Italian spring accelerometer (ISA) a high sensitive accelerometer for “BepiColombo” ESA CORNERSTONE

Planetary and Space Science 49 (2001) 1609–1617www.elsevier.com/locate/planspasci

Italian spring accelerometer (ISA) a high sensitive accelerometer for“BepiColombo” ESACORNERSTONE

V. Iafolla ∗, S. NozzoliIstituto di Fisica delle Spazio Interplanetario, CNR, Via del Fosso del Cavaliere, 00133 Rome, Italy

Received 4 August 2000; accepted 12 January 2001

Abstract

The targets of the ESA CORNERSTONE mission to Mercury “BepiColombo” are concerned with both planetary and magnetosphericphysics and to test some aspects of the general relativity.

A payload devoted to a set of experiments named radio science is located within one of the three proposed modules, the MercuryPlanetary Orbiter (MPO). In particular, a high sensitivity accelerometer (amin ¡ 10−9g=

√Hz in the range 10−4–10−1 Hz) will measure

the inertial acceleration acting on the MPO. Such data, together with tracking data are used to evaluate the purely gravitational trajectoryof the MPO, transforming it to a virtual drag-free satellite system. The ISA accelerometer, considered for this mission, is a well-studiedinstrument developed at the Istituto di Fisica dello Spazio Interplanetario (IFSI), with the ;nancial support of the Agenzia Spaziale Italiana(ASI). A prototype of such an instrument was constructed, matching the requirements of the radio science experiment. Results of thestudy concerning the use of ISA in the BepiColombo mission are reported here, particular care being devoted to the description of theinstrument and to its sensitivity and thermal stabilisation. c© 2001 Elsevier Science Ltd. All rights reserved.

1. Introduction

Following the successful completion of the Mercury Cor-nerstone (MeCS) System and Technology Study (Baloghet al., 2000; Balogh, 1997; Grard et al., 1994; Vilas et al.,1988), ESA awarded a supplementary contract to the sameindustrial team, plus some new industrial and scienti;c part-ners, including the authors institute. The study results herereported, concern the de;nition of an accelerometer to beincluded within the complex of radio science experimentsproposed for the MPO. The MPO is stabilised along thethree-axes in its 400×1500 km polar orbit for a coverage ofthe whole planet. The onboard payload is devoted to exper-iments in remote sensing and radio science. In particular, aglobal mapping of Mercury gravity and tests of some mostfundamental aspects of general relativity (GR), are accom-plished by means of an accelerometer for detecting the iner-tial acceleration acting on MPO, and a K-band transponderfor detecting the MPO and Mercury positions relative to theEarth.

∗ Corresponding author. Tel.: +39-06-4993-4391; fax:+39-06-4993-4383.

E-mail address: [email protected] (V. Iafolla).

The scienti;c goals to be achieved by the radio scienceexperiments are as follows: (a) measure of Mercury rotationfor allowing a precise determination of the size and physicalstate of the planet core; (b) measure of the global structure ofMercury gravity ;eld; (c) measure of its local gravitationalanomalies for inferring information on mantle structure andon crust=mantle boundary; (d) measure of Mercury orbitaround the Sun and propagation of electromagnetic wavesbetween Earth and Mercury, for improving the determina-tion of (i) the parametrised post-Newtonian (PPN) parame-ters (�; �; �), (ii) the coeFcient of the quadrupolar momentof the Sun (J2), and (iii) eventually, the variations of thegravitational constant (d(lnG) dt). A simulation, includingall possible sources of noise, indicates the possibility of im-proving the precision of the parameters by one to two ordersof magnitude. The non-gravitational accelerations on MPO(direct solar radiation and thermal emission from the planet)must be limited or compensated to a level of 10−9g=

√Hz, in

order to meet the requirements imposed on the radio scienceexperiment. Solar radiation alone causes an eGect, which isthree orders of magnitude larger than such a value. Such aforce is particularly intense due to the vicinity of the Sunand due to the high temperature of Mercury surface. Theonboard accelerometer has the essential task of providingthe information needed to transform the real spacecraft into

0032-0633/01/$ - see front matter c© 2001 Elsevier Science Ltd. All rights reserved.PII: S 0032 -0633(01)00097 -6

1610 V. Iafolla, S. Nozzoli / Planetary and Space Science 49 (2001) 1609–1617

a virtually drag-free test particle during the orbit determina-tion process.

