Table of contents

Carrying out fundamental physics experiments in the relatively noise-free environment of space seems to be a natural and inevitable consequence of the continuing need to improve our understanding of Nature's weakest force, gravity. The experiments discussed in this special issue are attempting not only to measure some of the untested predictions of Einstein's theory of General Relativity but also to look for cracks at its very foundations. The motivation is not to deliberately try to disprove General Relativity but to search for clues as to how to improve the theory in a way which makes it more conducive to unification with the other forces of Nature. The main emphasis of the meeting was on three key missions of which two, STEP and LISA, are being studied within the programme of the European Space Agency (ESA) and one (GP-B) which is an approved mission within the National Aeronautics and Space Administration (NASA).

A short account is given of some of the basic problems encountered in attempts to construct a quantum theory of gravity. These include deep conceptual issues as well as difficulties of a more mathematical nature.

New experiments designed to observe or measure the -order (second post-Newtonian) modifications of the global speed of light function will as a matter of course also measure the -order PPN coefficient, , to one part in or better precision. This latter achievement would perhaps be the more scientifically significant, permitting a test of the scenario in which scalar-metric gravitational theories tend toward (without quite reaching) pure `local' general relativity by means of the cosmologically driven dynamics of the background scalar field(s). It is shown, independent of field theory assumptions, that any anomaly in the spatial metric component, and consequently in the global speed of light, will quite generally be accompanied by more easily measured -order anomalies in the same metric field component and the speed function.

We discuss the general features of a new force that could be induced by the exchanges of a spin-1 particle, in extensions of the standard model of electroweak and strong interactions.

The possible couplings of such a particle (the U-boson) can be restricted using gauge invariance, in connection with: (i) the presence or absence of a grand unification between electroweak and strong interactions, and (ii) the presence or absence of a supersymmetry between bosons and fermions (since supersymmetric theories require two electroweak Higgs doublets instead of one, and naturally allow for the gauging of extra U(1) symmetries).

With only one Higgs doublet any extra U(1) symmetry generator should act as a linear combination of baryonic and leptonic numbers with the weak hypercharge, Y. With two Higgs doublets - as in supersymmetric theories - it may also involve an axial symmetry generator. In both cases it is blind to quark generation.

After mixing effects with the Z are taken into account, we get the current to which the U-boson should couple. In general, it involves a vector part, as well as an axial part if there is more than one Higgs doublet.

The vector part is associated with the (additive) `fifth-force charge' ; within grand unification, B and L only appear through their difference B-L, so that for neutral matter would effectively be proportional to the number of neutrons. The corresponding force (which does not act on strangeness) is in general `composition-dependent'. It could superpose its effects onto those of gravitation, leading to apparent violations of the equivalence principle, or of Newton's law. Furthermore, the axial part in the U-current would lead to new spin-dependent forces, which may well be significantly stronger than in the axion case.

The intensities and ranges of such possible new forces are essentially unknown, but may be related to the symmetry-breaking scale. For a given scale the intensity of the (spin-independent) new force varies like , where is the range. If the new current has an axial part the U-boson could be directly produced in particle physics experiments. Quarkonium decays constrain the symmetry-breaking scale, restricting the possible intensities and ranges of a spin-1-induced `fifth-force'.

Part of the theoretical motivation for improving the present level of testing of the equivalence principle is reviewed. The general rationale for optimizing the choice of pairs of materials to be tested is presented. A simplified rationale is introduced based on a trichotomy of competing classes of theoretical models.

The weak equivalence principle (WEP) has currently been shown to be valid to an accuracy of . Free-fall experiments over short distances have attained an accuracy of only . Microgravity facilities such as the `Bremen drop tower' enable long-distance free-fall experiments which may improve the accuracy to .

The scientific objectives of the M3 STEP mission are threefold. Firstly, and most importantly, the aim is to test the equivalence principle (EP) to one part in , following the beautifully elegant STEP method conceived originally some 25 years ago by P Worden and C W F Everitt. It is noteworthy that over this period of time the detailed design of the experiment has matured considerably.

