ARTICLE IN PRESS Planetary and Space Science 58 (2010) 300–308
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Planetary and Space Science journal homepage: www.elsevier.com/locate/pss
Italian Spring Accelerometer (ISA): A fundamental support to BepiColombo Radio Science Experiments V. Iafolla , E. Fiorenza, C. Lefevre, A. Morbidini, S. Nozzoli, R. Peron, M. Persichini, A. Reale, F. Santoli Istituto di Fisica dello Spazio Interplanetario - Istituto Nazionale di Astrofisica, Via del Fosso del Cavaliere, 00133 Roma, Italia
a r t i c l e in f o
a b s t r a c t
Article history: Received 29 April 2008 Received in revised form 23 February 2009 Accepted 6 April 2009 Available online 22 April 2009
The Radio Science Experiments of the BepiColombo mission will enable substantial improvement of the knowledge of Mercury’s orbit and rotation, and the relativistic dynamics in the solar system. A fundamental support to the spacecraft tracking data will be given by the Italian Spring Accelerometer (ISA). This is a three-axis accelerometer devoted to the measurement of the non-gravitational perturbations acting on the Mercury Planetary Orbiter (MPO), whose knowledge is important in order to fully exploit the quality ofpthe ffiffiffiffiffiffiffi tracking data. The intrinsic noise level of the instrument that will be onboard MPO, 109 m=s2 = Hz in the 3 105 to 101 Hz frequency range, guarantees the fulfilment of the RSE requirements. The main scientific and technological features of the instrument are discussed, together with its current error budget, experimental activities and foreseen calibration strategies. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Solar system Mercury Accelerometers Non-gravitational perturbations Gravimetry General relativity
1. Introduction—scientific objectives Among the main scientific objectives of the BepiColombo mission to planet Mercury, an important set is formed by the socalled Radio Science Experiments (RSE). These aim to perform precise measurements of
gravitational field of Mercury; rotation of Mercury; general relativistic effects, in particular Mercury perihelion precession by state-of-the-art radiometric tracking of Mercury Planetary Orbiter (MPO) spacecraft. The overall procedure is fairly complex and is fully described in Iess (2009) (see also Milani et al., 2001, 2002). From the point of view of orbit determination, the tracking data—which in our case are range and range-rate—need to be fitted with a dynamical model as complete as possible and a model for the measurement types. In particular the dynamical model is based on general relativity (at the relevant postNewtonian level) for the motion of bodies in the solar system and on a spherical harmonics expansion of the Hermean gravitational field, in order to determine accurately the MPO motion around Mercury. The models will depend in general on a Corresponding author. Tel.: +39 064 4548 8391.
E-mail address:
[email protected] (V. Iafolla). 0032-0633/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2009.04.005
set of parameters which will be adjusted in the orbit determination procedure; among them, the quantities of interest, like the PPN parameters and the spherical harmonics coefficients C lm and Slm of Mercury gravity field. A distinctive feature of BepiColombo with respect to other deepspace missions is its relative proximity to the Sun. This has two fundamental consequences. Firstly, general relativistic effects are enhanced (motion near a massive body): this is the main reason to perform such an experiment. Secondly, the harsh environment the spacecraft will move in: non-gravitational effects due to surface forces, mainly the solar radiation pressure, perturb the motion of the spacecraft and mix with the gravitational effects. These forces are very difficult to model, since they depend in a complex way on incoming radiation and spacecraft surface optical properties and spacecraft attitude (Lucchesi and Iafolla, 2006). Analytical models do indeed exist, but they are effective only in particular cases, the simplest of which is a spherically symmetric spacecraft (for a general review of this issue see Milani et al., 1987). This is a serious problem, since it limits the accuracy with which the relativistic and geophysical parameters could be recovered. In order to overcome it, an accelerometer onboard the MPO—the Italian Spring Accelerometer (ISA)—will directly measure the non-gravitational perturbations so as to precisely take them into account in the orbit determination procedure and make the MPO an a posteriori dragfree satellite. The use of high-performance accelerometers instead of analytical or numerical models, in order to improve the quality of orbit determination and especially of related parameter
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10−2 Tracking noise Thermal noise
10−4
Intrinsic noise