2. The ISA accelerometer

The accelerometer has been developed as a fundamentalcomponent of a space-borne, room temperature gravity gra-diometer having a sensitivity of 10−2 EU=

√Hz (Fuligni and

Iafolla, 1997a; Fuligni et al., 1997; Iafolla et al., 1997; Iafollaet al., 1998a). In this case, the accelerometers must have asensitivity of 5 × 10−13g=

√Hz. Although such a target re-

quires additional eGorts, sensitivity higher than 10−9g=√Hz,

which is necessary for radio science experiment, has alreadybeen attained by the present state of the art.A prototype of an accelerometer having sensitivity greater

than 10−9g=√Hz has been built and it is presently in oper-

ation at underground laboratory of the Istituto Nazionale diFisica Nucleare (INFN) located on Gran Sasso, L’Aquila.The present study aim is a discussion of the accelerometer

engineering, of its integration on-board the satellite, and ofits thermal stabilisation.

2.1. General description

The basic components of ISA are: the mechanical oscilla-tors with a resonance frequency f0 = 3:5 Hz, and the capac-itive bridge transducers, biased at frequency fp =10 kHz.Accelerations acting at frequency fs ¡f0, on the proof

mass, originate an unbalance in the capacitive bridge and amodulation in the output bias voltage. The signal is seen atthe two side bands, f± =fp±fs. The transfer of the signalto high frequency allows the ampli;er to work at a higherfrequency (10 kHz), where its temperature noise is lower,thus avoiding its 1=f noise.Fig. 1 shows the mechanical components of the ac-

celerometer. It consists of a sensing mass (the central

Fig. 1. Mechanical structure of the accelerometer.

Fig. 2. Three-axis con;guration.

plate), which is connected to an external rigid frame by acrank-shaped suspension. The spring restraint of the proofmass is due to the suspension torsion elements, shown inthe particulars of Fig. 1. The sensitivity axis is perpendi-cular to its face. This plate is made by machining a sin-gle piece of aluminium (Al 5056). Four additional platesare connected on the opposite sides of the central one, andare electrically separated by insulating washers that formplain capacitors. A couple of such capacitors provide thesignal reading. The other couple has multi-fold purpose: (i)to lower the electromechanical frequency of the oscillatorby introducing an elastic negative constant; (ii) to obtainthe capacitive bridge equilibrium by means of the applica-tion of constant voltage; and (iii) to excite the mechanicaloscillator by electrically known signals (used as actuators).The mechanical oscillator is described by the equation

I L#+ �t#+ �t#= M ; (1)

where �t represents the torsion elastic constant, I is themoment of inertia of proof mass, and �t is its dissipationcoeFcient. The mechanical resonance frequency is given by

f0 =12�

√�tI: (2)

A three-axis accelerometer can be realised by using threesuch elements, each along an orthogonal axis. Fig. 2 showssuch a three-axis con;guration.

2.2. Noise analysis

Fig. 3 shows the electric scheme of the accelerometer.It is divided into two sections: one for the control (as

V. Iafolla, S. Nozzoli / Planetary and Space Science 49 (2001) 1609–1617 1611

Fig. 3. ISA electric scheme.

Table 1List of elements appearing in the electric scheme

�x Voltage generator associated with signalvb Generator associated with the Brownian noiseen Generator associated with ampli;er noisein Current generator associated with ampli;er noiseZi Ampli;er input impedanceVrs Voltage generator associated with lossy capacitors

described above), and one for the signal detection. Two op-posite sensing capacitors, C1; C2 and two ;xed capacitorsCa; Cb, inserted into a bridge con;guration, provide the sig-nal extraction. The bridge is driven through the transformerby an alternating voltage Vp =Vpo cos(2�fpt). The accel-eration signal gives the capacity variation of the two detec-tor capacitors and their consequent output voltage, in termsof a modulation of Vp at the signal frequency (the signal isdetected as an unbalance of the bridge). The output of thecapacitive bridge is forwarded to a low noise ampli;er, char-acterised by an (high value) input impedance Zi, an equiv-alent generator of voltage noise en, and an equivalent gen-erator of current noise in. Table 1 gives the elements thatappear in Fig. 3, and their meanings.In the following, reference is made to the middle shifts

of the centre of mass of the harmonic oscillator rather thanto its rotation ( sb= xs). In such a frame, Eq. (1) can berewritten as