STEP (satellite test of the equivalence principle) is a candidate mission, in the discipline area of `fundamental physics', for the third medium-size project (M3) of ESA's long-term science programme `Horizon 2000'. A phase A study of the spacecraft and mission has been carried out by an industrial consortium led by Alenia Spazio, with Matra Marconi Space and Dornier Satellitensysteme as subcontractors. The concept that was studied was for an autonomous ESA mission with a payload provided by principal investigators. The model payload includes four equivalence principle accelerometers, a spin-coupling accelerometer and a gradiometer. A helium cryostat provides the required cryogenic temperatures for the payload. Spacecraft and warm payload equipment are accommodated on two platforms surrounding the cryostat. STEP will be launched with a Lockheed Martin LMLV-2 launch vehicle directly into its Sun-synchronous operational orbit at 400 km.

The concept of the three-axis electrostatic accelerometers based on the full electrostatic suspension of one unique proof mass is very suitable for space applications requiring very high resolution of acceleration measurement or drag-free control of satellite. This concept has been tested in orbit with the accelerometer CACTUS from ONERA in the late seventies and recently with the accelerometer ASTRE on board Columbia shuttle in June 1996. The accelerometer outputs are derived from the measurement of the electrostatic forces, necessary to maintain the mass motionless at the centre of the accelerometer cage. The relative test-mass position and attitude are servo-controlled from measurements of capacitive sensors exhibiting resolutions of better than depending on the geometrical configuration.

The test of the weak equivalence principle can be performed in orbit on board a drag-free satellite with two concentric electrostatic accelerometers including two cylindrical test masses made of different materials. The measured common acceleration is controlled to null along the three directions by the drag compensation system of the satellite. The differential acceleration is detected at the orbital frequency (or around the satellite spin frequency) along the common revolution axis with an expected resolution of . The differential disturbing acceleration induced by magnetic, electric and thermal disturbances must be limited to this value thanks to the 4 K environment of the sensor-head. The present definition of such an instrument is presented and the expected performances are detailed.

The superconducting differential accelerometers for the equivalence principle and geodesy experiments on the European STEP mission have been designed under common guiding principles. Both accelerometers rely on stable superconducting magnetic levitation. The suspension is stiff against all unwanted degrees of freedom while the axial differential mode is kept compliant to obtain a high intrinsic sensitivity of the differential accelerometer, . The sensitive axis of each component accelerometer is aligned to by adjusting persistent currents in the alignment coils and a restoring force is provided by persistent currents to prevent unwanted rotation about the sensitive axis. The dynamic alignment of the sensitive axes improves the common-mode rejection ratio to . The axial displacements of the two test masses in each differential accelerometer are coupled through two separate superconducting circuits to two DC SQUIDs. Persistent currents are stored in the two circuits such that the acceleration signals are differenced in one circuit and summed in the other before detection by the respective SQUIDs. The signal differencing before detection reduces the dynamic range requirement of the following amplifiers and analogue-to-digital (A/D) converters by orders of magnitude.

This is a report on the work done of a rather informal working group set up during the Phase A studies to suggest suitable materials for the test masses of the differential accelerometers for the ESA STEP-M3 mission. The most important work was done regarding theory by Thibault Damour (IHES, Paris) and for test-mass design by Nick Lockerbie (Strathclyde University, UK). Valuable ideas contributed by T Quinn, P Fayet, H J Paik, A Bernard and P Touboul are acknowledged.

The test masses for the proposed STEP (satellite test of the equivalence principle) experiment can be influenced, adversely, by time-varying gravitational coupling to other masses within the spacecraft. The liquid helium in the spacecraft's Dewar is a severe potential source of this effect, since its influence is at the same frequency as any actual equivalence principal violation. The pairs of STEP test masses must be made differentially immune to this effect, and a measure of this immunity can be quantified in terms of a `differential acceleration susceptibility', defined as . Here and a are the differential-axial and common-mode accelerations, respectively, of the two masses, for a perturbing source at relative position . This work presents the results of analyses for STEP's test masses having either four or six flats, included to prevent them from rolling in azimuth . Different schemes for minimizing are discussed in detail, and it is shown that the gravitational effect of the flats may be balanced between the inner and outer masses, leading to a `fully-balanced' pair. However, it is concluded that such a scheme is not practical, and the `susceptibility' may be minimized, alternatively, by choosing six flats rather than four. It is noted that the gravitational theory used here may be applied to six- or four-sided bodies, including cubic test masses - as proposed for LISA.