Spectral density (m/s2/√Hz)
Total noise Sensitivity requirement
10−6
10−8
10−10
10−12
10−14 10-5
10-4
10-3
10-2 Frequency (Hz)
10-1
100
101
Fig. 1. Noise contributions from the accelerometer and the tracking system as used in the simulations that have been performed to prove the reliability of the RSE. The total noise level is mainly due to the thermal effects on the accelerometer at low frequencies and to the tracking noise at high frequencies. The light blue bar represents the ISA bandwidth. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
determination, has been given increasing attention in recent years. Indeed, the performance of the tracking systems has been steadily improving, whereas this cannot be said about modelization. From near-Earth geodetic missions like the LAGEOS satellites to deep-space probes exploring the outer solar system, cases can be found where physical processes of non-gravitational origin could at least in principle play an important role (think to the socalled Pioneer anomaly, see Anderson et al., 1998, 2002). Examples of the accelerometers effectiveness are given by the CHAMP and GRACE geodetic missions, where the precise GPS position measurements are combined with accelerometric measurements (see van den Ijssel and Visser, 2007). The use of acceleration data improves the geophysical parameters estimation and is far better than the use of empirical acceleration terms in the modelization; these empirical accelerations could in fact improve the quality of the fit (post-fit RMS reduction), but at the cost of a predictivity lack (no or small correlation with physically relevant parameters). The accelerometer characteristics requirements follow from the RSE requirements (see also Iafolla and Nozzoli, 2001). As discussed in van Casteren et al. (2009), the MPO spacecraft will be three-axis stabilized, Nadir pointing, characterized by a 400 1500 km polar orbit around Mercury. This orbit configuration is suitable for the recovery, with a signal-to-noise ratio larger than 10, of Mercury’s gravity field up to degree l ¼ 25, corresponding to a spatial resolution of about 300 km (Milani et al., 2001, 2002; Iess, 2009). In order to reach the goals of the RSE, the orbit must be known with an accuracy of at least 1 m in the along-track direction over one orbital revolution of the MPO around Mercury, i.e., over 8355 s. This corresponds to an along-track acceleration accuracy of about 108 m=s2 . Therefore, this number has been considered equivalent to the acceleration measurement error over the typical arc length during one observation session from Earth’s ground antenna(s). However, it ffi is not necessary to retain a spectral density of pffiffiffiffiffiffi 108 m=s2 = Hz through all the accelerometer’s bandwidth.
Table 1 RSE related features and performances. Parameter
Value
Measurement frequency range
3 105 to 101 Hz
Maximum expected signal
3 106 m=s2 pffiffiffiffiffiffi 108 m=s2 = Hz pffiffiffiffiffiffi 9 2 10 m=s = Hz
Measurement total noise Instrument intrinsic noise Required measurement accuracy Read-out interval
108 m=s2 1s
Indeed, as shown in Fig. 1, which describes the noise contributions due to the accelerometer and to the tracking system, at low frequency the noise is dominated by the thermal disturbing effects at the interface between spacecraft and accelerometer while at higher frequencies the noise is dominated by the tracking errors. The red line represents ISA intrinsic noise; the green line represents the filtered thermal pffiffiffiffiffiffiffi noise effects due to a possible white noise at a level of 4 C= Hz, which may be present at the mechanical interface between the spacecraft structure and ISA; the blue line represents the equivalent acceleration associated with the Doppler noise; finally, the black line represents the total noise (quadratic sum of the previous noise sources). The various noise sources—ISA intrinsic noise, thermal noise, tracking noise—constrain the ISA sensitivity requirement. This requirement has been used in the error budget analysis described in Section 4 (sensitivity requirement, diamond line). The need to fully exploit the accelerometer performances only in a narrower bandwidth, between 104 and 103 Hz, is clear. We stress that these results have been obtained in the case of a passive thermal control. Currently, an active thermal control is foreseen as baseline; the thermal effects will be further attenuated by a factor 700. In Table 1 the main RSE-derived requirements are summarized.
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1369 1368
Irradiance (W/m2)
1367 1366 1365 1364 1363 1362 1361 −2000
0
2000
4000 6000 8000 Time (d, epoch 0 Jan 1980)
10000
12000
Fig. 2. Composite Total Solar Irradiance (TSI) at 1 AU. The data, over which this time series is built, are based on a number of records, merged to construct this composite.