54m Lx +

�tb2

x +ktb2

x=F; (3)

or, by assuming mr = 54m; �= �t=b2; k = kt=b2, it is

mr Lx + �x + kx=F: (4)

With such an assumption the mechanical quality factor be-comes Qm = �=mr!0.The accelerometer works at frequencies lower than the

resonance frequency of the mechanical oscillator. At suchfrequencies, the transfer function between the acceleration ofthe sensitive mass and its displacement is x(!) ≈ s(!)b ≈a(!)=!2

0.

The total noise of the acceleration, from the point of viewof the mechanical oscillator, can be expressed as

a2t (!) ≈4kb!0

mr

[TQ

+ Tn4ZnC!0

�

]Of: (5)

The ;rst term is the Brownian noise of the oscillator; thesecond one is the noise contribution from the electrical am-pli;er.Of=1=Ot is the inverse of the acquisition time,

Zn = en=in is the ampli;er noise impedance; Tn = enin=4kb isthe ampli;er temperature noise; 1=Q=1=Qm + 1=Qde is thetotal quality factor of the system, which includes dissipationin the mechanical oscillator and the thermal noise associatedwith the transducer loss; �= �2C=mr!2

0 is the electrome-chanical factor; 1=Qde = 4!0=(p tg )=� the electrical meritfactor, related to the electrical dissipation represented by theangle of loss of the electrical part of the transducer (tg )).

3. Description of the ISA prototype and its calibration

A prototype of a three-axis accelerometer was built,with sensitivity equal to 3:3× 10−12g=

√Hz in vacuum and

3× 10−10g=√Hz at atmospheric pressure (due to the limits

by Brownian noise).Such sensitivities are obtained by using experimentally

measured values for the parameters that appear in Eq. (4).The indicated operative limit of 10−9g=

√Hz is due to the

thermal instability of the accelerometer. A change of one de-gree in temperature gives an output signal equal to 5×10−7g.Therefore, one can meet the radio science requirements byan accelerometer temperature that must be stabilised at thelevel of 2× 10−3 ◦C.A picture of such prototype is shown in Fig. 4. In such a

case, however, ground tests were carried out using only thehorizontal axes.

Fig. 4. ISA prototype.


Table 2Mechanical parameters of the oscillators

M Proof mass 0.22I Inertia 4× 10−4

f0 Mechanical resonance frequency 3:5 HzQm Mechanical quality factor (environment-vacuum) 0:3− 104

kt Torsion elastic constant 1:9× 10−1

G Module of rigidity 2:6× 1010

L Arms length 45× 10−3

B Ray of proof mass 43× 10−3

The main components are the three mechanical units (de-scribed above), including their respective preampli;ers. Thesensitive axes of the three units are perpendicular to eachother. A computer, the power supply, and the electronics forcontrol and acquisition of the whole system are placed insidea box of 20 × 20 × 20 cm3 size. The base is equipped, forground calibration, with three support points, two of themelectronically controlled by micrometric screws. The grav-ity acceleration can be set parallel to a sensitive axis (e.g.z) and perpendicular to the other two axes (x; y) by adjust-ing such screws. In such conditions, the unit with sensitiveaxis along the vertical is subjected to acceleration equal to1g; the other two units are sensitive to a component of g de-pending on the angles #x; #y, with respect to the horizontalaxes. Their value in radians corresponds, for small varia-tions of #x; #y, to the acceleration in g to which the unitshave been subjected.Table 2 shows a list of mechanical parameters of the

