometer space antenna for gravitational wave measurements

LISA (laser interferometer space antenna) is designed to observe gravitational waves from violent events in the Universe in a frequency range from to which is totally inaccessible to ground-based experiments. It uses highly stabilized laser light (Nd:YAG, ) in a Michelson-type interferometer arrangement. A cluster of six spacecraft with two at each vertex of an equilateral triangle is placed in an Earth-like orbit at a distance of 1 AU from the Sun, and behind the Earth. Three subsets of four adjacent spacecraft each form an interferometer comprising a central station, consisting of two relatively adjacent spacecraft (200 km apart), and two spacecraft placed at a distance of from the centre to form arms which make an angle of with each other. Each spacecraft is equipped with a laser. A descoped LISA with only four spacecraft has undergone an ESA assessment study in the M3 cycle and the full six-spacecraft LISA mission has now been selected as a cornerstone mission in the ESA Horizon 2000-plus programme.

Confusion noise level due to galactic and extragalactic binaries

We have revised our earlier rough estimate of the combined galactic and extragalactic binary confusion noise level curve for gravitational waves. This was done to correct some numerical errors and to allow for roughly three frequency bins worth of information about weaker sources being lost for each galactic binary signal that is removed from the data. The results are still based on the spectral amplitude estimates for different types of galactic binaries reported by Hils et al in 1990, and assume that the gravitational wave power spectral densities for other galaxies are proportional to the optical luminosities. The estimated confusion noise level drops to the LISA instrumental noise level at between roughly 3 and 8 mHz.

LISA and its in-flight test precursor SMART-2

LISA will be the first space-home gravitational wave observatory. It aims to detect gravitational waves in the 0.1 MHz+1 Hz range from sources including galactic binaries, super-massive black-hole binaries, capture of objects by super-massive black-holes and stochastic background. LISA is an ESA approved Cornerstone Mission foreseen as a joint ESA-NASA endeavour to be launched in 2010-11. The principle of operation of LISA is based on laser ranging of test-masses under pure geodesic motion. Achieving pure geodesic motion at the level requested for LISA, 3×10^(−15) ms^(−2)/√Hz at 0.1 mHz, is considered a challenging technological objective. To reduce the risk, both ESA and NASA are pursuing an in-flight test of the relevant technology. The goal of the test is to demonstrate geodetic motion within one order of magnitude from the LISA performance. ESA has given this test as the primary goal of its technology dedicated mission SMART-2 with a launch in 2006. This paper describes the basics of LISA, its key technologies, and its in-flight precursor test on SMART-2.

Satellite-Satellite Laser Links for Future Gravity Missions

A strong candidate for use in future missions to map time variations in the Earths gravity field is laser heterodyne measurements between separate spacecraft. At the shortest wavelengths that can be measured in space, the main accuracy limitation for variations in the potential with latitude is expected to be the frequency stability of the laser. Thus the development of simple and reliable space-qualified lasers with high frequency stability appears to be an important goal for the near future.In the last few years, quite high stability has been achieved by locking the second harmonic of a Nd:YAG laser to a resonant absorption line of iodine molecules in an absorption cell. Such a laser system can be made quite robust, and temperature related frequency shifts can be controlled at a low value. Recent results from laboratory systems are described. The Allan standard deviation for the beat between two such lasers was 2 × 10−14 at 10 s, and reached 7 × 10−15 at 600 s.

Gravitational Radiation from Helium Cataclysmics

For a gravitational wave antenna in space, radiation from very large numbers of galactic binaries will be present in the observable frequency band from roughly 10-5 Hz to 1 Hz. At frequencies above about 3 mHz, signals from thousands of compact binaries will be resolvable in both frequency and direction. At lower frequencies, there will be confusion noise from having more than one binary per frequency resolution bin, even with a year or more of data. In this paper, we extend previous discussions of the galactic binaries to include an improved estimate of the contributions to the confusion noise from AM CVn binaries and their probable progenitors, which we refer to as helium cataclysmics. We find only a slight increase in the confusion noise below about 3 mHz, and essentially no increase at higher frequencies.

LISA Orbit Selection and Stability

The Laser Interferometer Space Antenna (LISA) is a space mission designed to detect gravitational waves in the frequency range from below 0.0001 Hz to 1 Hz by measuring changes in the distance between spacecraft separated by several million kilometres. The spacecraft orbit in a triangular formation forming three (not independent) interferometers with arm lengths determined by the distances between the vertices. The nominal orbit configuration is described and contrasted with an alternative configuration. Changes in the distances between the vertices cause a Doppler shift in the laser signals between spacecraft. The size of the measurement error introduced by this Doppler shift is dependent on the stability of the spacecraft formation.