Why Doing Fundamental Physics on the ISS?—The Experimental Conditions

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General Relativity and Gravitation, Vol. 36, No. 3, March 2004 (C 2004)

H. Dittus1

Received September 19, 2003

The International Space Station (ISS) already serves as a laboratory for experiments in fundamental physics. It could be used for a much wider range of experiments if the operational concept of the ISS will be changed. Operational constraints set limits for the precision level of experiments. Free-ﬂying platforms with high precision attitude and orbit control (drag-free control) could co-orbit with the ISS and improve the experimental conditions. The paper summarizes the main constraints and discusses concepts for improvement.

KEY WORDS: International Space Station; free fall; gravitation.

1. INTRODUCTION

The International Space Station (ISS) developed by the international space agen- cies is still under construction. The completion of its assembly is expected within the next five years. It is now being offered as an opportunity for scientific experimentation under conditions of weightlessness, in a quite unique environment that cannot be attained in terrestrial laboratories. Although the range of 1st generation experimental facilities on board the ISS has nearly been fixed, it is worth emphasiz- ing the possibility of carrying out more high precision experiments in Fundamental Physics on board the ISS, in order to develop guidelines and requirements for the next generation of ISS facilities, and for future operation of the ISS. During the last few years experimental capabilities have increased hugely through advances in technology and improvements in our scientific understanding. These give us very good reasons for exploring standard physics with much higher precision than

1 ZARM, University of Bremen, Am Fallturm, 28359 Bremen, Germany; e-mail: [email protected] bremen.de

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hitherto. New experimental devices for performing greatly improved high precision tests of the basic tenets of physics have been developed. Laser-cooling, atomic interferometry, and atomic fountain clocks, are examples of new tools for exploring the interaction of quantum matter with gravitational and inertial fields. And these may even be improved further using Bose-Einstein condensates as coherent atomic sources. Very high precision frequency standards are now provided by ultrastable resonators, new devices for measuring tiny forces have been developed, and ma- chining techniques have been improved tremendously, so that sub-m accuracy can be achieved in the dimensions of metre-scale parts. Partly as a result of this technical progress, the domain of Fundamental Physics has become a burgeoning, dynamic, and hugely exciting area of science – driven by the potential for new discovery. On the theoretical side, the search for a theory combining Quantum Theory and Gravitation is still the most challenging task of modern physics, whilst on the experimental side new methods of carrying out better high precision measurements may in the future enable discriminating tests of the current physical theories to be made. A significant aspect of these high precision tests of the fundamental principles underlying physics is metrology. This encompasses the very important task of preparing, reproducing, and transporting from place to place the fundamental physical units like the second, the metre, the kilogram, and the Ampere. All efforts to redefine units in terms of uniquely reproducible quantum effects are only effective, if the underlying non–gravitational physical laws are locally valid everywhere. The procedure of basing the second on a certain atomic transition is possible only because time-keeping in a gravitational field is universal – although General Relativistic corrections must be made to account for different gravitational potentials; and that of defining the metre in terms of the second is only possible because of the constancy of the speed of light, a cornerstone of Special Relativity. Modern developments like the reduction of electrical units using the quantum Hall or Josephson effect, which have come about because of the close-to-ideal reproducibility of these units, are only possible if quantum theory and Maxwell’s theory are valid. Consequently, Fundamental Physics plays an important role, and it is clear that our ability to carry out high precision experiments in space becomes an increasingly pressing issue, in order to test the predictions of the current universal theories for all four physical interactions.

2. ADVANTAGES OF FREE FALL CONDITIONS

In many cases the sensitivity of measuring devices and/or the accuracy of the measurement itself will increase if the experiments can be performed under conditions of free fall, that is, under conditions of weightlessness. The advantages of such conditions are: P1: GAD General Relativity and Gravitation (GERG) PP1066-gerg-477711 December 22, 2003 12:42 Style ﬁle version May 27, 2002

