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CHAMP
Satellite Gravity Field Determination
Satellite geodesy
Eva Howe
January 12 2006
CHAMP
CHAMP
Weight 522 kg
Length 8,3 m
Launched July 2000
Near circular orbit
Initial altitude 454km
Inclination i=87.3º
January 12 2006 Satellite geodesy Eva Howe | Page 2
CHAMP
January 12 2006 Satellite geodesy Eva Howe | Page 3
CHAMP
STAR accelerometer
Measurement bandwidth 10-4 - 10-1 Hz
Linear accelerations:
Measurement range ± 10-4 ms-2
Resolution:
< 3 × 10-9 ms-2 (y- and z-axis)
< 3 × 10-8 ms-2 (x-axis)
January 12 2006 Satellite geodesy Eva Howe | Page 4
A proof mass is floating freely
inside a cage supported by an
electrostatic suspension.
Electrodes inside the cage is
controlling the motion of the
test-mass.
The force needed is proportional
to the detected acceleration.
CHAMP
Expected accuracy:
A geoid with accuracy of cm with a resolution of
L=650 km (degree and order 30)
Achieved accuracy:
A geoid with accuracy of 5 cm.
A gravity field model with accuracy of 0.5 mGal.
Both with a resolution of 400 km (degree and
order 50).
January 12 2006 Satellite geodesy Eva Howe | Page 5
Energy conservation
The Energy conservation Method
The general energy law: The sum of all energy in an isolated
system is constant
Ekin  E pot  Fouter
Where Fouter represents the non-conservative outer forces.
The gravitational potential V can be related to the kinetic
energy Ekin of the satellite minus the energy loss.
January 12 2006 Satellite geodesy Eva Howe | Page 6
Energy conservation
Gravity field determination by Energy
conservation
From the state vector (x, y, z, vx, vy, vz) and the
accelerometer data (ax, ay, az) from CHAMP a model of the
gravity field of the Earth can be estimated by energy
conservation.
Data from the period July 2002 – June 2003 are used.
January 12 2006 Satellite geodesy Eva Howe | Page 7
Energy conservation
The outer forces must be considered:
Tidal effects from the other planets -consider only the Sun and
•Moon
Energy loss due to atmospheric drag, sun pressure, thermal
•forces
and cross winds -consider only the air drag in the solutions
•Rotation of the potential in the inertial frame
Earth normal potential is subtracted and the sum of all the
integration constants.
From this you get the anomalous potential.
January 12 2006 Satellite geodesy Eva Howe | Page 8
Energy conservation
T 
1 2
v  Vsun  Vmoon   ( xvy  yv x )  F  E0  U
2
Vsun 
F 
where
U
E0
ω
µ
AU
r
Φ
g sunr
,
2
 
v
  adt ,
g sun 
F 

M sunr
AU 3
(3 cos 2   1)

v a y dt
Normal potential of the Earth
Integration constant
Angular velocity 7.292115*10-5 s-1
GM
Astronomical unit
Distance from the satellite to the centre of the Earth
Zenith angle of the Sun
January 12 2006 Satellite geodesy Eva Howe | Page 9
Energy conservation
Chosen only to use the along-track
component of the acceleration vector
(ay)
The accelerometer suffer from bias
and scale factor.
Determined a scale factor for each half
day (recommendations are for every
revolution) by correlating the friction
with the difference between the
calculated potential and an a priori
model.
January 12 2006 Satellite geodesy Eva Howe | Page 10
Data processing
Acceleration
vector
state
vector
Mean
pole
coordinates
EGM96
to
degree
24
readacc
Reformat of
accelerations
stat2pot
Calculation of
anomalous
potential
sphgric
Estimation of
coefficients
GEOCOL
Removal of
reference field
Up-/downward
continuation
FSC
correl
Estimate scale
factor subtract
friction
January 12 2006 Satellite geodesy Eva Howe | Page 11
Type of
solution
LSC
GEOCOL
Estimation of
coefficients
GEOGRID
Gridding of
data
Data processing
How do we represent the gravity field?
- by spherical harmonic coefficients!
1 2 
anm    T  ,   cosm Pnm cos sin  dd
4  0  0
1 2 
bnm    T  ,  sin m Pnm cos sin  dd
4  0  0
From these we can get for instance the anomalous potential
T  ,     anm cosm   bnm sin m Pnm cos 

n
n 0 m 0
January 12 2006 Satellite geodesy Eva Howe | Page 12
Results
Geoid heights of UCPH2004 [m]
January 12 2006 Satellite geodesy Eva Howe | Page 13
Results
Gravity anomalies of UCPH2004 [mGal]
January 12 2006 Satellite geodesy Eva Howe | Page 14
Gravity missions
January 12 2006 Satellite geodesy Eva Howe | Page 15