Space-borne physics experiments involving the measurement of small motions of test bodies are likely to be limited by disturbance forces. Of particular concern are forces arising from electrostatic charging of the test body due to interactions with particle radiation. Estimates of charging rates have been computed using Monte Carlo particle-transport codes in combination with semi-empirical particle flux models. Results are presented for the STEP and LISA geometries, and are extrapolated for GP-B. The consequences of the charging are assessed for each experiment, and a method for alleviating the problem is discussed which uses the photoemission technique already in the hardware development phase for GP-B.

Calculations are presented which define the optimum geometry for the spin-coupling experiment (SCE) on STEP. It is shown that the spin source must be composed of two sections in which spin-polarized electrons make different contributions to the net magnetization. Design features of the SCE on STEP are reviewed and the projected sensitivity of a configuration optimized for short-range (1 mm) interactions using a vacuum gap in the spin source is compared with other experiments.

The geodesy experiment on STEP aims at the precise and detailed determination of the spatial variations of the Earth's gravitational field by measuring the cross-track gradient along the orbit. If the envisaged gradiometer precision of can be reached and all other potential error sources, such as alignment, pointing and time-varying eigengravitation can be kept below this limit, a spatial resolution of about 100 km half-wavelength will be attained with a cumulative geoid error of below 2 cm (except in the polar areas).

The superconducting gravity gradiometers for the European STEP and GEM missions have common design features. Both gradiometers have their test masses magnetically levitated, stiff against all unwanted degrees of freedom. The sensitive axes of the component accelerometers are aligned to with respect to each other, by adjusting persistent currents in the alignment coils, to improve the common-mode rejection ratio to . The axial displacements of the two test masses in each gradiometer are coupled through two superconducting circuits to two DC SQUIDs. Persistent currents are stored in the circuits such that the acceleration signals are summed and differenced at the respective SQUID inputs. This signal differencing before detection reduces the linearity and dynamic range requirements of the electronics by several orders of magnitude. The STEP gradiometer will be a single-axis device with a baseline of about 60 cm and with its sensitive axis oriented along the orbit normal. Its intrinsic noise is expected to be above . Below this frequency 1/f power noise should appear. A compact three-axis superconducting gravity gradiometer with a baseline of 12 cm is proposed for GEM. This gradiometer will have an intrinsic noise of above . Below this frequency 1/f noise will dominate.

In connection with the Gravity Explorer Mission study of the European Space Agency we have made an independent comparison of the noise performance and the disturbance rejection ability of a superconducting and of a capacitive gravity gradiometer. 0490, 0630G, 0707M, 9385, 9555

In an Earth-bound laboratory, we have improved the sensitivity of the spin-coupling experiment by two orders of magnitude using a paramagnetic salt with a DC SQUID to search for a possible axion-like interaction of a rotating mass with a paramagnetic salt. Two orders of magnitude more improvement in the Earth-bound laboratory is envisaged. Here we propose to use a similar scheme for a space spin-coupling experiment. Both paramagnetic materials and ultra-soft ferromagnetic materials are considered.

The Mini-STEP concept was conceived from a desire by NASA to reduce the cost of the satellite test of the equivalence principle (STEP) experiment below that of the already downsized Quick STEP concept. The goal was for the total cost, including payload, spacecraft, launch vehicle, reserves and operations, to be in the $50 million range. Stanford University and the Jet Propulsion Laboratory studied this simplified STEP concept between March and June 1995. A similar concept was developed in parallel by the European Space Agency (ESA) as an alternative to the M3 STEP mission.

Testing the equivalence principle (EP) has been recognized by the scientific community as a short term prime objective for fundamental physics in space. In 1994 a phase 0/A study of the GeoSTEP mission was initiated by CNES in order to design a space experiment to test the EP at the accuracy of , with the concern to be compatible with the small versatile platform `PROTEUS' under study. The GeoSTEP payload includes a set of four differential accelerometers placed at cryogenic temperature on board a drag-free, three-axis stabilized satellite in low-Earth orbit. Each accelerometer contains a pair of test masses A - A, A - B, A - C, B - C (inner mass - outer mass) made of three different materials A, B, C with decreasing densities. The accelerometer concept is the fully electrostatic levitation and read-out device proposed by ONERA (`SAGE'). The drag-free and attitude control system (DFACS) is monitored by the common mode data of the accelerometers along their three axes, while the expected violation signal is detected by the differential mode data along the longitudinal sensitive axis. The cryostat is a single chamber supercritical helium dewar designed by CEA. Helium boiling off from the dewar feeds a set of proportional gas thrusters performing the DFCAS. Error analysis and data processing preparation is managed by OCA/CERGA. The satellite will be on a 6 am - 6 pm near polar, near circular, Sun-synchronous orbit, at an altitude of 600 to 900 km, depending upon the atmosphere density at the launch date. The mission will last at least 4 months and could be launched in 2002. A descoped, room-temperature version of the project using electric thrusters (FEEPs) and called MidiSTEP has also been considered.