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1. The inﬁnitely long, and periodic, free-fall: As an example, long free fall conditions enable high precision tests of the Universality of Free Fall for all kinds of structureless (i.e. pointlike) matter. 2. Long interaction times: This is, for example, hugely advantageous in atomic or molecular interferometers, where the atoms or molecules may interact with other external ﬁelds for a long time and do not fall down. 3. High potential differences: In a large class of experiments (e.g. tests of the gravitational redshift), the search for signals depends on the difference in the gravitational potential. It is obvious that this can be achieved best in space. 4. Large velocity changes: For macroscopic devices (e.g. testing the depen- dence of light speed with respect to the laboratory velocity (Kennedy- Thorndike-tests) the maximum velocity on Earth might be of the order a few thousand km/h. In space this can be increased by about one order of magnitude. For example, the velocity variations along the orbit (e.g. in a high elliptical Earth orbit) are 30 times higher than one can attain using the Earth’s rotation. 5. Long distance measurements: In space, much longer distances are available than in any laboratory on Earth, and this may be essential, e.g., for the study of low frequency (103 Hz) gravity waves using interferometric techniques, where the strain of spacetime is to be measured at or below the 1021 level. 6. A low noise/vibration environment: Seismic noise is a limiting factor for many experiments on Earth (e.g. for gravitational wave detectors and for torsion balances) in the frequency range below 10 Hz.

It is clear that many, but not all, of these advantages are realized on board the ISS. Furthermore, there are some disadvantages due to the very existence and construction of the ISS: Due to the atmospheric drag, the true free-fall inside the ISS is rather short and, due to the circular orbit, the difference in the gravitational potential of the Earth is small. In addition, the large structure and movable parts on the ISS create a rather large vibrational noise, and the non-negligible Earth’s gravitational gradient as well as the gravitational ﬁeld of the ISS itself gives a relatively high level of residual acceleration. Therefore, there are many high-precision experiments in Fundamental Physics that must be carried out on specially designed satellites, having highly precise attitude and orbital (drag-free) control. Equally, however, there are still important advantages so that there is a substantial number of experiments in the area of Fundamental Physics which may yield remarkable improvements compared to existing terrestrial laboratory results, if carried out aboard the ISS. Moreover, the ISS may be used as an important and very appro- priate test bed for certain dedicated Fundamental Physics mission satellites. On the other hand, the ISS environment enables experiments to be conducted in a P1: GAD General Relativity and Gravitation (GERG) PP1066-gerg-477711 December 22, 2003 12:42 Style ﬁle version May 27, 2002

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way that would be quite impossible using satellites. Due to the regular servicing of the space station, exchange, repair, and improvements of experimental facilities on board the ISS are possible. Facilities also can be brought back to Earth for post-mission analysis of effects that may have been causing (e.g.) potential systematic errors, and, from a physical point of view, it is of prime importance to have the capacity to repeat experiments, and to test the reproducibility of results. Undeniably, one of the most powerful arguments for the utilization of the ISS for FP experimentation, notwithstanding the less than ideal environmental conditions on board, is the unrivalled opportunity for quicker and easier access to the experimental apparatus than is conceivably possible using dedicated satellites. In consequence, this facility must reduce considerably the time scales and costs involved in the realisation of such experiments. In what follows the present International Space Station’s design and operation is discussed. Although it becomes clear that the ISS environment currently circumscribes what may be achievable as regards very high precision experiments, it is interesting nevertheless to discuss proposals on how the Space Station’s operation and the facilities on board could be improved with respect to the feasibility of carrying out even higher precision experiments in the future.

3. ISS ENVIRONMENT AND OPERATIONAL MODES

The ISS is a manned space platform. Therefore, its design, orbit, structure, and operation has been determined by safety and logistics consideration. It is a multi-purpose facility which requires compromises for any experimental activity. ISS is designed to be a laboratory, but has to serve as the home for astronauts also. Crew motion, ventilation systems, motors, pumps etc. disturbe the weightlessness environment and cause a relatively high level of residual acceleration acting on the experiments. These internal sources as well as outside sources (radiation, gravity gradient, charging, drag, cosmic rays etc.) need a careful analysis for high precision experiments. A comprehensive description of the general conditions can be found in different ISS Users Guides, e.g.[1].

