The Equivalence Principle, formulated by Einstein generalizing Galileo’s and Newton’s work, is a fundamental principle of modern physics. As such it should be tested as accurately as possible. Its most direct consequence, namely the Universality of Free Fall, can be tested in space, in a low Earth orbit, the crucial advantage being that the driving signal is about three orders of magnitude stronger

than on Earth. GALILEO GALILEI (GG) is a small space mission designed for such a high-accuracy test. At the time of print, GG has been selected by ASI (Agenzia Spaziale Italiana) as a candidate for the next small Italian mission. Ground tests of the proposed apparatus now indicate that an accuracy of 1 part in 1017 is within the reach of this small mission

Bramanti, D.

Catastini, G.

Nobili, A. M.

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IL NUOVO CIMENTO Settembre-Ottobre 1997VOL. 20 C, N. 5The GALILEO GALILEI small-satellite missionwith FEEP thrusters (GG) (*)A. M. NOBILI, D. BRAMANTI and G. CATASTINIGruppo di Meccanica Spaziale, Dipartimento di Matematica, Università di Pisa - Pisa, Italy(ricevuto il 5 Dicembre 1996; approvato il 18 Marzo 1997)Summary. — The Equivalence Principle, formulated by Einstein generalizingGalileo’s and Newton’s work, is a fundamental principle of modern physics. As suchit should be tested as accurately as possible. Its most direct consequence, namely theUniversality of Free Fall, can be tested in space, in a low Earth orbit, the crucialadvantage being that the driving signal is about three orders of magnitude strongerthan on Earth. GALILEO GALILEI (GG) is a small space mission designedfor such a high-accuracy test. At the time of print, GG has been selected by ASI(Agenzia Spaziale Italiana) as a candidate for the next small Italian mission. Groundtests of the proposed apparatus now indicate that an accuracy of 1 part in 1017 iswithin the reach of this small mission.PACS 04.80 – Experimental studies of gravity.PACS 01.30.Cc – Conference proceedings.An experiment to test the equivalence of inertial to gravitational (passive) mass inspace offers two main advantages: a signal about a factor of a thousand bigger than onEarth and the possibility of exploiting the absence of weight. GALILEO GALILEI(GG) is a small-satellite mission currently under study in Italy by eight researchinstitutions with approval and funding by ASI (Agenzia Spaziale Italiana). The missionconcerns a small, low Earth satellite (150 kg total mass, 520 km altitude) with twoobjectives. One is scientific, in the field of fundamental physics, and the othertechnological in the frame of spacecraft propulsion and drag compensation. Thescientific goal is to test the equivalence principle to 1 part in 1016 , four orders ofmagnitude better than the best ground results. The technological goal is a full,comprehensive test of FEEP (Field Emission Electric Propulsion) thrusters foraccurate drag compensation. FEEPs have been invented, designed and developed byESA (European Space Agency) and will most probably become an essential componentof all space experiments which require measurement of small forces. The GG(*) Paper presented at the VII Cosmic Physics National Conference, Rimini, October 26-28, 1994.G Società Italiana di Fisica 651A. M. NOBILI, D. BRAMANTI and G. CATASTINI652Fig. 1. – Section through the spin axis of the spacecraft showing the spacecraft, the PGB (PicoGravity Box) laboratory and the test masses (not to scale). The PGB laboratory and the testmasses are suspended with springs. The suspensions of the test masses also employ «elastic»gimbals (i.e. gimbals pivoted with torsion wires) on two movable rods for the balancing of inertialforces. The capacitive plates of the read-out system, between the test masses, are attached to inchworms for adjusting their distance from the surfaces of the test masses.experiment is carried by a small, cylindrical spacecraft of about 100 cm base diameterand 70 cm height stabilized by single-axis rotation at 5 Hz (fig. 1). The symmetry axis ofthe cylinder is, by construction, the axis of maximum moment of inertia so as to stabilizethe rotation around it. The orbit is almost circular, almost equatorial at about 520 kmaltitude, which allows the satellite to avoid the perturbing effects of radiation from theTHE GALILEO GALILEI SMALL-SATELLITE MISSION ETC. 653TABLE I. – Main characteristics of the GG satellite.Total mass (payload included) 150 kgShape and size cylinderdiameter 100 cmheight 70 cmantenna dipole-array (like METEOSAT)solar cells around external surface of cylinder (no panels)Stabilization passive, one-axis rotation (5 Hz) almost