Time series versus argument of latitude
GOCE Aerodynamic Torque Modeling
T. Visser, E.N. Doornbos, C.C. de Visser, P.N.A.M. Visser
Faculty of Aerospace Engineering, Delft University of Technology, Delft, The Netherlands
B. Fritsche
Hyperschall Technologie Göttingen GmbH, Katlenburg-Lindau, Germany
·10−5
5
270
0
180
90
Torque [Nm]
Argument of latitude [deg]
360
−5
0
10/16
10/17
10/18
10/19
10:19
Date [mm/dd]
(a) T̄ roll
·10−4
6
4
270
2
0
180
−2
90
Torque [Nm]
Argument of latitude [deg]
360
−4
−6
0
10/16
10/17
10/18
10/19
10:19
Date [mm/dd]
(b) T̄ pitch
·10−4
5
270
180
0
90
−5
0
10/16
10/17
10/18
10/19
10:19
Date [mm/dd]
(c) T̄ yaw
Figure 1: Total modeled torque T̄ as a function of time and argument of latitude in 2013.
1
Torque [Nm]
Argument of latitude [deg]
360
·10−5
4
270
2
180
0
Torque [Nm]
Argument of latitude [deg]
360
−2
90
0
10/16
−4
10/17
10/18
10/19
10:19
Date [mm/dd]
(a) T roll
Argument of latitude [deg]
270
2
180
0
90
Torque [Nm]
·10−4
360
−2
0
10/16
10/17
10/18
10/19
10:19
Date [mm/dd]
(b) T pitch
Argument of latitude [deg]
270
5
180
0
90
−5
0
10/16
10/17
10/18
10/19
10:19
Date [mm/dd]
(c) T yaw
Figure 2: Measured torque T as a function of time and argument of latitude in 2013.
2
Torque [Nm]
·10−4
360
Argument of latitude [deg]
270
2
180
0
90
0
10/16
Torque [Nm]
·10−5
360
−2
10/17
10/18
10/19
10:19
Date [mm/dd]
(a) T̄ +T̂D,P roll
Argument of latitude [deg]
270
2
180
0
90
0
10/16
Torque [Nm]
·10−4
360
−2
10/17
10/18
10/19
10:19
Date [mm/dd]
(b) T̄ +T̂D,P pitch
·10−4
5
270
0
180
90
0
10/16
Torque [Nm]
Argument of latitude [deg]
360
−5
10/17
10/18
10/19
10:19
Date [mm/dd]
(c) T̄ +T̂D,P yaw
Figure 3: Total modeled torque T̄ , and fitted payload dipole torque T̂D,P as a function of time and argument of
latitude in 2013.
3
·10−5
360
270
2
0
180
Torque [Nm]
Argument of latitude [deg]
4
−2
90
−4
0
10/16
10/17
10/18
10/19
10:19
Date [mm/dd]
(a) T̄C roll
·10−4
5
270
0
180
Torque [Nm]
Argument of latitude [deg]
360
90
−5
0
10/16
10/17
10/18
10/19
10:19
Date [mm/dd]
(b) T̄C pitch
·10−4
2
270
1
180
0
−1
90
−2
0
10/16
10/17
10/18
10/19
10:19
Date [mm/dd]
(c) T̄C yaw
Figure 4: Magentic control torque T̄C as a function of time and argument of latitude in 2013.
4
Torque [Nm]
Argument of latitude [deg]
360
·10−4
1
270
0.5
180
0
−0.5
90
0
10/16
Torque [Nm]
Argument of latitude [deg]
360
−1
10/17
10/18
10/19
10:19
Date [mm/dd]
(a) T̄D,B roll
·10−4
2
270
180
0
90
0
10/16
Torque [Nm]
Argument of latitude [deg]
360
−2
10/17
10/18
10/19
10:19
Date [mm/dd]
(b) T̄D,B pitch
Argument of latitude [deg]
270
5
180
0
−5
90
0
10/16
10/17
10/18
10/19
10:19
Date [mm/dd]
(c) T̄D,B yaw
Figure 5: Residual bus dipole torque T̄D,B as a function of time and argument of latitude in 2013.
5
Torque [Nm]
·10−5
360
·10−5
6
4
270
2
180
0
−2
Torque [Nm]
Argument of latitude [deg]
360
90
−4
0
10/16
−6
10/17
10/18
10/19
10:19
Date [mm/dd]
(a) T̂D,P roll
·10−4
4
270
2
180
0
−2
90
0
10/16
Torque [Nm]
Argument of latitude [deg]
360
10/17
10/18
10/19
10:19
−4
Date [mm/dd]
(b) T̂D,P pitch
·10−4
360
270
0.5
180
0
−0.5
90
−1
0
10/16
Torque [Nm]
Argument of latitude [deg]
1
10/17
10/18
10/19
10:19
Date [mm/dd]
(c) T̂D,P yaw
Figure 6: Fitted payload dipole torque T̂D,P as a function of time and argument of latitude in 2013.