3.1. ISS Structure and Cabin Environment

At the end of its build-up period, ISS will consist of several pressurized modules with a total volume of ca. 1,200 m3. The modules and truss, including the supporting structures for solar panels will cover an area of about 100 100 m2. The total mass will be about 420 t. The huge structure causes a lot of vibrations in the frequency range below 0.1 Hz and a non-negligible gravity gradient along the laboratory modules. The complicated structure makes it difficult to analyse the influence of vibrational noise in the low frequency range for a specific experiment and location. P1: GAD General Relativity and Gravitation (GERG) PP1066-gerg-477711 December 22, 2003 12:42 Style file version May 27, 2002

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Usually, experiments are carried out in experimental racks inside the pressurized modules. The standard double rack structure is about 2,000 mm high, 1,000 mm wide, and about 850 mm deep. This size limits the ability of carrying out free fall experiments. Any free-ﬂying platform inside a rack would hit the wall of the rack within short time due to the drag decelerating the station permanently. The total mass of an internal rack at launch cannot exceed 2,500 kg. The in-orbit mass can be increased up to ca. 10,000 kg. Electrical power supply, data manage- ment, gas supply, or vacuum venting is designed individually and depends on the experimental requirements of the rack type. The nominal atmosphere onboard the ISS is an Earth-normal 101.4 kPa [2].

3.2. ISS Orbit, Periodic Manoeuvres, and Operation Modes

ISS moves on a near circular orbit inclined at an angle of 51.6 and an eccentricity of only 7 104. The very small eccentricity does not allow to carry out experiments requiring a variation of the gravitational potential (e.g. in-situ clock tests of the universality of the gravitational redshift with respect to the gravitational ﬁeld of the Earth). The orbital height is varying between 340 and 460 km. The variation depends on the solar activity and is strongly correlated to the 11-year solar cycle expanding the Earth atmosphere and lowering its density at solar activity maximum. Due to the large cross section of the station, atmospheric drag causes an altitude decrease of 150 to 200 m per day which needs to raise the orbit once all 10 to 45 days. Fig. 1 shows the ISS altitude as a function of time. Reebost and rendezvous manoeuvres, as well as station maintenance require a timeline for operational modes. Quiescent periods (microgravity mode) are interrupted frequently by periods for maintenance and manoeuvers. A typical cycle is about 100 days: Following the time of about 15 to 25 days for the rendezvous of spacecrafts supplying the ISS, the reboost to a higher orbit, and checkout procedures, the ISS will be operated in the microgravity mode for about 30 days; 10 days maintenance (standard mode), again 30 days microgravity mode, and additional 10 days of standard mode will follow. Therefore, any experimental operation requiring a low residual acceleration level has to be stopped time by time. ISS moves in an attitude that the truss should always be oriented approximately perpendicular to the orbital plane. The truss is the supproting structure for the solar panels and is oriented perpendicular to most of the laboratory modules. Therefore the tangential velocity vector points along the station axis. To optimize the thermal control, the power generation, and the communication links, the ISS has to be re-oriented along roll, pitch, and yaw axis which causes additional cen- trifugal accelerations. For example, the solar panels change position continuously to face towards the sun. P1: GAD General Relativity and Gravitation (GERG) PP1066-gerg-477711 December 22, 2003 12:42 Style ﬁle version May 27, 2002

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Figure 1. The orbital height varies with the solar activity. The saw-tooth shape of the curve causes from the altitude decrease through to atmospheric drag and the reboost manoeuvres occuring once every 10 to 45 days and lasting about 1.5 to 3 hours (from [1]).

3.3. Residual Acceleration and Gravity Gradient

The level of the residual acceleration acting on experiments is depending on their location in the ISS. The huge structure has many eigenfrequencies of varying amplitudes. In addition to these station movements, a huge number of sources (fans, gyros, pumps, and crew motion) create higher frequency vibrational noise. Fig. 2 shows the mean residual acceleration as function of the frequency. The anticipated level (red line) exceeds the station requirement in most parts of the frequency range above 0.1 Hz. According to the ISS microgravity control plan, the rms amplitude should not exceed 1g0 (g0 is the mean gravitational acceleration of the Earth’s surface) between 0.01 and 0.1 Hz, and for frequencies up to 100 Hz the acceleration can increase to about 2 mg0. Transient disturbances should not exceed a magnitude of atransR 1,000g0 per axis within a bandwidth up to 300 Hz and an integration limit of 10s atransdt 10 g0 s [3]. Due to the large extension of the ISS, a gravity gradient of up to 2g0 occurs perpendicularly to the station axis as quasi-steady disturbance acceleration. The gravity gradient sets the quasi-steady acceleration limit for experiments mounted P1: GAD General Relativity and Gravitation (GERG) PP1066-gerg-477711 December 22, 2003 12:42 Style ﬁle version May 27, 2002