Concerning the non-gravitational perturbations acting on the spacecraft, the near-Mercury environment the MPO will move in is particularly harsh. Due to the relative proximity to the Sun, the radiation and particle fluxes are very strong. In Fig. 2 the solar irradiance—Composite Total Solar Irradiance (TSI)—as measured by several space missions1 is shown (Fro¨hlich, 2000). The solar cycle of about 11 years, with several small-scale fluctuations, is clearly visible. The radiation exerts a push on the spacecraft body in a way that depends on the optical properties of its surfaces. One can identify at least three different types of perturbations due to electromagnetic radiation impinging on the spacecraft surfaces:
visible radiation coming directly from the Sun (direct solar radiation pressure);
visible radiation from the Sun being reflected by the Mercury surface (albedo radiation pressure);
infrared radiation emitted from the surface of Mercury. The ISA accelerometer will measure the combined effect of all of them on the MPO spacecraft. In Lucchesi and Iafolla (2006), the effect of the first two types of perturbations has been studied, and the advantages of using on-board accelerometer data with respect to models of the non-gravitational perturbations have been shown.
2. Instrument design and scientific performance 2.1. Measurement principle A common problem to different fields of physics, disregarding whether experiments are conducted in ground-based laboratories or in space-borne enclosures, consists in the detection of small 1 The data are available composite/DataPlots/.
on
ftp://ftp.pmodwrc.ch/pub/data/irradiance/
Fig. 3. ISA sensing element. Three of these elements are arranged with the electronics to compose the ISA three-axis accelerometer.
forces or accelerations that act on the proof mass of an harmonic oscillator, producing exceedingly small displacements. When it is possible, harmonic oscillators having a very low resonance frequency are used to magnify this effect, in spite of the frequency range of the instrument (a free mass is the ideal tool). The fundamental part of each of the three ISA accelerometer elements (one is shown in Fig. 3) is a mechanical harmonic oscillator with a resonance frequency f 0 ¼ 3:5 Hz. This oscillator can be regarded as a test mass connected to the spacecraft through a spring with low elastic constant; the accelerations acting on the spacecraft can be regarded as inertial accelerations acting on the test mass, in the reference frame of the spacecraft itself. To detect these accelerations it is necessary to measure the related displacements of the proof mass in this reference frame. As an example, the displacements of the proof mass due to an acceleration of 108 m s2 at frequency f s below the resonance
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frequency of the oscillator (f s of 0 ) are: x ¼ as =ð2pf 0 Þ2 ’ 5 1010 m. The accelerometer is hard-mounted on the spacecraft and its external structure becomes the spacecraft reference frame. A capacitive transducer detects these displacements. In principle, a single test mass can be used to detect the three components of a linear acceleration acting on the spacecraft, but in the ISA design there are three different test masses, one for each axis. The spacecraft frame must be considered as a non-inertial reference frame and every point of it experiences not only linear accelerations, as previous considered, but also apparent accelerations (due to its angular velocity and angular acceleration) as well as gravity gradients. These effects must be regarded as disturbances and big efforts must be done to reduce them (see Section 4). Basically, the measurement of an accelerometer is described by the following formula: ~ B þ Sf ~ Anoise , Atrue þ ~ Ameas ’ ~
(1)
where ~ Ameas and ~ Atrue are the measured acceleration and the true acceleration, which are affected by a bias ~ B and a scale factor Sf (omitting possible non-linear contributions), and ~ Anoise is the contribution due to stochastic and deterministic noises. The true acceleration acting on each ISA sensing element can be written as ~ aTID þ ~ aAPP ~ aNGP , Atrue ¼ ~
(2)
where ~ aTID is the contribution of the gravity gradients ~ aTID ¼ T ~ R;
2
T ij ¼
@ V . @xi @xj
(3)
~ aAPP the contribution of the apparent accelerations _ € _ ~ ~ ~ ðo ~ ~ ~ ~ ~ RÞ o R 2ðo RÞ ~ R, aAPP ¼ o
(4)
where V is the gravitational potential of the primary (i.e., Mercury), ~ R the position vector of each proof mass with respect ~ the spacecraft angular to the spacecraft centre of mass (COM), o velocity; ~ aNGP represents the part due to the non-gravitational perturbations, i.e., the goal of ISA measurements. We can notice aAPP terms depend on the position vector ~ R. that both ~ aTID and ~ Hence the most obvious position for the proof masses—in order to null these spurious effects—would be the one with all three of them in the spacecraft centre of mass. The fact that three different sensing elements are used (and therefore all three cannot be placed at the same position), together with allocation constraints in the spacecraft body and non-negligible centre of mass variations during operations, forced the selection of a different choice for their positions. This is discussed in Section 2.3. We have to stress, however, that what is important is not the magnitude of these effects (as long as these do not saturate the instrument read-out) but the related uncertainty. In this way these can be reliably removed from the read-out signal and do not enter in the error budget (see Section 4). 