Full text: International cooperation and technology transfer

21 
The Spacewise Approach to the Data Treatment for the 
SAGE Mission Project 
A.Albertella, F.Migliaccio, F.Sansó 
Dip. IIAR, Sez. Rilevamento, Politecnico di Milano, Milano, Italy 
ABSTRACT: 
After a call for proposals for small satellite missions from the Italian Space Agency (ASI), a group of Italian 
research teams and industries led by the Politecnico di Milano proposed the concept of SAGE, a mission aimed 
at determining the gravity field of the Earth by means of high-low SST, which means that the satellite orbit is 
determined by GPS, while the non-gravitational perturbations are determined by a three-axes accelerometer. 
This is basically the same concept of the CHAMP mission [Reigber et al., 1996]. SAGE underwent a Phase A 
Study during the year 1998 [ASI, 1998]. In this framework, the task of the Politecnico di Milano group was to 
analyze the data by means of the spacewise approach. The complete spacewise approach, besides studying new 
simulations of the data to be expected from SAGE, requires to perform the inversion of Hill’s equations, to form 
average values on a regular grid over the sphere and to recover the gravity field coefficients. The simulations are 
requested in order to: assess the accuracy of the data obtained after the inversion of Hill’s equations introducing 
a realistic measurement noise; formulate the overdetermined boundary value problem to be solved; determine 
indices enabling to evaluate the performances of the solution. 
1 The concept of space ac- 
celerometry 
The proposal of the mission SAGE (Satellite Ac- 
celerometry by Gravity field Exploration) consisted in 
using a GPS receiver together with an accelerometer on 
a low, polar orbit satellite. The accelerometer proof- 
mass, positioned in the centre of mass of the satellite, is 
subject to a purely gravitational acceleration g, while 
the centre of mass of the satellite is subject (besides the 
same acceleration g) also to all non-gravitational forces 
which act on the surface, whose sum is /. Therefore 
the accelerometer gives a direct measure of /. 
The GPS tracking (aided by a SLR device) allows to 
reconstruct (with very high relative precision between 
two points along an orbit arc) the satellite trajectory 
x(t). The difference between the “observed” orbit x(t) 
and the orbit x(t) modelled by all available information 
is due to the residual gravitational effects: 
£(*) = x{t) - x(t) (1) 
where £(£) is the orbit anomaly, equivalent to a “virtu 
al” orbit ruled by the residual gravitational potential. 
From £(£) it is possible, by differencing and smooth 
ing, to obtain observed values of g along the orbit, 
which can be integrated to give the harmonic coeffi 
cients of the field, in the framework of an overdeter- 
mined boundary value problem. 
In particular, we write the equation of motion of the 
satellite as [Bassanino et al., 1992] 
x — VuoGD + V<5it(r) + (x) + / (x) (2) 
considering the gravitational potential u(x) as the sum 
of a reference potential uo(x) and a residual part du(x). 
In this equation f g (x) represents the effects of the sun, 
moon and tides (which can be modelled) and / (®) 
represents the effect of the surface forces (mainly due 
to the drag, which is measured by the accelerometer). 
It must be remarked that f g and f ng can be computed 
along the nominal orbit without significant errors. 
The residual gravitational effects 5g along the orbit 
can be obtained by inverting Hill’s equations, which 
are written here under the hypotheses that £ is small 
and that the orbit arc is circular: 
Ca +2u£ r = Sg a 
ir -2w{ a -3u 2 ( r = <5g r (3) 
L +w 2 fo = Sg„ 
The indices a, r, o respectively denote the along track, 
radial and orthogonal (out of plane) component. 
This system is inadequate to produce realistic orbit 
ephemerides; nevertheless it is useful because it can 
certainly be used to produce simulations, to under 
stand how well (3) can be inverted. The general so 
lution of (3) can be written as 
¿(i)=ifc(t)+S p (i) (4)
	        
Waiting...

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.