- Email: [email protected]
The accuracy of orbit estimation for the low-orbit satellites LARETS and WESTPAC
Advances in Space Research 36 (2005) 498–503 www.elsevier.com/locate/asr
The accuracy of orbit estimation for the low-orbit satellites LARETS and WESTPAC Milena Rutkowska
*
Space Research Centre, Polish Academy of Sciences, ul. Bartycka 18 A, 00-716, Warsaw, Poland Received 30 November 2004; received in revised form 4 April 2005; accepted 15 April 2005
Abstract The LARETS satellite was launched on September 26, 2004, into a circular orbit at an altitude of 690 km and with an inclination of 98.2°. This mission is a successor to the WESTPAC satellite which was launched to an altitude of 835 km six years before. The study is based on the observations taken by the global network of laser stations during the period from December 30, 2003 to March 17, 2004 for LARETS. This study is aimed at the precise orbit computation of LARETS. The experience acquired during the orbit estimation of WESTPAC was applied to the orbit investigation of LARETS. The WESTPAC was merely used for reference and initial parameters of the force model [Rutkowska, M., Noomenn, R., Global orbit analysis of the satellite WESTPAC, Adv. Space Res., 30(2), 265–270, 2002]. The orbit of LARETS was estimated with an rms-of-fit to the SLR measurements of 3.9 cm, using the following computation model: the CSR TEG-4 gravity field up to degree and order (200,200), the Ray tide model, the MSIS86 model for atmospheric density [Hedin, A.E., MSIS-86 Thermospheric Model, J. Geophys. Res., 92 (A5), 4649–4662, 1987], and the solution of 8-hourly CD-values. It has been verified that the modeling of the gravity field up to degree and order (100,100) which gives the same rms-of-fit value. Estimated orbits for both satellites are compared to each other in Fig. 2. All computations are performed with the NASA program GEODYN II [Eddy, W.F, McCarthy, J.J., Pavlis, D.E., Marshall, J.A., Luthce, S.B., Tsaoussi, L.S., GEODYN II System Operations Manual, vol. 1–5, ST System Corp., Lanham MD, USA, 1990]. Ó 2005 Published by Elsevier Ltd on behalf of COSPAR. Keywords: Satellite orbit; Low-orbit satellites; LARETS; WESTPAC
1. Introduction The aim of this study is the computation of the orbit of the satellite LARETS with the highest accuracy possible. The satellite LARETS is very similar to WESTPAC (Shargorodsky, 1997) and both are designed to address scientific and applied problems in the areas of geodesy and geodynamics. The orbits of low flying satellites are strongly influenced by perturbing forces such as: the gravity field, atmospheric drag, solid earth and ocean tides. To obtain a high-quality orbit solution, the perturbing forces need to be modelled as accurately *
Tel.: +48 22 840 37 66; fax: +48 22 840 3131. E-mail address: [email protected].
0273-1177/$30 Ó 2005 Published by Elsevier Ltd on behalf of COSPAR. doi:10.1016/j.asr.2005.04.063
as possible. This paper discusses the influence of the modelling of different physical effects on the motion of LARETS, in particular in terms of orbit quality. A brief description of the characteristic parameters of WESTPAC and LARETS is given in Table 1. Both satellites are spherical and have an inclination equal to 98°, but altitude of LARETS is significantly smaller (about 160 km). Both satellites are shown in Fig. 1.
2. Analysis method The study is based on the observations taken by the global network of laser stations during the period from December 30, 2003 to March 17, 2004. Three-month
M. Rutkowska / Advances in Space Research 36 (2005) 498–503
499
Fig. 1. The satellites WESTPAC (left) and LARETS (right).