2.2. Instrument hardware description The ISA instrument configuration is based on two units: the ISA Detector Assembly (IDA) (see Fig. 4) and the ISA control electronics (ICE). IDA contains the three detector units, the preamplifier and the analog-to-digital conversion section, while ICE contains the remaining control electronics and interfaces electrically with the MPO. The main characteristics of the instrument are presented in Table 2. As said before, the three sensing elements constitute the core of the instrument. A capacitor transducer in a bridge configuration, followed by a low noise amplifier, provides the detection of the signal (see Fig. 5). The bridge is biased at frequency f p ¼
Fig. 4. ISA Detector Assembly (IDA).
Table 2 ISA characteristics. Parameter
Value
Mechanical Proof masses Resonance frequency Mechanical quality factor
0.2 kg 3.5 Hz 10
Physical Mass (total) Dimensions (IDA) Dimensions (ICE)
5.8 kg 300 170 180 mm 170 130 86 mm
Power Electronics power dissipation (without heather) Total average power dissipation with heather and in worst case condition Total peak power dissipation with heather and in worst case condition
7.4 W 10.1 W 12.1 W
Thermal IDA operative range IDA non-operative range IDA I/F orbital stability IDA I/F sidereal stability ICE operative range ICE non-operative range Sensor heads temperature sensitivity
0; þ40 C 10; þ55 C 2 C=orbit 12:5 C=Mercury year 20; þ50 C 40; þ60 C
Front end electronics temperature sensitivity
5 108 m=s2 = C
5 107 m=s2 = C
These are divided in mechanical, physical, power and thermal characteristics.
10 kHz and accelerations at frequency f s, acting on the proof mass, cause an unbalance of the capacitive bridge and a modulation of the bias voltage: at the output of the capacitive bridge the signal is seen at the two side bands, f ¼ f p f s . Transferring the signal to high frequency allows the amplifier to work at a frequency (10 kHz), where its temperature noise is lower, avoiding its 1=f noise. The other important characteristic of the mechanical oscillators, besides their resonance frequency, is the mechanical quality factor: Q m ¼ 10. A value of the order of units is sufficient, in our case, to make the Brownian noise contributions negligible. The transducer must have a high electromechanical coupling factor b (ratio of the mechanical energy of the oscillator to the electric power to be measured). The elements of the
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Fig. 5. ISA measurement main elements.
accelerometer must be stable in time and independent from the variation of temperature. Each single axis accelerometer is constituted by three main parts:
mechanical oscillator; actuation and control; signal detection. Depending on the thermal sensitivity of the accelerometer, a spurious signal arises if a temperature change occurs; the instrument thermal control acts to keep the temperature variations as low as possible, in order to avoid spurious effects exceeding the required sensitivity in the instrument bandwidth. pffiffiffiffiffiffiffi The accelerometer has an intrinsic noise of 109 m=s2 = Hz in the frequency band of 3 105 to 101 Hz. As described in Milani et al. (2001), the typical arc length2 will be about 8 h. Therefore, this value has been assumed as the lower limit of the accelerometer band (about 3 105 Hz). The upper limit for the band is dictated by the requirement of a linear response of the accelerometer to a given perturbation. This means that the accelerometer must be used in a frequency region where its transfer function is flat, i.e., below the oscillator resonance frequency. Fig. 7 shows a recent measurement of the transfer function performed on a bread-board built by the industrial contractor. The measurement total noise, intrinsic plus induced by the pffiffiffiffiffiffi ffi spacecraft, is equal to 108 m=s2 = Hz; this means that over a time integration Dt the accelerometer performance can be much better than 108 m=s2 , that is the accuracy required by the RSE for the MPO orbit reconstruction. Several sources of error have to be added to the intrinsic noise of the instrument. These are addressed in Section 4. Here we notice that thermal effects play an important role. In fact, each sensing element is affected by temperature variations, which produce spurious acceleration readings. The thermal environment the MPO will face will be characterized by noticeable variability that will result in temperature variations estimated to be 4 1C per orbit and 25 1C per Mercury year for IDA, at the spacecraft/instrument interface. In 2 Between 4 and 12 h depending on the visibility conditions. The visibility conditions constrain the way in which the data are collected in the case of range and range-rate measurements, which will not be continuous.