Preflight prototype differential accelerometers for STEP are being developed at Stanford under NASA funding. Subsystem development in progress includes work on thin-film superconducting circuits deposited on cylinders, SQUID-based superconducting position measurement and electrostatic positioning and charge control. A thorough programme of testing and qualification of the subsystems is an essential part of the experiment. We have built a flux microscope and magnetometer probe to study magnetic flux motion, one of the limiting factors in the accelerometers; a position sensor study facility; a tipper table for testing and qualification of bearings in three degrees of freedom and a `mechatronics' lab for the manufacture of critical circuits on cylinders.

A rigorous testing programme is a necessary part of any space experiment because it is presently impossible, or prohibitively expensive, to repair any failure after the experiment is in orbit. This is particularly true of fundamental physics experiments such as STEP and GP-B in which the sensitivity of the apparatus depends directly on the absence of gravity. Thus the apparatus cannot be tested at full sensitivity until it is in orbit. The STEP development work at Stanford is directed toward a partial answer to this problem, which guarantees that the instrument will at least function and tests it to the extent possible on the ground.

I describe the development of an inductance position sensor for the STEP (satellite test of the equivalence principle) accelerometer. I have measured the inductance (with an experimental error of 0.5%) of a single-turn thin-film niobium pick-up coil as a function of the distance from a thin-film niobium disc (both at 4.2 K and superconducting). The circular pick-up coil had a diameter of 4 cm with a track width of . The disc (mock test mass) had a diameter of 4 cm. The distance range between the coil and disc was set by the range of a low-temperature differential capacitance sensor: 0 - 2 mm with a resolution of . The full range of the low-temperature translation stage was 0 - 4 mm. The inductance was measured using an LCR meter in a four-wire configuration. The measured inductance was compared to the inductance of a circular loop above a superconducting plane. Due to the fact that the thin-film disc is of finite size, the calculation differed from experiment by as much as 12%. I have also calculated the inductance by segmenting the thin-film niobium disc into 500 concentric rings (each with a width of ). A discrepancy between calculation and experiment of approximately 3% was found.

Ground-based testing and qualification of the STEP differential accelerometers is important for instrument development and overall mission success. A facility for testing the various subsystems of the flight accelerometer, including the superconducting magnetic bearings, is under development at Stanford University. Achieving the required sensitivity led to the development of an apparatus comprising cryogenics, a multiple degree-of-freedom tipper table, an active control system, electrostatic suspension and a capacitive sensing system.

The test of the equivalence principle to one part in requires the use of a drag-free spacecraft to shield free-falling test masses from any environmental disturbances. Potential violations of the equivalence principle are detected by very small relative displacements of these test masses measured by high-sensitivity differential accelerometers. The accelerometer assembly is contained in a superfluid helium cryostat. The cryogenic temperature (about 2 K) is required to provide a high degree of mechanical (i.e. thermal) stability, to provide superconducting shielding against electromagnetic radiation and to ensure an ultra-high vacuum environment reducing gas-molecule impacts. For GEOSTEP, electrostatic suspension and capacitive sensing of the test masses are baselined. Helium cooling may also allow for the use of superconducting magnetic suspension and sensing. The cryogen boil-off also provides a source of propellant for the proportional gas thrusters used for the drag-free and attitude control.

The MiniSTEP drag-free control system must reduce the atmospheric drag forces acting on the spacecraft by seven orders of magnitude, to yield an average residual acceleration of less than averaged over the measurement bandwidth. The origins of the drag-free requirements are discussed, and a control system is presented which meets the requirements under realistic assumptions for noise levels.

The Gravity Probe B relativity mission experiment is designed to measure the frame dragging and geodetic relativistic precessions in a 650 km polar orbit. We describe some of the advanced experimental techniques used to achieve the required gyroscope accuracy of between 0.05 and . The subjects discussed are: (i) the development of high-precision gyroscopes with drift rates of less than , (ii) a low-temperature bake-out procedure resulting in a helium pressure of less than at 2.5 K, (iii) a read-out system using DC SQUID magnetometers with a noise figure of at 5 mHz and (iv) AC and DC magnetic shielding techniques which produce an AC attenuation factor in excess of and a residual DC field of less than .