oscillator that were experimentally measured (units are inSI System).Recall that the mechanical quality factor Qm depends

on the vacuum conditions surrounding the sensor, beingstrongly dependent on the gas trapped within the gap be-tween the capacitor planes. (The two values indicated in Ta-ble 2 for Qm refer to the pressure of 1000 and 10−4 mbar.)The ISA prototype can work either at environmental pres-sure or in vacuum although with diGerent Qm and, therefore,diGerent sensitivity. Unfortunately, depending on the pres-ence of seismic noise, it is impossible to perform measureswith small signals. The Pight prototype is to be implementedfor vacuum operation.Table 3 shows the electrical parameters of the accelerom-

eter. The main electric components are: computer, low-noiseampli;er, A=D and D=A converters. The accelerometer isconnected to a modem for remote system control: per-forming data acquisition, micrometry screws adjustment,program change and a quick-look of the output of the ac-celerometer on a diagram. In our working conditions theampli;er noise is essentially represented by its voltagenoise en, that is seen directly by ampli;er input, while thein current noise acts in two diGerent ways: (i) it gives acontribution directly to the ampli;er input, by circulatingin the impedance capacitive bridge; and (ii) by determininga feedback force that acts on the harmonic oscillator, con-

Table 3Electrical parameters of the accelerometer

C1 =C2 =C3 =C4 Detection capacitor 300 pFtg )C1 Angle of electrical 4× 10−4

loss in C1Ca =Cb External ;xed 300 pF

capacitortg )Ca Angle of electrical 3× 10−4

loss in Ca

vn Equivalent voltage 3× 10−9 V=√Hz

noise generatorin Equivalent current 7× 10−15 A=

√Hz

noise generatorTn Ampli;er noise 0:38 K

temperatureZi Ampli;er input 8× 105 R

impedanceA Ampli;cation. 50� Transducer factor 105 V=m� Electromechanical 3× 10−2

transducer factor

sequent to the charge Puctuations, produced on the bridgeimpedance. Depending on the low value of in, and on thelow eFciency (in our case) for the oscillator excitation byelectrical signals, the noise terms that depend on in can beneglected compared to en.

4. ISA characterisation

The ;rst characterisation consists of separating measure-ments of all accelerometer parameters and using them forthe evaluation of ISA sensitivity. In Tables 2 and 3 suchvalues are reported. By such values, the estimate sensitiv-ity reported below was obtained, for the oscillator either at1 atm or in vacuum.The diFculty of performing a direct measurement of ISA

sensitivity at ground is related to the presence of the envi-ronment seismic noise and gravity acceleration g. It is noteasy to ;lter the seismic noise close to the accelerometer fre-quency range. Usually, ground measurement performancerequires to use a system with one degree of freedom onwhich g does not act.

4.1. The accelerometer transfer function

Fig. 5 shows the transfer function for one single axis ofISA. In this case, the z sensitivity axis is perpendicular to thelocal vertical axis. It is obtained by exciting the accelerom-eter by sweeping the frequency of a voltage applied to thecontrol capacitors (C3; C4), which are used as actuators.The exciting signal must be much higher than the seis-

mic noise. The Qm is kept low (by avoiding a high vacuum)to permit a correct working of signal analyser. As it can beseen, the system has a harmonic at 16:6 Hz above the funda-mental frequency equal to 3:5 Hz, such harmonic is related


Fig. 5. Transfer function of the mechanical oscillator.

to the mechanical structure of the harmonic oscillator. Themeasurement of the mechanical oscillator Q, under vacuum,was performed by exciting its resonance at high level andwatching its free exponential decay.

4.2. Linearity of the system and its C.C. calibration

It is possible to calibrate every single unit of theaccelerometer by applying a known component of gravity

acceleration (i.e. of the support angle variations) and byreading its associate output. Fig. 6 shows the output of oneaccelerometer unit alone, excited with DC acceleration.The angle variations are produced by applying a suitable

voltage to a piezoelectric device, located under one of itssupports.The x-axis is the acceleration read by the accelerometer,

and the y-axis is the voltage given to the piezoelectric. Theinclination is given in rad (multiplied by a conversion factor


Fig. 6. Calibration and linearity of the accelerometer.