order to overcome this problem, apart from isolation layers, an active thermal control system has been designed; currently its performances guarantee a reduction of the thermal variation of a factor 700.
2.3. Sensing elements positioning The ideal positioning for the sensing elements would be the one with all three elements in the spacecraft centre of mass. In this way, they would directly measure the accelerations acting on this reference point, without the spurious parts due to gravity gradients and apparent accelerations (Eqs. (3) and (4)). Of course, ISA accelerometer being composed by three different elements (each of them measuring the acceleration acting on a definite direction), this positioning is not possible for all of them. An analysis has been performed, then, considering the three elements subject to gravity gradients and apparent accelerations in a rotating reference frame3 (the so-called nominal solution). The best configuration is that with the three proof masses aligned with the spacecraft (nominal) rotation axis, and led to the current design for the accelerometer (see Fig. 4). The nominal solution has been obtained on the assumptions of perfect knowledge of the proof masses positions and absolute reliability of the spacecraft Attitude and Orbit Control System (AOCS). This is not strictly true, since there is an uncertainty in the elements positions and in the spacecraft pointing; moreover, the spacecraft COM is not fixed (with respect to a body-fixed reference frame), but moves due to movements of spacecraft appendices (in order to follow the position of the Earth and thus provide a nearly continuous communication channel) and fuel consumption and sloshing. While this motion could be considered of negligible magnitude for other applications, in our case it is relevant. The effects due to COM movements are among the main sources of error in the measurement4; in order to minimize them, requirements have been set both on sensing elements and on 3 In fact, the MPO will be nominally Nadir pointed, so it will be constantly rotating about an axis orthogonal to its orbital plane. 4 The COM movement has also the effect of ‘‘modulating’’ some terms in the equations for gravity gradients and apparent accelerations which were constant in the fixed-COM case (and thus the accelerometer was not sensitive to them), making them effective in the error budget.
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COM position knowledge. It has to be noticed that this scenario has been simplified by the new concept of radio science measurement recently introduced. For a discussion of these issues we refer to Section 4.
3. Current experimental activities The development of the instrument relies on a strong ensemble of laboratory experimental activities. These are aimed at testing the various technological solutions on prototypes, measuring the various features (see Table 2), testing selected effects, doing performance checks on bread-boards built by the industrial contractor. The main tasks—described in the following—concern tests on thermal control system and measurements of the intrinsic noise level of the instrument (using common-mode-rejection); activities are also devoted to the development of the read-out electronics and finally an important role is performed by tests on bread-boards built by the industrial contractor. 3.1. Rejection tests An important test to be performed on the instrument is the check of its sensitivity, which is identified with the instrument intrinsic noise, comprehensive of the various sources (mechanical, electronics and so on), but not of the interface noise (mechanical and thermal) induced by the spacecraft and of the spurious effects described by Eqs. (3) and (4). Such a test is difficult in a laboratory environment, mainly due to seismic noise: this noise pffiffiffiffiffiffiffiis indeed higher than the instrument sensitivity of 109 m=s2 = Hz, and it is not possible to distinguish it from the noise produced by the instrument itself. A way to overcome this difficulty is to arrange two equal accelerometers in a differential configuration: the two sensing elements are mounted rigidly one with each other, so that their sensing axes are parallel. The seismic signal acts the same way for the two elements (common mode) and can be rejected by subtracting one element’s output from the other, thereby leaving the noise coming from the instruments alone. The result of such a
305
procedure can be seen in Fig. 6, where the power spectral density of the two output and that of their difference (‘‘rejection’’) is shown. The rejection is taken as the upper limit of the single elements intrinsic noise. The noise coming from the environment is about two orders of magnitude higher than the noise coming from the instruments. This result thus confirms that the instrument achieves the required level of performance. 3.2. Bread-boards tests It has been performed a series of tests on two bread-boards of the sensing element provided by the industrial contractor. These two bread-boards are representative of flight version (at current design status), apart from mass suspension elements (for one of the two, replaced by a rigid part) and sensing heads feet. These tests aimed mainly at checking the compatibility of the breadboards with the requirements on sensing elements. Among the various tests, we want to underline here the thermal sensitivity tests and the measurement of the transfer function in vacuum (see Fig. 7). It has to be noted that this measurement has been done under the local Earth gravity; this condition increases the system frequency.