Table 1 The characteristic parameters of LARETS and WESTPAC
Launch date COSPAR id. Weight Altitude Inclination COM correction
WESTPAC
LARETS
July 07, 1998 9804301 23.28 kg 850 km 98.7° 6.28 cm
September 27, 2003 0304206 23.28 kg 690 km 98.2° 5.62 cm
period of measurements (4431 normal points) was divided into 12 7.5-day arcs with half day overlaps between successive arcs. An overview of the normal points obtained on LARETS by the laser stations is given in Table 2. The average number of normal points for each arc is 370. A detailed investigation of the orbit estimation of the WESTPAC is described in (Rutkowska and Noomenn,
Table 2 Overview of SLR stations and number of normal points to LARETS satellites No. Name
No. of station Number of n.p.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1884 7080 7090 7105 7110 7210 7237 7501 7811 7832 7836 7837 7838 7839 7840 8834
Riga, Latvia Fort Davis, USA Yarragadee, Australia Washington, USA Monument Peak, USA Maui, USA Changchun, China Hartebeesthoek, South Africa Borowiec, Poland Riyadh, Saudi Arabia Potsdam, Germany Shanghai, China Simosato, Japan Graz, Austria Herstmonceux, UK Wettzell, Germany
The coordinates of stations are fixed.
52 13 1421 200 400 247 229 21 46 246 93 84 407 505 423 132
2002). The experience acquired during the orbit estimation of WESTPAC was applied to the orbit investigation of LARETS. In this study three test cases were analyzed: 1. The best computation model derived for WESTPAC (Rutkowska and Noomenn, 2002), gravity field GRGS/GFZ GRIM-5S1(99,99) (Biancale and Schwintzer, 2000), atmospheric density MSIS 86 with CD solved for half-day intervals used for LARETS. 2. The computation model which uses the: gravity field GRIM5-S1(99,99) and the atmospheric density model MSIS 86 with CD solved for the 8-h intervals.
Table 3 Description of the force model used for the LARETS orbit computations Dynamic model
GRIM5-S1 (99,99) or Teg4 (200,200) gravity field Wahr solid earth tides, NASA/GSFC Ray ocean tides Atmospheric drag (MSIS 86 for density), CD solved for in half-day or 8-h intervals Direct solar radiation pressure, CR solved for in 7.5day intervals 3rd body attraction (Sun, Moon, Venus, Mars, Jupiter, Saturn) Albedo, Pole tide, Relativistic effects Empirical 1-cpr accelerations in along-track and crosstrack directions
Reference frame
ITRF2000 station positions at epoch 1997.0 Pole tide Precesion according to IAU 1976 (Lieske model) Nutation according to IAU 1980 (Wahr model) Love model for tidal uplift Ocean loading applied
Measurement model
15 s normal points provided by CDDIS and EDC Marini-Murray model for tropospheric delay Center-of-mass offset (5.62 cm) Station-dependent data weighted
Integration
Cowell 11th-order predictor-corrector, step-size 15 s
500
M. Rutkowska / Advances in Space Research 36 (2005) 498–503
3. The computation model which uses the CSR gravity field TEG-4(200,200) (Tapley, 2002) and the atmospheric density model MSIS 86 with CD solved for the 8-h intervals.
Table 4 Estimated rms values for three test cases and for 7.5-day orbital arcs No. of 7-day arc
No. of normal points
GRIM5-S1 CD-12 h int. rms (cm)
GRIM5-S1 CD-8 h int rms (cm)
Teg4 (200,200) CD-8 h int. rms (cm)
The parameters and computation model describing all forces acting on the satellite, are given in Table 3.