2 × 10−8 rad=V). The plot shows also the linearity of theaccelerometer response for a wide range of accelerations.The piezoelectric device has been used to determine small

angle variations. The minimum in the plot corresponds tothe best equilibrium of the capacitive bridge.

4.3. ISA thermal stability measurements

The thermal stability of the accelerometer as already men-tioned is ∼= 5 × 10−7g=◦C. Fig. 7a shows the temperaturevariation vs. time, measured inside the accelerometer box.Fig. 7b shows the output of the accelerometer, used as incli-nometer, in response to such previous temperature variation.A temperature variation of 0:3 ◦C, for the steep slop signal,corresponds to an acceleration of 1:5× 10−7g. The relationbetween temperature vs. signal is not direct, as it dependson the presence of the seismic inclinometric signal, acting atthe same time. The temperature instability of the harmonicoscillator depends on various factors, the main eGect be-ing concerned with the thermal contraction of the materials(washers, bolts of connection, etc). The diGerential structureof the mechanical part of the accelerometer provides a con-sistent reduction in such instability. Other contributions areoriginated by thermal inPuence on the electrical part. Thethermal constant of time of the accelerometer prototype isapproximately equal to 8 h. Considering the thermal ;lter-ing and the small thermal variations in the high and middlefrequencies, it seems to be not possible to carry out directmeasurements of thermal stability in such a frequency range.An accurate evaluation of the stability coeFcient has to takeinto account that the slow temperature variation results alsoin a variation of the support plane of the accelerometer, andin a corresponding signal in its output. It is diFcult to carryout a calibration for high temperature variations, becausein this way high gradients ought to be introduced. On theother hand, it is not an easy task to remove, at low level,the real accelerometric signal occurring at the input of theaccelerometer.

Fig. 7. (a) Temperature variation of the accelerometer vs. time. (b)Accelerometer output vs. time during the temperature variation showedin Fig. 7(a).

4.4. Geophysical measurements

ISA performances are tested in the INFN undergroundlaboratory of Gran Sasso, L’Aquila (Fuligni et al., 1997),where the seismic noise is low and temperature is stable. Thespectral density of the horizontal component of the seismicnoise measured by ISA, in the range 10−6–1 Hz, completelyagrees with the data recorded by classical geophysical in-struments.Fig. 8 shows the horizontal component of solid Earth tide,

recorded by the accelerometer used as an inclinometer. Datawere collected during August 1996, a vacation time bywhichthe anthropic seismic noise is minimum. Fig. 9 shows thepower spectral density evaluated in the same period, withlevel lower than 10−9g=

√Hz at 4× 10−2 Hz.

5. Dynamic shock

An accelerometer for space use must be able to absorb avery high level of dynamic shock. ISA was tested in free fallconditions in the INTA Madrid drop tower. The accelerom-eter was installed inside a sphere and released from 18 maltitude. After the free fall, the system was recovered usingan energy absorber, but in any case the deceleration was


Fig. 8. Horizontal component of solid Earth tide.

Fig. 9. Power spectral density of the seismic noise.

larger than 20g. The stops of the proof mass avoid damageto the accelerometer, and we were able to use it for sev-eral drops. Such a preliminary test shows the possibility ofimplementing a prototype capable of absorbing high accel-eration shocks due to satellite launch.

6. Noise and signal acting on the accelerometer

The satellite orbiting around Mercury is not an inertialsystem; the accelerations act at every point according to thewell-known formula

g(r; t) =−∇V (r; t)− ( ∧ (( ∧ r)

−2( ∧ v− ˙( ∧ r − �(t); (6)

where V (r; t) is the gravitation potential, ( the angular ve-locity, r the position vector on the satellite from the reference

origin on the platform itself, v its velocity vector, and �(t)the linear acceleration acting on MPO. The ;rst three termson the right-hand side can be easily recognised as gravi-tational, centrifugal and Coriolis acceleration, respectively.The last two terms depend on angular velocity variation andlinear acceleration, respectively.