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6 5 2 Figure 2. The anticipated level of the residual acceleration (in units of 1 10 g0 10 m/s )as function of the frequency. The dashed line marks the ISS requirement (from [1]).

on the station. It is obvious that high precision gravitational experiments which require a residual acceleration level of less than 108 m/(s2 Hz1/2) cannot be carried out under these circumstances. Active damping of experimental racks on the station is possible in principle with the Microgravity Isolation Mounts (MIM), but these systems are not effective in the low frequency range less than 0.01 Hz. Operation of these kind of precision experiments can only be done on specially designed free ﬂying platforms co-orbiting with the ISS, which will be discussed in detail below.

3.4. External Conditions

Many external effects may inﬂuence experiments inside and outside the ISS. One has to distinguish between effects caused by external sources like the P1: GAD General Relativity and Gravitation (GERG) PP1066-gerg-477711 December 22, 2003 12:42 Style ﬁle version May 27, 2002

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electromagnetic and particle radiation of the sun or the South Atlantic Anomaly of the Earth’s atmosphere and effects caused by the station itself like outgasing or thermal radiation. The most prominent effects are summarized in the following.

3.4.1. Temperature

Although the temperature inside the ISS modules (about room temperature) is stabilized and can be controlled very well, any experiment mounted to the outside structure or on an orbiting platform is subject of strong temperature variations. Due to the inclined orbit, ISS is exposed to large variations between 120 and 420 K. Experiments requiring temperature gradients of less than 1 mK Hz1/2 need active thermal control and thermal shielding. ISS will also carry a liquid helium Dewar (Low Temperature Microgravity Physics Facility, LTMPF), see below.

3.4.2. Charging

Charging through to high energy particle radiation is a serious problem for all high precision experiments in space. In particular for gravitational experiments, charging of free-flying test masses without electrical conducts to the outside causes non-negligible electrostatic forces. Continuous discharging by ultraviolet light sources exciting the electrons on the test mass and its housing might allow charging control, but needs careful analysis. The charging rate is generally proportional to the radiation dose on the test masses. Charging results from solar particle radiation, trapped particle belts, and cosmic rays. The ISS frequently passes the South Atlantic Anomaly, a region of enhanced radiation caused by the misalignment of the Earth’s rotation axis with its geomagnetic axis. Because the orbital height of ISS is relatively low and permanently below 1,000 km and the Van-Allen-Belt, energetic proton flux originating from solar flares is nearly completely shielded and does normally not affect experiments on the ISS. Nevertheless, high energetic ions from cosmic ray fluxes cannot be shielded.

3.4.3. Drag and ISS Environment

It is mentioned above that the drag of the rest gas atmosphere in the relatively low orbit causes a permanent deceleration and decay of the station. The station cross section with respect to the flight direction varies with attitude corrections and with changes of the position of the huge solar panels between ca. 3,700 and 850 m2 when the ISS is finally completed. For an average gas density of 7 1012 kg/m3 (corresponding to an orbital height of 350 km), the drag force varies between ca. 2 and 0.5 N. With the station’s total mass of 420 t, the resulting drag acceleration is calculated to 1 106 to 5 106 m/s2. This value related to the centre of mass of the P1: GAD General Relativity and Gravitation (GERG) PP1066-gerg-477711 December 22, 2003 12:42 Style file version May 27, 2002

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entire station sets also an upper quasi-steady acceleration limit for any experiment on free-flying platforms co-orbiting with the station and is a strong restriction, in particular for gravitational experiments. The rest gas atmosphere around the station is contaminated from outgassing, venting, leaks, or thruster exhausts which degrade surfaces and lower the vacuum quality. In addition, atomic oxygen, the dominant component of the Earth atmosphere at ISS orbital height causes significant erosion of surfaces which might be important for experiments on platforms outside the laboratory modules. Controls on these effects include the specification that ISS contamination sources will con- tribute no more than 1014 molecular cm2 to the molecular column density along any unobstructed line of sight, and produce no more than 1016 g cm2 a1 total deposition on sampling surfaces at 300 K.