1 2 3 4 5 6 7 8 9 10 11 12
224 356 552 445 415 352 298 305 306 328 429 421
6.63 7.47 7.69 7.37 7.66 6.66 5.66 6.68 6.52 5.80 8.88 7.76
6.21 7.17 7.14 6.98 7.11 6.31 5.30 6.33 6.09 5.52 8.08 7.23
2.89 4.05 4.41 4.06 4.36 3.59 3.41 3.91 4.11 4.28 4.75 3.89
Average
370
7.05
6.61
3.97
3. Results The following unknowns were estimated in each solution: The satellite state vector for each 7.5-day arc. Drag coefficients CD, solar radiation pressure scaling parameters CR. Empirical satellite accelerations in different directions.
intervals. It has been verified that the modeling of the gravity field up to degree and order (100,100) which gives the same rms-of-fit value. The estimated rms-offit for each arc separately are shown in Table 4. The average rms-of-fit value is equal to 3.97 cm for case 3. Generally, it can be concluded that the best solution obtained here for LARETS is for case 3. The two examples of residuals for the best solution are shown in Figs. 3 and 4. The frequency of solving parameters CD (atmospheric drag) and CR (direct solar radiation pressure) have a big influence on the accuracy of orbit determination. The changes of the solved CD parameters for the half-day intervals by the 8-h intervals is a reason of diminish of rms-of-fit about 0.44 cm for each arc separately. The estimated CD (for 8-h intervals) and CR one for each arc values for the best solution are shown in Figs. 5 and 6, respectively.
An overview of the results which have been obtained for each scenario is given in Fig. 2. As a reference, the dashed line represents the average value of the rms-of-fit equal to 3.6 cm for WESTPAC (the force model is given in Table 3). The solid black diamonds represent the estimated rms values for LARETS in this case 1 (Fig. 2). The average value of rms-of-fit is equal to 7.05 cm. The plot with white diamonds (case 2) represents rms values solved for 8-h intervals. The change of solving CD parameters from half-day intervals to 8-h intervals is the reason for the reduction of the rms-of-fit by about 0.44 cm. The plot with black triangles (case 3) represents rms values for LARETS obtained with the gravity field model TEG-4 up to degree and order (200,200) and atmospheric density model MSIS 86 with CD solved for 8-h
9.00
rms (cm) 8.00 7.00 6.00 5.00 4.00 3.00 average rms for WESTPAC LARETS case 1
2.00
LARETS case 2
1.00
LARETS case 3
number of arc
0.00 1
2
3
4
5
6
7
8
9
10
Fig. 2. The rms values for LARETS for the total 3-month interval.
11
12
M. Rutkowska / Advances in Space Research 36 (2005) 498–503
501
0.12
(m)
0.10
RESIDUALS 2003.12.30- 2004.01.06
0.08 0.06 0.04 0.02 0.00 –0.02 –0.04 –0.06 –0.08 –0.10
no. of obs.
–0.12 0
20
40
60
80
100
120
140
160
180
200
220
Fig. 3. Residuals for 7.5-day arc (example 1).
0.12
(m)
0.10
RESIDUALS 2004.02.10- 2004.02.17.5
0.08 0.06 0.04 0.02 0.00 -0.02 -0.04 -0.06 -0.08 -0.10
no. of obs.
-0.12 0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
Fig. 4. Residuals for 7.5-day arc (example 2).
3.00 2.80 2.60 2.40 2.20 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00
Estimated Cd coefficients
0
no. of coefficient 0
20
40
60
80
100
120
140
160
180
200
220
Fig. 5. The atmospheric drag coefficients CD estimated for LARETS (case 3).
240
260
502
M. Rutkowska / Advances in Space Research 36 (2005) 498–503 1.80 1.60
Estimated Cr coefficients
1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00
no. of coefficient
-0.20 0
1
2
3
4
5
6
7
8
9
10
11
12
Fig. 6. The radiation pressure coefficients CR estimated for LARETS (case 3).
0.60
(m)
Overlap for 2004.02.17 radial
0.40
along track cross track
0.20
0.00
-0.20
minutes
-0.40 0
60
120
180
240
300
360
420
480
540
600
660
720
Fig. 7. The 12-h overlap for estate orbital arcs for radial, along track and cross track directions (example 1). 0.60
Overlap for 2004.03.02
(m)
radial
0.40
along track cross track
0.20
0.00
-0.20
minutes -0.40 0
60
120
180
240
300
360
420
480
540
600
660
720
Fig. 8. The 12-h overlap for estate orbital arcs for radial, along track and cross track directions (example 2).