4. Error budget The assessment of the measurement errors is fundamental to fix the requirements on the spacecraft/instrument interface and for the definition of the data products in the overall RSE procedure. The various sources of uncertainty in the measurement can be broadly divided in two categories, based on their spectral content: periodic or pseudo-sinusoidal and random. They have to be compared with the requirements coming from RSE (see Table 1); to this end, two quantities are defined, the measurement accuracy and A0 ¼ 108 m=s2 p ffiffiffiffiffiffiffi the measurement noise (spectral density) S0 ¼ 108 m=s2 = Hz. It has to be remarked that the construction of the error budget has a two-fold meaning. On one side, it has the purpose of assessing the effects on the experiment uncertainty and evaluating their relative contribution, in order to guarantee the fulfilment
Fig. 6. Rejection test with two equal sensing elements, mounted rigidly with their sensing axes parallel. The power spectral density of the two instrument output is shown, together with that of their difference.
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Fig. 7. The transfer function measured for a bread-board of the sensing element, amplitude (upper part) and phase (lower part).
Table 3 Error budget: deterministic part. Type
Due to
Spectral content
Requirement on
Error (% A0 )
Residuals of gravity gradients, apparent forces and MPO rigid body motion after the process of removal Thermal effects Components coupling
MPO nominal attitude
Orbital period P and 1=2P
MPO COM position knowledge
80
ISA thermal sensitivity Axes misalignment and crosstalk
Orbital period P Orbital period P
MPO thermal variations Sensing axes misalignment with respect to an inertial reference system
15 5
Total
100
of the RSE objectives. On the other side, it establishes the requirements to put on the overall spacecraft environment (attitude, microvibrations, and so on). The periodic error sources—mainly at the MPO mean motion frequency n or its harmonics—are summarized in Table 3. These are also termed deterministic. We have to underline that the listed phenomena can cause effects also at other frequencies outside the band of the instrument (as is the case for thermal effects, see below), but these are not relevant.5 The random error sources have effects which are not characterized by definite frequencies, but are instead spread over the instrument band; they are summarized in Table 4. The various contributions to both types of errors (deterministic and stochastic) are briefly discussed in the following. For their evaluation we refer to Iafolla et al. (2007). The gravity gradients and the apparent accelerations, described by Eqs. (3) and (4), respectively, depend on the distance ~ R between each proof mass and the spacecraft centre of mass, and on the _ . They are characterized by ~ ~ and o spacecraft attitude, given by o both periodic and random effects. The periodic contributions are connected with the error in the knowledge of ISA position in the spacecraft frame, while the random ones (only related to apparent
5
Apart from possible long-term stability issues.
forces) are connected to the value of ISA position and to the attitude control errors. These contributions have been estimated with the following assumptions:
The ISA sensing axes are aligned with Gauss reference axes.6 The nominal angular velocity and angular acceleration vectors are aligned with Z-axis.
The MPO true anomaly has been expanded up to second order in eccentricity. Their magnitude has been estimated to amount at 80% A0 for periodic errors and 60% S0 for random errors. We have to underline that these contributions to the error budget come only from those spurious signals which cannot be reliably removed a posteriori from the accelerometer measurements. The signal of interest is much larger; for an appropriate functioning of the accelerometer, it needs only not to exceed the dynamic range of the instrument. 6 The Gauss reference axes are defined with respect to the spacecraft orbit osculating ellipse. The three axes of this orthogonal reference frame, usually termed R, W and T, are radial, normal to the orbital plane and transversal in the orbital plane, respectively. See for example Bertotti et al. (2003).