3.5. On Board Resources and Facilities for Fundamental Physics Experiments

The ISS will offer some facilities and infrastructure which could be used for speciﬁc experiments in Fundamental Physics.

3.5.1. Low Temperature Microgravity Physics Facility (LTMPF)

The LTMPF is a self-contained, reusable, cryogenic facility filled with 270 l liquid helium that will accommodate low temperature experiments. It will be in- stalled on the Japanese Experiment Module (JEM) Exposed Facility of the ISS, i.e. on the outer side of the JEM module. LTMPF allows access to temperatures down to 1.4 K for durations up to six months and enables parallel operation of two experiments. Each experiment attached to the Dewar probe can occupy a volume of 19 cm diameter and 70 cm long, weighting up to 6 kg. Standard available electronics to measure and control temperature in the range of 1010 Kat2Kisavailable. Attached to each probe are the cells and sensors for each experiment. Each probe can have several stages of isolation platforms with separate temperature regulations on each stage to provide the maximum temperature stability. Ultra high-resolution temperature and pressure sensors are based on SQUID (Super-conducting Quan- tum Interference Devices) magnetometers. There are up to 12 SQUIDs shared between the two experiments. The high-resolution thermometers have demon- strated sub-nK temperature resolution in past space experiments. Other existing measurement techniques include resistance thermometers, precision heaters, ca- pacitance bridges, precision clocks and frequency counters, modular gas handling systems, and optical access capability. An onboard flight computer controls all facility and instrument electronics, all ISS interfaces, command, telemetry, and data storage during on-orbit operations. P1: GAD General Relativity and Gravitation (GERG) PP1066-gerg-477711 December 22, 2003 12:42 Style file version May 27, 2002

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Typical experiments to be carried out in the LTMPF are the SUMO Spe- cial Relativity tests, the experiments to study predictions of statistical physics and renormalization theory (BEST and SUE), and the Microgravity Scaling The- ory Experiment (MISTE) [4]. Most LTMPF experiments are sensitive to random vibrations, charged particles, and stray magnetic fields. The rms amplitude of random vibrations at frequencies less than 0.1 Hz is several g0. A passive vibration isolation system attenuates higher frequency vibration inputs from the ISS to a level less than 500 g0. Several layers of magnetic shielding are built into the instrument probe to protect the experiments from on-orbit variations in the magnetic field environment. Vibration and radiation monitors will provide experi- menters near real-time data. The facility will be launched filled with liquid helium, and retrieved when the helium is depleted, in an approximately 16 to 24 months cycle [5].

3.5.2. Atomic Clocks

Presently, there are two atomic clock ensembles under development to be mounted on the ISS: (i) Atomic Clock Ensemble in Space/Projet d’Horloge Atom- ique par Refroidissement d’Atomes en Orbite (ACES/PHARAO) developed by a team of French research institutes and (ii) Primary Atomic Reference Clock in Space (PARCS) devloped by a team of US research institutes. The microgravity environment of space affords the possibility of slowing down atoms to speeds well below those used in terrestrial atomic clocks, allowing for substantial improvement in clock accuracy. The PHARAO clock [4] will be operated on board ISS together with a hydrogen maser, to establish a time scale which can be compared with terrestrial clocks to an accuracy of 1016 – which would be an enormous improvement over the present level of synchronization that is possible using GPS (Global Positioning System) clocks. Thus an ultra-high performance global time-synchronization system should be realised, which will make possible new navigation and positioning applications. The clock ensemble consists of an atomic clock based on a fountain of cold Cesium atoms, and the hydrogen-maser clock. Additional components are the MWL (MicroWave Link), which sends short bursts of light (100 ps) between clocks on Earth and the clocks on the ISS, to synchronize them. The payload will be placed outside the cabin space of the ISS on an external platform. In this mission–for the first time–laser cooling techniques and atom traps will be estab- lished and tested in space. Furthermore, also for the first time the performance of atom-optical elements can be tested in space. PARCS [4] is a similar atomic-clock mission scheduled to be mounted on the ISS. The ensemble involves a laser-cooled cesium atomic clock, and a time- transfer system using Global Positioning System (GPS) satellites. PARCS will be operated concurrently with SUMO (Superconducting Microwave Oscillator), a P1: GAD General Relativity and Gravitation (GERG) PP1066-gerg-477711 December 22, 2003 12:42 Style file version May 27, 2002

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different sort of clock that will be compared against the PARCS clock to carry out the same type of Special Relativity tests mentioned above.