M. Rutkowska / Advances in Space Research 36 (2005) 498–503
For LARETS (case 3), 12 successive data arcs were solved, of 7.5-day length each and with 12-h overlaps. In addition to the rms-of-fit, these overlaps can be used to evaluate the quality of the orbit solutions as well. Two examples of such overlaps, the plots in radial, along-track and cross-track directions are shown in Figs. 7 and 8. The differences between successive arcs in radial direction are about 3–5 cm, for cross-track direction about 12–16 cm. For along-track direction differences systematically increase.
503
This best scenario includes the CSR TEG-4 gravity field model up to degree and order (200,200), the Ray tides model, the MSIS 86 model for atmospheric density, and the solution of 8-hourly CD-values, and one pressure scaling parameter for arc CR.
Acknowledgement The author wants to thank the International Laser Ranging Service for providing the SLR data on the WESTPAC and LARETS satellites.
4. Conclusions Based on analysis of 3 months of SLR observations of the LARETS satellite, the following conclusions can be drawn: A best computation model has been developed according to which the orbit of LARETS can be computed with an rms-of-fit of SLR measurements of 3.9 cm. The accuracy of the orbit itself is estimated at 5 and 15 cm in radial and cross-track directions, respectively.
References Biancale, R., Schwintzer, P., The GRIM5-S2/C2 Earth Gravity Field Models, paper presented at the EGS XXV General Assembly, Nice, France, 2000. Rutkowska, M., Noomenn, R. Global orbit analysis of the satellite WESTPAC. Adv. Space Res. 30 (2), 265–270, 2002. Shargorodsky, V. WESTPAC Satellite, the Scientific-technical Note for User, Science Research Institute for Precision Device Engineering, Moscow, Russia, 1997. Tapley AGU Fall 2001Õ 01 Meeting, Abstract G51A-0236. USA, 2002.
The accuracy of orbit estimation for the low-orbit satellites LARETS and WESTPAC Milena Rutkowska
*
Space Research Centre, Polish Academy of Sciences, ul. Bartycka 18 A, 00-716, Warsaw, Poland Received 30 November 2004; received in revised form 4 April 2005; accepted 15 April 2005
Abstract The LARETS satellite was launched on September 26, 2004, into a circular orbit at an altitude of 690 km and with an inclination of 98.2°. This mission is a successor to the WESTPAC satellite which was launched to an altitude of 835 km six years before. The study is based on the observations taken by the global network of laser stations during the period from December 30, 2003 to March 17, 2004 for LARETS. This study is aimed at the precise orbit computation of LARETS. The experience acquired during the orbit estimation of WESTPAC was applied to the orbit investigation of LARETS. The WESTPAC was merely used for reference and initial parameters of the force model [Rutkowska, M., Noomenn, R., Global orbit analysis of the satellite WESTPAC, Adv. Space Res., 30(2), 265–270, 2002]. The orbit of LARETS was estimated with an rms-of-fit to the SLR measurements of 3.9 cm, using the following computation model: the CSR TEG-4 gravity field up to degree and order (200,200), the Ray tide model, the MSIS86 model for atmospheric density [Hedin, A.E., MSIS-86 Thermospheric Model, J. Geophys. Res., 92 (A5), 4649–4662, 1987], and the solution of 8-hourly CD-values. It has been verified that the modeling of the gravity field up to degree and order (100,100) which gives the same rms-of-fit value. Estimated orbits for both satellites are compared to each other in Fig. 2. All computations are performed with the NASA program GEODYN II [Eddy, W.F, McCarthy, J.J., Pavlis, D.E., Marshall, J.A., Luthce, S.B., Tsaoussi, L.S., GEODYN II System Operations Manual, vol. 1–5, ST System Corp., Lanham MD, USA, 1990]. Ó 2005 Published by Elsevier Ltd on behalf of COSPAR. Keywords: Satellite orbit; Low-orbit satellites; LARETS; WESTPAC
1. Introduction The aim of this study is the computation of the orbit of the satellite LARETS with the highest accuracy possible. The satellite LARETS is very similar to WESTPAC (Shargorodsky, 1997) and both are designed to address scientific and applied problems in the areas of geodesy and geodynamics. The orbits of low flying satellites are strongly influenced by perturbing forces such as: the gravity field, atmospheric drag, solid earth and ocean tides. To obtain a high-quality orbit solution, the perturbing forces need to be modelled as accurately *
Tel.: +48 22 840 37 66; fax: +48 22 840 3131. E-mail address: [email protected].
