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less at the same altitude for at least two years, 
allowing for a reciprocal (indirect) calibration of the 
two instruments, which are based on different 
technologies. 
The relation to the other two gravity missions, GRACE 
and GOCE, is the same as that of CHAMP (namely, 
SAGE works on medium-high wavelengths, increasing 
the accuracy of the estimated coefficients), but 
strengthened by the fact that CHAMP and SAGE 
together can provide a highly reliable and dense data 
set at an average altitude of 400 km. 
In case SAGE should fly polar, it could also reach the 
important aim of filling the “polar gaps”, which are 
normally not avoided by similar missions. 
2. INSTRUMENTS 
The main instruments designed to constitute the 
payload of SAGE are made after Italian technology. 
The ISA accelerometer has been developed at the IFSI 
Institute (Istituto di Fisica dello Spazio Interplanetary) 
of the CNR (National Research Council) . This 
accelerometer has been designed to be the 
fundamental element of a space-borne, room 
temperature, gravity gradiometer having a sensitivity of 
10' 2 EU/VSz. In this case the accelerometers must 
have a sensitivity of 5 10‘ 13 g/*JHz . Even if this target 
requires further effort, the sensitivity of 10 ■ 9 gI-Jhz. 
required for the SAGE experiment, has been reached at 
the present state of the art. A prototype of an 
accelerometer having sensitivity better than 10' 9 
g/Vtfz has been built and is operating in the 
underground laboratory of Gran Sasso (L’Aquila). The 
fundamental part of this equipment is a mechanical 
harmonic oscillator. Typical displacements of the 
oscillating proofmass due to accelerations of 10' 9 g are 
of the order of 2 10' 11 m. A capacitor transducer in a 
bridge configuration, followed by a low noise amplifier, 
provides the detection of the signal. 
Fig. 2 Prototype of the Italian Spring Accelerometer 
(ISA). 
Fig. 3 Power spectral density of the seismic noise 
measured at the Gran Sasso laboratory by the spring 
accelerometer ISA, at the level of 10 ‘ 9 gijHz. 
The Lagrange instrument is under development at 
Laben S.p.A. . This equipment has been designed as a 
GPS/GLONASS receiver to be used not only for 
navigation purposes but also for scientific objectives like 
Precise Orbit Determination (POD). The error of 
Lagrange is less than 1 mm at a sampling rate of 10 Hz. 
3. SCIENTIFIC OBJECTIVES OF THE MISSION 
To describe the overall scientific performance of the 
SAGE gravimetry mission we can use the maximum 
degree £ for which the error is larger than the signal; 
i.e., the RMS value of the error in the £2.£ + 1) 
coefficients with the same degree (and different order 
m) is larger than the RMS value of the coefficients 
themselves. For the error we use the square root of the 
formal variance of the determined coefficients, that is 
the standard error according to the Gaussian theory. 
This formal error, however, must also be compared with 
the systematic errors, in particular with those resulting 
from dynamic model errors and those resulting from 
coloured noise. This check has been performed with 
two different methods for the two different approaches 
used to treat the SAGE simulated data (timewise and 
spacewise) and it turns out that the systematic errors 
are not dominant for the timewise approach, while they 
can be significant for some noise models in the 
spacewise approach. 
The largest complete simulation we have performed 
has used six months of data with the timewise 
approach. The maximum degree £ max for which the 
signal exceeds the error has been found to be 62. If this 
result is extrapolated to a data span ten times longer, 
by using the Gaussian statistics which is well known to 
be applicable in this kind of simulations, then £ max can 
be estimated to be about 72. Taking also into account 
one year of extended mission, when SAGE should be 
orbiting at a lower altitude (about 360 km), the value of 
£ max could be as high as 74. 
The largest simulation with the spacewise approach has 
been performed with one year of data. The results of 
the spacewise treatment are similar to the ones of the 
timewise approach, if the noise is assumed to be white;