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Table 4 Error budget: random part. Type
Due to
Spectral content
Requirement on
Error (% S0 )
Apparent forces
Error in MPO attitude knowledge
Random
60
Thermal effects MPO structural vibrations
ISA thermal sensitivity Reaction wheels, MPO mechanisms, etc. COM displacement due to the HGA movements, fuel consumption, etc. Axes misalignment and crosstalk
Random Random
MPO AOCS performance and MPO COM position MPO thermal noise
MPO rigid body motion removal residual Components coupling ISA intrinsic noise
Random
MPO COM displacements knowledge Random component of misalignment angle
Random Random
(1) Misalignments of sensing axes with respect to the inertial reference frame with periodicity at orbital period (as those related to thermoelastic distortions). (2) Misalignments of sensing axes with respect to the inertial reference frame having a random noise behaviour (as those related to structural vibrations). (3) Internal crosstalk of sensing elements causing an effect with the same frequency content of input signal, as that related to mechanical tolerances. (4) Internal crosstalk of sensing elements having a random noise behaviour, as that related to out of band noise. These effects cause essentially a mixing of the sought—for signal components, which must be avoided. Finally, the contribution of the instrument intrinsic noise must be considered in the error budget. This noise, coming from the internal parts of the accelerometer (mechanical elements, electronics) is random and has been fixed to 10% S0 . This value is consistent with experimental measurements of ISA noise level done in a differential configuration (see Section 3.1). The error budget as shown here is fundamentally based on a ‘‘standard’’ concept of radio science procedure, in which the spacecraft equation of motion is referred to its COM, and the various measurements involved in the procedure (range and range-rate, acceleration) are to be corrected accordingly. This referencing (as seen in Section 2.3 for accelerometric data) introduces an error in the data ‘‘pre-processing’’ and a consequent bias in the parameter estimation procedure, and ultimately
70 10 10 o100
Total (not correlated noise)
Thermal variations at the spacecraft/instrument interface will cause a spurious signal on the accelerometer output. The most sensitive part of the instrument (sensing head mechanics) has a thermal sensitivity of 5 107 m=s2 = C. This means that a temperature variation of 1 1C gives a spurious acceleration signal equal to 5 107 m=s2 . Taking into account the maximum foreseen temperature variation inside the instrument bandwidth (2 1C peak, at the MPO orbital period around Mercury) and the attenuation factor of 700, a value of 15% A0 is obtained. A similar pffiffiffiffiffiffiffi calculation for the random part, with a thermal noise of 4 C= Hz, gives a value of 30% S0 . The accelerometer is also subject to inertial accelerations related to the linear (rigid body) motion of the MPO (due to change in its configuration and then to its COM displacement). It is considered to perform their removal during data analysis: then the error considered in the error budget is related to the removal residual. The assigned share is of 70% S0 . In Tables 3 and 4 ‘‘component coupling’’ indicates the error in ISA measurements caused by the following four different effects:
30 10
implies very strict requirements on the spacecraft/instrument interface. In order to overcome these problems, a new concept of radio science procedure has been recently introduced, in which the equation of motion is referred to the accelerometer position (more precisely, to the reference point of the accelerometer itself). In this new procedure, the proof mass whose motion is tracked is—at least ideally—one of the three proof masses of the accelerometer. Using the new concept the requirements coming from the abovepresented error budget are much less demanding and easy to match.
5. Calibration For ‘‘calibration’’ we mean a series of measurements that define all the instrument characteristics, in all the phases and operative conditions. This implies a complete set of tests and procedures. The main tests to perform for the ISA characterization are:
transfer function; transducer factor; linearity of response; intrinsic noise; thermal stability.
These are planned on ground and some of them will be repeated in the various phases of the mission, to verify that the instrument works properly, with the declared performance. Calibrations in the strict meaning, i.e., calibrations of the transducer factor (relating the output of the capacitive bridge to the measured acceleration), are planned throughout the entire mission. The transducer factor measurement is strictly related to the quality of the final data product, and various strategies have been studied to perform its measure. The baseline is to use the ISA actuators to give each proof mass a known (electric) acceleration, and then obtain the transducer factor. Another (backup) possibility is to perform some MPO manoeuvres at selected times and by a precise knowledge of the spacecraft attitude (given by the AOCS) calculate the corresponding acceleration on each sensing element and then again the transducer factor. A further opportunity will be available during the Superior Conjunction Experiment (SCE) during cruise (see Iess, 2009). In that phase of the mission the Mercury Composite Spacecraft (MCS) will travel in a relatively stable dynamical environment (far from the Sun and with constant attitude) in such a way that the non-gravitational perturbations acting on the MCS will be nearly constant; high-
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precision tracking will also be performed. The comparison of accelerometer with tracking data will enable at least in principle a calibration of the accelerometer.