0273-1177/$30 Ó 2005 Published by Elsevier Ltd on behalf of COSPAR. doi:10.1016/j.asr.2005.04.063
as possible. This paper discusses the influence of the modelling of different physical effects on the motion of LARETS, in particular in terms of orbit quality. A brief description of the characteristic parameters of WESTPAC and LARETS is given in Table 1. Both satellites are spherical and have an inclination equal to 98°, but altitude of LARETS is significantly smaller (about 160 km). Both satellites are shown in Fig. 1.
2. Analysis method The study is based on the observations taken by the global network of laser stations during the period from December 30, 2003 to March 17, 2004. Three-month
M. Rutkowska / Advances in Space Research 36 (2005) 498–503
499
Fig. 1. The satellites WESTPAC (left) and LARETS (right).
Table 1 The characteristic parameters of LARETS and WESTPAC
Launch date COSPAR id. Weight Altitude Inclination COM correction
WESTPAC
LARETS
July 07, 1998 9804301 23.28 kg 850 km 98.7° 6.28 cm
September 27, 2003 0304206 23.28 kg 690 km 98.2° 5.62 cm
period of measurements (4431 normal points) was divided into 12 7.5-day arcs with half day overlaps between successive arcs. An overview of the normal points obtained on LARETS by the laser stations is given in Table 2. The average number of normal points for each arc is 370. A detailed investigation of the orbit estimation of the WESTPAC is described in (Rutkowska and Noomenn,
Table 2 Overview of SLR stations and number of normal points to LARETS satellites No. Name
No. of station Number of n.p.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1884 7080 7090 7105 7110 7210 7237 7501 7811 7832 7836 7837 7838 7839 7840 8834
Riga, Latvia Fort Davis, USA Yarragadee, Australia Washington, USA Monument Peak, USA Maui, USA Changchun, China Hartebeesthoek, South Africa Borowiec, Poland Riyadh, Saudi Arabia Potsdam, Germany Shanghai, China Simosato, Japan Graz, Austria Herstmonceux, UK Wettzell, Germany
The coordinates of stations are fixed.
52 13 1421 200 400 247 229 21 46 246 93 84 407 505 423 132
2002). The experience acquired during the orbit estimation of WESTPAC was applied to the orbit investigation of LARETS. In this study three test cases were analyzed: 1. The best computation model derived for WESTPAC (Rutkowska and Noomenn, 2002), gravity field GRGS/GFZ GRIM-5S1(99,99) (Biancale and Schwintzer, 2000), atmospheric density MSIS 86 with CD solved for half-day intervals used for LARETS. 2. The computation model which uses the: gravity field GRIM5-S1(99,99) and the atmospheric density model MSIS 86 with CD solved for the 8-h intervals.