6
Argument of latitude [deg]
270
2
180
0
90
0
10/16
Torque [Nm]
·10−6
360
−2
10/17
10/18
10/19
10:19
Date [mm/dd]
(a) T̄T roll
Argument of latitude [deg]
270
1
180
0
90
0
10/16
Torque [Nm]
·10−5
360
−1
10/17
10/18
10/19
10:19
Date [mm/dd]
(b) T̄T pitch
·10−4
1
270
0.5
180
0
−0.5
90
0
10/16
Torque [Nm]
Argument of latitude [deg]
360
−1
10/17
10/18
10/19
10:19
Date [mm/dd]
(c) T̄T yaw
Figure 7: Thruster misalignment torque T̄T as a function of time and argument of latitude in 2013.
7
Argument of latitude [deg]
270
2
180
0
90
0
10/16
Torque [Nm]
·10−6
360
−2
10/17
10/18
10/19
10:19
Date [mm/dd]
(a) T̄S roll
·10−6
5
270
180
0
90
0
10/16
Torque [Nm]
Argument of latitude [deg]
360
−5
10/17
10/18
10/19
10:19
Date [mm/dd]
(b) T̄S pitch
·10−5
2
270
1
180
0
−1
90
0
10/16
−2
10/17
10/18
10/19
10:19
Date [mm/dd]
(c) T̄S yaw
Figure 8: Solar radiation pressure torque T̄S as a function of time and argument of latitude in 2013.
8
Torque [Nm]
Argument of latitude [deg]
360
Argument of latitude [deg]
270
5
180
0
90
0
10/16
Torque [Nm]
·10−6
360
−5
10/17
10/18
10/19
10:19
Date [mm/dd]
(a) T̄D,T roll
·10−4
2
270
1
180
0
−1
Torque [Nm]
Argument of latitude [deg]
360
90
−2
0
10/16
10/17
10/18
10/19
10:19
Date [mm/dd]
(b) T̄D,T pitch
·10−5
6
4
270
2
180
0
−2
90
−4
0
10/16
−6
10/17
10/18
10/19
10:19
Date [mm/dd]
(c) T̄D,T yaw
Figure 9: Thruster dipole torque T̄D,T as a function of time and argument of latitude in 2013.
9
Torque [Nm]
Argument of latitude [deg]
360
Argument of latitude [deg]
270
5
180
0
−5
90
0
10/16
Torque [Nm]
·10−6
360
10/17
10/18
10/19
10:19
Date [mm/dd]
(a) T̄G roll
·10−4
1
270
180
0
90
0
10/16
Torque [Nm]
Argument of latitude [deg]
360
−1
10/17
10/18
10/19
10:19
Date [mm/dd]
(b) T̄G pitch
·10−6
4
270
2
180
0
−2
90
−4
0
10/16
10/17
10/18
10/19
10:19
Date [mm/dd]
(c) T̄G yaw
Figure 10: Gravity gradient torque T̄G as a function of time and argument of latitude in 2013.
10
Torque [Nm]
Argument of latitude [deg]
360
·10−6
5
270
0
180
90
0
10/16
Torque [Nm]
Argument of latitude [deg]
360
−5
10/17
10/18
10/19
10:19
Date [mm/dd]
(a) T̄A roll
·10−5
360
270
2
0
180
−2
Torque [Nm]
Argument of latitude [deg]
4
90
−4
0
10/16
10/17
10/18
10/19
10:19
Date [mm/dd]
(b) T̄A pitch
·10−4
5
270
180
0
90
0
10/16
−5
10/17
10/18
10/19
10:19
Date [mm/dd]
(c) T̄A yaw
Figure 11: Aerodynamic torque T̄A as a function of time and argument of latitude in 2013.
11
Torque [Nm]
Argument of latitude [deg]
360
·10−5
2
270
1
180
0
−1
90
0
10/16
Torque [Nm]
Argument of latitude [deg]
360
−2
10/17
10/18
10/19
10:19
Date [mm/dd]
(a) T -(T̄ +T̂D,P -T̄A ) roll
·10−4
2
270
1
180
0
−1
90
0
10/16
Torque [Nm]
Argument of latitude [deg]
360
−2
10/17
10/18
10/19
10:19
Date [mm/dd]
(b) T -(T̄ +T̂D,P -T̄A ) pitch
·10−3
1
270
0.5
180
0
−0.5
90
0
10/16
Torque [Nm]
Argument of latitude [deg]
360
10/17
10/18
10/19
10:19
−1
Date [mm/dd]
(c) T -(T̄ +T̂D,P -T̄A ) yaw
Figure 12: Measured torque T , total modeled torque T̄ , fitted payload dipole torque T̂D,P , and aerodynamic torque
T̄A as a function of time and argument of latitude in 2013.
12