6. Conclusions The BepiColombo mission will give the scientific community an opportunity for studying in detail the planet Mercury and its environment; in particular, the important scientific objectives of the RSE will be achievable using a dedicated set of instrumentation. The standard procedure of precise orbit determination and parameter estimation (in order to recover the geophysical and PPN parameters) will be augmented and enriched by an on-board accelerometer, ISA, for the direct measurement of the nongravitational accelerations acting on the spacecraft, which—in the case of BepiColombo MPO—are particularly strong and difficult to model precisely. The instrument itself comes from a long research activity in fundamental physics and geophysics; its high sensitivity and low intrinsic noise make possible to ‘‘filter out’’ the strong ‘‘noise’’ of non-gravitational perturbations. With BepiColombo it will be the first time an accelerometer will fly on a deep-space mission, opening a new field of possibilities for fundamental physics studies.
Acknowledgements The authors wish to thank Roberto Formaro (ISA Program Manager, Agenzia Spaziale Italiana), Thales Alenia Space and the two referees.
References Anderson, J.D., Laing, P.A., Lau, E.L., Liu, A.S., Nieto, M.M., Turyshev, S.G., 1998. Indication, from Pioneer 10/11, Galileo, and Ulysses data, of an apparent anomalous, weak, long-range acceleration. Phys. Rev. Lett. 81, 2858–2861. Anderson, J.D., Laing, P.A., Lau, E.L., Liu, A.S., Nieto, M.M., Turyshev, S.G., 2002. Study of the anomalous acceleration of Pioneer 10 and 11. Phys. Rev. D 65 (8), 082004. Bertotti, B., Farinella, P., Vokrouhlicky´, D., Physics of the solar system—dynamics and evolution, space physics, and spacetime structure. Astrophysics and Space Science Library, vol. 293. Kluwer Academic Publishers, Dordrecht. Fro¨hlich, C., 2000. Observations of irradiance variations. Space Sci. Rev. 94, 15–24. Iafolla, V., Lucchesi, D.M., Nozzoli, S., Santoli, F., 2007. ISA accelerometer onboard the mercury planetary orbiter: error budget. Celestial Mech. Dyn. Astr. 97, 165–187. Iafolla, V., Nozzoli, S., 2001. Italian spring accelerometer (ISA) a high sensitive accelerometer for ‘‘BepiColombo’’ ESA CORNERSTONE. Planet. Space Sci. 49, 1609–1617. Iess, L.e.a., 2009. MORE: geodesy, geophysics and relativity with BepiColombo, in preparation. Lucchesi, D.M., Iafolla, V., 2006. The non-gravitational perturbations impact on the BepiColombo radio science experiment and the key role of the ISA accelerometer: direct solar radiation and albedo effects. Celestial Mech. Dyn. Astr. 96, 99–127. Milani, A., Nobili, A.M., Farinella, P., 1987. Non-gravitational Perturbations and Satellite Geodesy. Adam Hilger, Bristol. Milani, A., Rossi, A., Vokrouhlicky´, D., Villani, D., Bonanno, C., 2001. Gravity field and rotation state of mercury from the BepiColombo radio science experiments. Planet. Space Sci. 49, 1579–1596. Milani, A., Vokrouhlicky´, D., Villani, D., Bonanno, C., Rossi, A., 2002. Testing general relativity with the BepiColombo radio science experiment. Phys. Rev. D 66 (8), 082001. van Casteren, J., Novara, M., Best, R., Hayakawa, H., Ferri, P., 2009. The BepiColombo mission, Planet. Space Sci., submitted for publication. van den Ijssel, J., Visser, P., 2007. Performance of GPS-based accelerometry: CHAMP and GRACE. Adv. Space Res. 39, 1597–1603.