perpendicularto orbit planeOrbit 520 km altitude, almost equatorial, almost circularPointing accuracy 1–3 degreesLifetime C 6 monthsDrag compensation to 1023 by FEEP thrusters with liquid Cs propellantTotal mass of propellant C 5 g of liquid CsTotal power C 85 WData rate C 1 kbitOs for a few minutes each orbitVan Allen belts in the so-called South Atlantic Anomaly. The spin axis of the satellite isalmost perpendicular to the orbit plane. This maximizes the signal and makes itunnecessary to perform any attitude manoeuvres after initial set-up and for the totalC6 month duration of the mission. There are no severe requirements as far as orbitinjection and spacecraft attitude are concerned. The satellite is very similar (butfor the smaller mass and size) to the spin-axis–stabilized METEOSAT satellites usedby ESA for meteorological prediction. Similarly to them it has solar cells around theexternal surface, which can easily generate the required power of C85 W, and aMETEOSAT-like dipole array antenna for communication with Earth. This antennadoes respect the cylindrical symmetry of the satellite and needs no moving parts, whichwould perturb the experiment. Since the orbit is low and equatorial the satellite will bein view of the ground station only for a fraction of its orbital period. However, sincethere is no special need for continuous tracking, the experimental data can be stored onboard and downloaded once per orbit. The required bit rate is low (C1 kilobitOs for afew minutes every orbit). The spacecraft is equipped with FEEP thrusters, arranged incylindrical symmetry, in order to partially compensate for the effect of air drag whichamounts to C1 dyn. FEEPs require only C5 g of cesium for 6 months nominalduration of the mission. They are operated in pulsed mode, driven by four capacitancesensors symmetrically placed around the suspended PGB (Pico Gravity Box)laboratory inside the spacecraft (see fig. 1), which acts as test body for drag-freeoperation. Table I gives a summary of the satellite main characteristics. The satellitecarries two mechanically suspended, concentric, cylindrical test bodies (10 kg each)made of different material whose relative displacements are measured by capacitivesensors to detect a possible violation of the equivalence principle. Rotation insupercritical conditions and absence of weight are exploited for ensuring self-centringand to reduce vibrational perturbations. Stabilization in supercritical rotation isachieved with active electrostatic dampers because the required force is very small;their contribution to thermal noise is shown to be negligible. The experiment isperformed at room temperature. The differential acceleration to be detected isC8.4 Q1014 cmOs2 , giving rise to a relative displacement at the satellite spinning frequencyA. M. NOBILI, D. BRAMANTI and G. CATASTINI654Fig. 2. – Qualitative representation, in the orbital plane and for one pair of test masses, of thedifferential displacements obtained from the synchronous demodulation of the 2-phase 5 Hzsignal. The X-axis is in the Earth-to-satellite direction and the vector OP is the differentialdisplacement, directed along the X-axis and constant in amplitude, of the two masses due to an EPviolation. The perturbation PD due to the initially unbalanced atmospheric drag will be found inthe area between the two dashed lines crossing in P: the angle between them is about 0.8 rad, andis due to the fact that the drag has a variable component in the radial direction because of the solarradiation pressure (of amplitude about 0.4 times the atmospheric drag and in the Sun-satellitedirection). Smaller contributions to the PD vector come from the Earth albedo, the Earth infraredradiation and, by a smaller amount, from a possible small eccentricity of the orbit. By finelyadjusting the lengths of the suspension arms the point D is displaced up or down inside this area,and this balancing of the drag should be continued until D is as close as possible to P. In doing so,also the radial component is automatically balanced. The resonant variations of the drag (notshown) will oscillate inside the same area. The vector DQ is the instability due to the internaldissipation of the springs, slowly rotating and increasing: it must be actively damped until Q is asclose as possible to D (and P). The circle around point Q represents the error in the measurementdue to the thermal noise of the mechanical oscillations in a few days of integration time. The actualvalues of all these quantities have been computed.and with known signature of amplitude C2.1Q10210 cm. The read-out system is capacitiveand the sensitivity