3.5.3. Exposed Facilities

Beside the standard racks inside the laboratory modules, there are exterior attach points to carry exposed experiments. There are four dedicated sites on the starboard side of the truss where external payloads can be attached. There are two attach points on the nadir, or Earth-facing, side of the truss, and two on the opposite, or zenith, side. These points can be used for detectors like the Alpha Magnetic Spectrometer (AMS), a detector to search for antimatter and dark matter by measuring with high accuracy the cosmic rays composition. There are also some exposed platforms attached to laboratory modules which can carry additional experimental facilities as EUSO (Extreme Universe Space Observatory), an experiment to observe high energetic cosmic rays by observing and detecting the reﬂected Cherenkov radiation when an extremely energetic cosmic ray interacts with the Earth atmosphere. EUSO is mounted to the Columbus External Payload Facility from where an unobstracted nadir view is possible.

4. PROPOSAL OF IMPROVEMENT

A very low residual acceleration level in the low frequency range is a strong requirement for many fundamental physics experiments and it seems to be impossible to carry out these kind of experiments on the ISS precisely enough. Nevertheless, changes in the operational concept could improve the conditions tremendously and will be discussed brieﬂy in this chapter.

4.1. Operational Concept

The operational concept of the ISS is based on the combination of laboratory modules and astronauts habitats. This concept results in many compromises with respect to the experimental conditions. Although various parameters (e.g. the orbital height and inclination) are fixed and cannot be changed, it is worth to discuss how laboratory operations and crew activities can be separated. Experiments running on small free-flying platforms co-orbiting with the ISS would experience a much lower level of residual accelerations. Because the platforms have to be serviced from the station, they cannot be in a perfect free fall, but could be bound to the station that they are operated in free fall mode for at least several days be- fore they have to be pushed back to the station. A docking mechanism on the ISS would enable exchange, repair, or recovery of the platforms and fix the platforms during reboost manoeuvres. Depending on their masses, the platforms could separated from the station between 500 and 2,000 m. High precision attitude and orbit P1: GAD General Relativity and Gravitation (GERG) PP1066-gerg-477711 December 22, 2003 12:42 Style file version May 27, 2002

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control would guarantee an acceleration level of at least 1010 m/(s2 Hz1/2)inthe frequency range above 103Hz. Tidal forces (gravity gradient) resulting from the ISS (mass: 420 t) are negligible at a distance of more than 100 m. The concept would not only improve the conditions for fundamental experiments but would also allow to repeat high precision experiments after checking them on Earth which is never possible for satellite experiments. 4.2. Free-Flying Platforms with Drag-Free Control

The ﬁne attitude control, also called the drag-free control of the platform, should be carried out with an accuracy of at least 1010 m/(s2 Hz1/2). The general principle of drag-free control is to make the trajectory of the satellite’s or the platform’s centre of mass as close as possible a geodesic. Therefore, a gravity reference sensor has to be used consisting of a test mass whose movements relative to the satellite are measured with respect to all 6 degrees of freedom (see Fig. 3). A common concept is to control the movement capacitively. Electrodes for sensing and active servo-control are surrounding the freely ﬂoating test mass. The control signal is used to control the satellite’s movement and attitude by a set of thrusters. For low Earth orbits, colloidal thrusters with a maximum thrust of about 0.2 mN are applicable. The thrust-force must be controlled with an accuracy of 0.1 N. To control all 6 degrees of freedom a minimum of 3 clusters of 4 thrusters each is necessary.