GGG is a supercritical rotor to test, on the ground, the equivalence principle to one part in and to prepare for the space experiment.

An experiment to test the equivalence of inertial to gravitational (passive) mass in space offers two main advantages: a signal about a factor of a thousand larger than on Earth and the possibility of exploiting the absence of weight. `Galileo Galilei' (GG) is a small satellite mission currently under study in Italy with the financial support of ASI (Agenzia Spaziale Italiana). The mission concerns a small, low Earth satellite ( total mass, altitude) with two objectives. One is scientific, in the field of fundamental physics, and the other technological within the framework of spacecraft propulsion and drag compensation. The scientific goal is to test the equivalence principle to one part in , four orders of magnitude better than the best ground results. The technological goal is a full, comprehensive test of FEEP (field emission electric propulsion) thrusters for accurate drag compensation, a technology developed in Europe by the ESA (European Space Agency) which is likely to become an essential component of all space experiments which require measurement of small forces. The GG experiment is based on novel concepts and does not require low temperatures.

A really inertial platform for highest sensitivity instruments needing to be absolutely free from any disturbances like drag and other forces in space is proposed for the case of an equivalence principle test with differential accelerometers. A spin-stable platform, inside a co-rotating outer spacecraft shielding it, constitutes the reference proof mass for a simple position servo system. Position measurements, as well as signal transmissions, are achieved optically. Power is supplied by microwave beams. The proposed ambient temperature EP-mission Eötvös in an 800 km equatorial orbit would constitute a simple, very economic experiment. Limitations to the potentially very high precision are expected to be set by thermal disturbances.

We discuss the feasibility of the detection of relic neutrinos that may be present in the Galactic halo. We analyse their effect on macroscopic targets, comparing the detection proposals made so far and presenting new experimental schemes. In all cases the acceleration of the test masses is bounded by the value of the refractive index of neutrinos N as follows: , where for all materials and x = 0.5 in the best case. 1315, 9880, 0480

The sources of gravitational radiation that seem to be most likely to be detected by planned ground- and space-based gravitational-wave detectors are reviewed, with particular attention to the likely information that observations of them will reveal. A particular emphasis is placed on observations by LISA, the fundamental-physics Cornerstone project of the European Space Agency's Horizon 2000+ programme.

The next generation of gravitational-wave detectors holds out the prospect of detecting a stochastic gravitational-wave background generated in the very early Universe. In this paper, we review the various cosmological processes which can lead to such a background, including quantum fluctuations during inflation, bubble collisions in a first-order phase transition and the decay of a network of cosmic strings. We conclude that signals from strongly first-order phase transitions, possibly at the end of inflation, and networks of local cosmic strings are within the sensitivity of the proposed detectors. However, backgrounds from standard slow-roll inflation and the electroweak phase transition are too weak.

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.

A gravitational-wave observatory is recommended as the seventh cornerstone in ESA's long-term programme in space science, known as `Horizon 2000 Plus'. A concept for such a gravitational-wave mission, LISA, was studied within ESA in order to assess its feasibility and technological requirements. Six spacecraft in a triangular configuration form a laser interferometer with baselines of . This interferometer will orbit the Sun at a heliocentric radius of approximately 1 AU, following the Earth at an angular distance of . Launch of all six spacecraft will be with an Ariane 5 launch vehicle and jettisonable propulsion modules will place the spacecraft in their respective orbits. All six spacecraft are identical and accommodate a payload module which houses a test mass with capacitive sensors, a transmit - receive telescope and lasers. The interferometer arms are determined by the test masses and the spacecraft must shield the test mass from all extraneous disturbances, requiring a `drag-free' control system which uses electric thrusters to make the spacecraft follow the test mass.

The interferometer of the LISA mission is realized with V-formations of drag-free spacecraft in heliocentric orbit. Each spacecraft will have at its centre a cubic proof mass made in gold - platinum alloy, that defines one end of the interferometer arms. These masses are also those of the inertial reference sensors used for the drag compensation control of the satellites. The goal of the LISA sensor is to obtain a proof mass free of any parasitic forces, at a level of in the very low frequency domain from up to several . Furthermore, the compensation of the satellite drag must limit its relative motion to less than , thus reducing the disturbances that may be induced as variations of the satellite self-gravity effects.