needed for such measurements is well feasible. With a FEEP dragcompensation by a factor 103 the capacitance bridge can detect the expecteddisplacement provided it is balanced to within only a few 1025 , amounting to anaccuracy of a fraction of a micrometre in the positioning of the capacitance plates inTHE GALILEO GALILEI SMALL-SATELLITE MISSION ETC. 655between the test bodies, which is well feasible with piezoelectric actuators. Forceswhich, unlike the expected one, act in common mode must be rejected to a few 1026 toallow detection of the expected differential signal. This is achieved by suspending thetest bodies on the opposite ends of two arms pivoted at their centres like in balancesand torsion balances. In the latter systems the level of balancing (i.e. rejection) neededhere is well feasible even in the more difficult 12g environment. Arms lengthadjustments will be performed with piezoelectric actuators whose properties andreliability are well known. Figure 2 shows the procedure for the recovery of the signal.Temperature gradients in space across the test bodies are negligible thanks to the fastspin as compared to orbital motion. Those along the spin axis are much larger, but therequirement is far less strict and can be easily fulfilled. Temperature in the PGBexperimental chamber containing the test bodies must be constant for the entireintegration time of a few days to 0.01 K. We have shown that this can be achieved bymeans of an insulation shell on the inner surface of the spacecraft, vacuum in betweenthis surface and the PGB and multilayer insulation (less than 10 layers) of the PGB.Experience with metallic springs in gravimeters used for accurate measurements ofEarth tides shows that springs with good properties of stability, both in time and withtemperature, can be built. Appropriate machining, annealing and attaching proceduresare available. Ground testing of the actual springs to be used in the space experiment ispossible using torsion balances and the test procedure is being checked in thelaboratory. No electrostatic problems arise due to the absence of free floating massesand the presence of conducting hair-like suspension springs instead. Magnetic effectshave been computed and it has been demonstrated that no m-metal shielding isrequired. Many perturbing effects which are usually a matter of concern in similarexperiments are irrelevant here thanks to the common rotation of the entire system(i.e. inhomogeneities of the test bodies, coupling of the higher mass moments of the testbodies to spacecraft mass anomalies, non-uniform thermal expansion, parasiticcapacitances, electrostatic patch effects...). A system of mechanical stops and staticlockers has been designed to withstand launch phase accelerations and limit thesuspended bodies to small movements only. Unlocking will take place once thespacecraft has reached its nominal supercritical rotation rate. A scientific requirementdocument is in preparation in which all the perturbing effects and noise sources that weare aware of at present are analyzed and the corresponding limit they set on relevantparameters is given. A less sensitive ground-based version of the experiment, whichretains its main characteristics, is under development. The goal is to provide the mostcomprehensive demonstration of the space experiment by performing, at the sametime, a valuable ground test of the equivalence principle. Wide reference to theavailable literature and more details can be found in [1-3].R E F E R E N C E S[1] NOBILI A. M., BRAMANTI D., POLACCO E., CATASTINI G., GENTA G., BRUSA E., MITROFANOV V.B., BERNARD A., TOUBOUL P., COOK A. J., HOUGH J., ROXBURGH I. W., POLNAREV A., FLURY W.,BARLIER F. and MARCHAL C., Proposed non cryogenic, non drag-free test of the EquivalencePrinciple in space, to be published in New Astronomy.A. M. NOBILI, D. BRAMANTI and G. CATASTINI656[2] NOBILI A. M., BRAMANTI D., POLACCO E., CATASTINI G., MILANI A., ANSELMO L., ANDRENUCCIM., MARCUCCIO S., GENOVESE A., GENTA G., DELPRETE C., BRUSA E., BASSANI D., VANNARONIG., DOBROWOLNY M., MELCHIONI E., ARDUINI C., PONZI U., LANEVE G., MORTARI D., PARISSEM., CURTI F., CABIATI F., ROSSI E., SOSSO A., ZAGO G., MONACO S., GORI GIORGI G., BATTILOTTIS., D’ANTONIO L. and AMICUCCI G., J. Astronaut. Sci., 43 (1995) 219.[3] “GALILEO GALILEI” (GG) Pre-Phase A Report, ASI (Agenzia Spaziale Italiana), Septem-ber 1996.

The GALILEO GALILEI small-satellite mission with FEEP thrusters (GG)

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The GALILEO GALILEI small-satellite mission with FEEP thrusters (GG)

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