6.1. Inertial e3ects

Such eGects are related to the last four terms of (6). Wecan divide them into linear and angular accelerations.

6.1.1. Linear accelerationsEvery point on the satellite is under the same action of

linear accelerations. Such accelerations can be external tothe satellite, such as the radiation pressure; or internal suchas the motion of the mechanical parts (reaction wheel), orfuel sloshing, or mechanical vibrations with high Q. Suchaccelerations are the main components that need to be mea-sured in order to reduce the eGect of the perturbations of thegravitational orbit of the MPO.It should be stressed that ISA is not an absolute accelerom-

eter. Therefore, it is not able to measure constant accelera-tions, and the reliability of its output is only for performingmeasurements in its dynamic range.

6.1.2. Angular accelerationsThe eGect on the satellite is diGerent on points at diGer-

ent distances from its rotation axis. In order to avoid sucheGects, the accelerometer is installed with its centre of massvery close to the MPO centre of mass (possibly they shouldcoincide). Numerical simulation of the inertial eGects dueto the rotation of the MPO around Mercury, in its ellipticorbit, was carried out. The accelerometer was supposed tolie on the orbital plan, along the local vertical, at a distanceof 10 cm from the MPO centre of mass. The analysis showsa nearly sinusoidal signal, a fundamental frequency equal tothe orbital one, has amplitude of the order of 10−8g, whilethe higher harmonics decrease quickly in amplitude. Such asignal can be easily modelled. In any case, the presence onthe MPO of a star mapper, necessary for performing rota-tion experiments, provides a high accuracy measurement ofMPO attitude.Also, in this case it is necessary to emphasise that ISA can

detect no constant angular acceleration, rather only termsvarying vs. time.

6.1.3. Coriolis accelerationThis eGect arises only if there is a motion of the proof

mass. Recalling that the accelerometer is hard-mounted onthe MPO and each proof mass can move only with one de-gree of freedom, the Coriolis acceleration, acting perpendic-ular to this direction, has no eGect on it.


6.2. Gravitational e3ects

The gravitational eGects on the ISA sensing mass can beinduced by a mass in the satellite and by a mass external toit. The gravitational eGects induced by the satellite mass are,in general, constant and therefore they cannot be detectedby ISA. Gravitational eGects induced by masses, which arein motion on the satellite, produce eGects that are variablewith time and can be detected. Such eGects can be origi-nated by reaction wheels, fuel sloshing, level change of thefuel, etc. Gravitational eGects induced by masses externalto the satellite are mainly originated by Mercury and theSun.

6.3. Thermal e3ects

Thermal variations inside MPO have strong implicationsfor the performance of the accelerometer, as they act directlyon it and induce perturbations through the thermal contrac-tion of MPO structure.The main thermal eGects are on the accelerometer, as its

stability is 5×10−7g= ◦C. This means that, in order to avoidthe thermal eGect on it, the spectral density of the thermalvariation must be less that 2×10−3 ◦C=

√Hz in the frequency

range of the accelerometer (10−4–10−1 Hz).A thermal analysis of ISA onboard MPO was performed

by Alenia Spazio in cooperation with the authors. The anal-ysis starts from three ;xed points: (a) preliminary experi-mental results concerning ISA thermal stability; (b) thermalanalysis considerations, derived from SAGE (SansSo et al.,1998) phase A ;nal report; (c) thermal evaluation for MPO,performed by Alenia, during theMercury Cornerstone study.The analysis was performed for two positions of Mer-

cury’s orbit around the Sun:Perihelion position, with 180◦ for MPO orbit inclination:

hot case, with solar Pux equal to 14:4 kW=m2. Aphelionposition, with 0◦ for MPO orbit inclination: cold case, withlower solar Pux.The relevant parameters of the thermal evaluation at per-

ihelion position are reported in the table, for a new ISAversion, without active thermal control and reduced power(5:3 W) and mass (8:15 kg).The sinusoidal thermal variation gives an eGect that re-

sults in the limits of sensitivity requirements, while the ex-ponential variation (due to Mercury’s orbit around the Sun)introduces a condition in the ISA dynamic.A correction of the thermal eGect by measuring the tem-

perature is also possible (ISA uses three thermometers onefor every axis element).