Table 3 Description of the force model used for the LARETS orbit computations Dynamic model
GRIM5-S1 (99,99) or Teg4 (200,200) gravity field Wahr solid earth tides, NASA/GSFC Ray ocean tides Atmospheric drag (MSIS 86 for density), CD solved for in half-day or 8-h intervals Direct solar radiation pressure, CR solved for in 7.5day intervals 3rd body attraction (Sun, Moon, Venus, Mars, Jupiter, Saturn) Albedo, Pole tide, Relativistic effects Empirical 1-cpr accelerations in along-track and crosstrack directions
Reference frame
ITRF2000 station positions at epoch 1997.0 Pole tide Precesion according to IAU 1976 (Lieske model) Nutation according to IAU 1980 (Wahr model) Love model for tidal uplift Ocean loading applied
Measurement model
15 s normal points provided by CDDIS and EDC Marini-Murray model for tropospheric delay Center-of-mass offset (5.62 cm) Station-dependent data weighted
Integration
Cowell 11th-order predictor-corrector, step-size 15 s
500
M. Rutkowska / Advances in Space Research 36 (2005) 498–503
3. The computation model which uses the CSR gravity field TEG-4(200,200) (Tapley, 2002) and the atmospheric density model MSIS 86 with CD solved for the 8-h intervals.
Table 4 Estimated rms values for three test cases and for 7.5-day orbital arcs No. of 7-day arc
No. of normal points
GRIM5-S1 CD-12 h int. rms (cm)
GRIM5-S1 CD-8 h int rms (cm)
Teg4 (200,200) CD-8 h int. rms (cm)
The parameters and computation model describing all forces acting on the satellite, are given in Table 3.
1 2 3 4 5 6 7 8 9 10 11 12
224 356 552 445 415 352 298 305 306 328 429 421
6.63 7.47 7.69 7.37 7.66 6.66 5.66 6.68 6.52 5.80 8.88 7.76
6.21 7.17 7.14 6.98 7.11 6.31 5.30 6.33 6.09 5.52 8.08 7.23
2.89 4.05 4.41 4.06 4.36 3.59 3.41 3.91 4.11 4.28 4.75 3.89
Average
370
7.05
6.61
3.97
3. Results The following unknowns were estimated in each solution: The satellite state vector for each 7.5-day arc. Drag coefficients CD, solar radiation pressure scaling parameters CR. Empirical satellite accelerations in different directions.
intervals. It has been verified that the modeling of the gravity field up to degree and order (100,100) which gives the same rms-of-fit value. The estimated rms-offit for each arc separately are shown in Table 4. The average rms-of-fit value is equal to 3.97 cm for case 3. Generally, it can be concluded that the best solution obtained here for LARETS is for case 3. The two examples of residuals for the best solution are shown in Figs. 3 and 4. The frequency of solving parameters CD (atmospheric drag) and CR (direct solar radiation pressure) have a big influence on the accuracy of orbit determination. The changes of the solved CD parameters for the half-day intervals by the 8-h intervals is a reason of diminish of rms-of-fit about 0.44 cm for each arc separately. The estimated CD (for 8-h intervals) and CR one for each arc values for the best solution are shown in Figs. 5 and 6, respectively.
An overview of the results which have been obtained for each scenario is given in Fig. 2. As a reference, the dashed line represents the average value of the rms-of-fit equal to 3.6 cm for WESTPAC (the force model is given in Table 3). The solid black diamonds represent the estimated rms values for LARETS in this case 1 (Fig. 2). The average value of rms-of-fit is equal to 7.05 cm. The plot with white diamonds (case 2) represents rms values solved for 8-h intervals. The change of solving CD parameters from half-day intervals to 8-h intervals is the reason for the reduction of the rms-of-fit by about 0.44 cm. The plot with black triangles (case 3) represents rms values for LARETS obtained with the gravity field model TEG-4 up to degree and order (200,200) and atmospheric density model MSIS 86 with CD solved for 8-h
9.00
rms (cm) 8.00 7.00 6.00 5.00 4.00 3.00 average rms for WESTPAC LARETS case 1
2.00
LARETS case 2
1.00
LARETS case 3
number of arc
0.00 1
2
3
4
5
6
7
8
9
10
Fig. 2. The rms values for LARETS for the total 3-month interval.