Figure 3. Schematic of a drag-free satellite. The test mass (TM) is shielded by the satellite against all disturbance forces. Following the test mass, the satellite moves on a geodetic (from [5]). P1: GAD General Relativity and Gravitation (GERG) PP1066-gerg-477711 December 22, 2003 12:42 Style ﬁle version May 27, 2002

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In low Earth orbits, aerodynamic drag is the dominant disturbing force on a satellite. Forces and torques are determined by Z 1 2 = v , Fairdrag 2 (r Sat) Sat(r Sat) cF Sat(ωSat)et dASat (1) Z 1 2 = v , . Dairdrag 2 (r Sat) Sat(r Sat) r Sat [cD Sat(ωSat)et dASat] (2)

vSat(r Sat) is the orbital velocity of the satellite, ASat the area of the cross section perpendicular to the flight direction, cF,Sat (ωSat) and cF,Sat (ωSat) are the drag coefficients combining all effects of interaction with the atmosphere and dependent 2 from the satellite’s attitude . et is the unit vector in flight direction. (r Sat) is the atmosperic density and must be determined from atmospheric models like the NASA Mass Spectrometer Incoherent Scatter (MSIS) or the Naval Research Lab MSIS Extended Model (NRLMSISE-00). Depending on the orbital height, the aerodynamical drag is between 10 and 150 mN, the resulting torques are between 10 und 100 N m (calculated for a cross section of 2m2). Many other disturbing effects occur in addition:

1. Disturbing forces from interactions with electromagnetic fields. Solar radiation, Earth albedo, and terrestrial thermal radiation cause forces on the satellite’s surface. 2. Gravitational forces: Tidal forces have strong influences, because the drag free reference point usually is not identical with the test mass centre of gravity. These effects must be determined from models like the NASA Earth Gravity Model from 1996 (EGM96). Additional effects occur through mutual attraction of satellite and reference mass (test mass), because of position variations of their centre of masses with respect to temperature variations on the orbit. 3. Coupling between test mass and satellite: Feed-back reactions between test mass position sensors and the test mass cage cause disturbances. 4. Interactions with the Earth magnetic field: These effects needs modelling (e.g. the International Geomagnetic Reference Field (IGRF)). 5. Charging: Electrostatic forces are caused by interactions with high energetic cosmic rays, but also by charging through protons during the frequent passages over the South Atlantic Anomaly. These passages can create charges of more than 1015 C/kg, as solar flares can cause a charging of up to 109 C/kg.

2 It is remarkable that the drag resulting from free molecular flux can be described by an aerodynamic approach. The drag coefficients are depending on emissivity and reflexibility of the surfaces and have values between 2 and 6. P1: GAD General Relativity and Gravitation (GERG) PP1066-gerg-477711 December 22, 2003 12:42 Style file version May 27, 2002

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Drag-free control needs modelling of the satellite and test mass dynamics. The control concept has to minimize the non-gravitational accelerations inside the satellite. The displacement of the satellite with respect to the test mass is observed to keep the stellite following it. The acceleration must be minimized at the test mass location which is denoted as the drag-free reference point. Usually, the states of satellite and test mass are measured directly or determined by an observer model based on real observations. The estimated states, the output of the observer model, are fed into the controller which then commands the thrusters. The external disturbances has in most cases a constant or modellable part. The estimated values are directly fed back to cancel out the disturbances. The residuals are compensated by the controller (for details see [6]). Drag-free control is a state-of-the-art concept for high precision attitude and orbit control and can easily be adapted to small free-ﬂying platforms.

5. CONCLUSION AND OUTLOOK

Fundamental Physics, in particular Gravitational physics, need experiments in space environment. Along many studies, various satellite experiments have been developed. Nevertheless, due to ﬁnancial reasons it seems questionable whether these experiments can be carried out on dedicated satellite missions in the near future. Therefore it is necessary, to work on concepts to realize fundamental physics experiments also on the ISS. Although the ISS seems not to be an ideal laboratory, there are concepts to improve the situation by free-ﬂying platforms orbiting the station. These concepts are based on state-of-the-art technology and could be realized within short time. Provided the operational concept of the ISS can be changed, it is worthwhile to study these concepts intensively.

ACKNOWLEDGMENTS

I would like to thank N. Lockerbie and C. L¨ammerzahl for very helpful discussions.

REFERENCES

[1] European Space Agency (2001). The International Space Station Users Guide, UIC-ESA-UM- 0001. [2] http://stationpayloads.jsc.nasa.gov [3] Hamacher, H. (1998). Micrograv. Sci. Technol. 11, 47. [4] L¨ammerzahl, C. (2004). Gen. Rel. Grav. 36: 615. [5] http://stationpayloads.jsc.nasa.gov/F-facilities/f1.html#ltmpf [6] Theil, S. (2002). Doctoral Thesis, University of Bremen.