The sensor proposed by ONERA is derived from the space electrostatic accelerometer GRADIO and ASTRE, the last one flew in Spacelab during a shuttle mission in June 1996. The challenge of the LISA inertial sensor is to exploit the existing concept and technologies with the best care in order to preserve the capacitive sensor resolution while limiting to a minimum the disturbing electrical effects and measurement backactions. The non-direct demonstration of the expected flight performances of such a sensor should be considered in detail in the future.

We discuss some of the details of the optical layout and interferometry in the LISA project. The limitations on performance imposed by a variety of constraints and noise sources are considered. In addition a scheme to acquire and maintain optimum optical alignment is presented.

LISA is a space-borne, laser-interferometric gravitational-wave detector currently under study by the European Space Agency. We give a brief introduction about the main features of the detector, concentrating on its one-year orbital motion around the Sun. We compute how the amplitude as well as the phase of a gravitational wave are modulated due to this motion by transforming an arbitrary gravitational-wave signal in a reference frame that is rigidly fixed to the arms of the detector. To see how LISA works the detector response to a gravitational wave which is purely monochromatic in the barycentric frame will be discussed.

A brief review of the theory of parameter estimation, based on the work of Finn and Cutler, will be given. Following this theory the detection of a gravitational-wave signal buried in detector noise was simulated numerically. We interpret the results of this simulation to determine the angular resolution of LISA.

The method for measuring changes in the lengths of the three arms for the LISA gravitational-wave detector is described. Accurate phase measurements are required on signals with Doppler shifts of about 1 MHz for the two main arms of the interferometer, and up to 15 MHz for the third arm. This is accomplished by shifting the signal frequencies down to near 100 kHz, filtering and then timing zero crossings of the signals. The basic methods for correcting for the laser phase noise and for phase noise in the ultra-stable oscillators used to derive various radio frequencies are described briefly. The corrections are made on the spacecraft, before the data are telemetred to the ground.

We derive expressions for the forces and force gradients which exist between infinite parallel metallic surfaces in terms of the spatial distributions of the surface potentials. The main motivation for this is to enable the forces and force gradients to be calculated from electrical measurements of the surface potentials. However, by making some worst-case assumptions about the potential distributions, we establish a limit for the relative displacement of the spacecraft and proof mass in the LISA mission of

where is the target acceleration sensitivity, is the proof-mass density, d is the dimension of the proof mass (assumed cubic) and a is the spacing between the proof mass and the surrounding electrodes. The magnitude of the patch-potential variations or contact-potential differences between the plates is parametrized as v.

We analyse superconducting magnetic levitation systems where both the suspended body and the field-generating conductors are perfectly diamagnetic. We develop a method to find a spatial distribution of the windings underneath a planar superconductor which maximizes the achievable magnetic support field, for a given maximum field at the windings. The basic method consists of tuning the horizontal and vertical field components according to the corresponding field enhancement factors at the windings. Using customized windings of varying pitch, it appears that improvements in lift force by factors of 2 or more are possible.

Since 1992, we have engaged in laboratory studies for astrodynamical missions to test relativistic gravity in the solar system. The techniques developed are also relevant to other fundamental space missions such as LISA and the space interferometer for astrometry. Here we report our progress in weak light phase-locking, long fibre-linked heterodyne interferometry, fibre delay line and picometre real-time motion control during the last year. We demonstrated that for two lasers with offset locking up to 2.5 GHz, the heterodyne linewidth after travelling through a 26.27 km fibre-linked interferometer is less than 1 mHz. For weak light phase-locking, we achieved 4.3 nW locking with a 3.4 mW local oscillator. We improved our side-polishing technique to polish more than eight fibres simultaneously and reached a tunable sensitivity as high as 85 - 90 dB in liquid-drop tests. Using these side-polished fibres, we are currently in the process of making tunable directional couplers and fibre delay lines. For laser metrology, we use mid-point cyclic averaging to reduce the nonlinearity error, and use a fitting method to cancel the drift, and have reached 1.5 pm linearity. Currently, with modulation and real-time cyclic averaging, we reach a real-time measuring precision of 560 pm and real-time motion-control precision of 700 pm.