11
12
M. Rutkowska / Advances in Space Research 36 (2005) 498–503
501
0.12
(m)
0.10
RESIDUALS 2003.12.30- 2004.01.06
0.08 0.06 0.04 0.02 0.00 –0.02 –0.04 –0.06 –0.08 –0.10
no. of obs.
–0.12 0
20
40
60
80
100
120
140
160
180
200
220
Fig. 3. Residuals for 7.5-day arc (example 1).
0.12
(m)
0.10
RESIDUALS 2004.02.10- 2004.02.17.5
0.08 0.06 0.04 0.02 0.00 -0.02 -0.04 -0.06 -0.08 -0.10
no. of obs.
-0.12 0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
Fig. 4. Residuals for 7.5-day arc (example 2).
3.00 2.80 2.60 2.40 2.20 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00
Estimated Cd coefficients
0
no. of coefficient 0
20
40
60
80
100
120
140
160
180
200
220
Fig. 5. The atmospheric drag coefficients CD estimated for LARETS (case 3).
240
260
502
M. Rutkowska / Advances in Space Research 36 (2005) 498–503 1.80 1.60
Estimated Cr coefficients
1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00
no. of coefficient
-0.20 0
1
2
3
4
5
6
7
8
9
10
11
12
Fig. 6. The radiation pressure coefficients CR estimated for LARETS (case 3).
0.60
(m)
Overlap for 2004.02.17 radial
0.40
along track cross track
0.20
0.00
-0.20
minutes
-0.40 0
60
120
180
240
300
360
420
480
540
600
660
720
Fig. 7. The 12-h overlap for estate orbital arcs for radial, along track and cross track directions (example 1). 0.60
Overlap for 2004.03.02
(m)
radial
0.40
along track cross track
0.20
0.00
-0.20
minutes -0.40 0
60
120
180
240
300
360
420
480
540
600
660
720
Fig. 8. The 12-h overlap for estate orbital arcs for radial, along track and cross track directions (example 2).
M. Rutkowska / Advances in Space Research 36 (2005) 498–503
For LARETS (case 3), 12 successive data arcs were solved, of 7.5-day length each and with 12-h overlaps. In addition to the rms-of-fit, these overlaps can be used to evaluate the quality of the orbit solutions as well. Two examples of such overlaps, the plots in radial, along-track and cross-track directions are shown in Figs. 7 and 8. The differences between successive arcs in radial direction are about 3–5 cm, for cross-track direction about 12–16 cm. For along-track direction differences systematically increase.
503
This best scenario includes the CSR TEG-4 gravity field model up to degree and order (200,200), the Ray tides model, the MSIS 86 model for atmospheric density, and the solution of 8-hourly CD-values, and one pressure scaling parameter for arc CR.
Acknowledgement The author wants to thank the International Laser Ranging Service for providing the SLR data on the WESTPAC and LARETS satellites.
4. Conclusions Based on analysis of 3 months of SLR observations of the LARETS satellite, the following conclusions can be drawn: A best computation model has been developed according to which the orbit of LARETS can be computed with an rms-of-fit of SLR measurements of 3.9 cm. The accuracy of the orbit itself is estimated at 5 and 15 cm in radial and cross-track directions, respectively.
References Biancale, R., Schwintzer, P., The GRIM5-S2/C2 Earth Gravity Field Models, paper presented at the EGS XXV General Assembly, Nice, France, 2000. Rutkowska, M., Noomenn, R. Global orbit analysis of the satellite WESTPAC. Adv. Space Res. 30 (2), 265–270, 2002. Shargorodsky, V. WESTPAC Satellite, the Scientific-technical Note for User, Science Research Institute for Precision Device Engineering, Moscow, Russia, 1997. Tapley AGU Fall 2001Õ 01 Meeting, Abstract G51A-0236. USA, 2002.