6.3.1. Inertial e3ect induced by the thermal variationIn the previous paragraph, it was reported that ISA can-

not monitor constant signals (gravitational and inertial), butdepending on the temperature change, inertial and gravita-tional constant eGects can be “modulated” by changes in the

Table 4ISA sensitivity estimation in diGerent pressure conditions

Sensitivity (g) Conditions Qm

10−9 1 atm 33:3× 10−12 10−4 mbar 104

Table 5ISA on board the MPO thermal analysis

Could case

ISA mass (kg) 8.15ISA power dissipation (W) 5.3N

◦of orbits 120

OT sinusoidal per orbit 2:3 mKOT exponential 50 �KOrbit period (s) 8355MPO thermal constant (s) 7× 104

Equilibrium temperature◦C 50.37

centre of mass position of the proof mass and in the sensi-tive axis direction.

6.4. Intrinsic accelerometer noise

The last term of noise here recalled is the intrinsic noise ofthe accelerometer, expressed by (4). Recall that such a noiseis Pat in the ISA frequency range, and as low as 10−9g=

√Hz.

All previous eGects can be divided into three categories:

6.4.1. SignalIt includes all inertial eGects that produce a real displace-

ment of the MPO centre of mass, as measured by ISA.Such measurements give useful information for recoveringthe MPO gravitational trajectory by tracking MPO from theEarth.

6.4.2. False signalIt includes gravitational eGects inducing signals on the

accelerometer, but is not useful for recovering the gravi-tational trajectory of MPO, because tracking already takesthem into account. (Table 4)

6.4.3. NoiseIt includes eGects on the accelerometer that are not related

to the displacement of MPO centre of mass.In Table 5 a list of such eGects is reported.An error model for the accelerometer was constructed for

performing a simulation of the entire radio science exper-iments, and a FORTRAN program was written for gener-ating noise related to ISA accelerometer. The intrinsic ISAaccelerometer noise, as mentioned above, is white in theinstrument frequency range and below 10−9g=

√Hz. It is

necessary to add to such a white noise, also the sinusoidalcontribution due to the temperature variation at the orbital


Table 6Signals and noise acting on the accelerometer

EGect Type Characteristic

Solar radiation pressure Signal Modulated at orb. freq. and spinAlbedo and infrared emission from Mercury Signal Modulated at spin freq.Attitude manoeuvres and spacecraft buGeting Signal RandomElectromagnetic eGects Signal Random + modulated at orb. freq.Orbiter spin rotation Signal Modulated at spin freq.Changing of orbiter mass False signal Coloured noise during manoeuvresMercury gravity gradient on the accelerometer False signal Modulated at orb. freq.Thermal variations in the instrument mounting plate Noise Coloured noise, 1=fSinusoidal thermal variations Noise Modulated at orb. freq.DiGerential heating of the MPO Signal Modulated at orb. freq.Instrumental noise Noise White noise

periods. In a more pessimistic case a 1=f noise is also intro-duced. In such a last case, the noise is equal to 10−9g=

√Hz

at 10−2 Hz, while it is lower at high frequency and higherat low frequency. The hypothesis is that the thermal noiseis ;ltered by the thermal MPO constant. (Table 6)

7. Conclusion

The ISA accelerometer considered for the BepiColombomission to Mercury seems to match all the requirements ofthe radio science experiment. During the de;nition study,the problem of integration on board the MPO has been con-sidered with particular attention to power dissipation, vol-ume, and mass. The ISA sensitivity can be higher thanthe indicated requirements (Iafolla et al., 1998b; Lorenziniet al., 1994), but its real limit is in its sensitivity to thermalvariations. Preliminary analyses indicate the possibility to;t the mission requirement by avoiding the use of an activethermal control. It seems also possible to attain an improve-ment of ISA thermal stability or a correction by measuringits temperature.

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Italian spring accelerometer (ISA) a high sensitive accelerometer for “BepiColombo” ESA CORNERSTONE