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Orbit Determination of Chinese Rocket Bodies from the Picosecond Full-Rate Laser Measurements

Paweł Lejba
Paweł Lejba
   | Jan 19, 2024
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Published Online: Jan 19, 2024
Page range: 256 - 277
Received: Oct 27, 2023
Accepted: Nov 24, 2023
DOI: https://doi.org/10.2478/arsa-2023-0010
Keywords
© 2023 Paweł Lejba, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1.

Number of successful passes in years 2016–2021 registered by BORL sensor. The black line and labels represent all registered passes, including satellite and space debris. The gray line and labels show the number of successful passes specifically for space debris.
Number of successful passes in years 2016–2021 registered by BORL sensor. The black line and labels represent all registered passes, including satellite and space debris. The gray line and labels show the number of successful passes specifically for space debris.

Figure 2.

Pass of CZ-2C R/B (NORAD 31114) registered by Polish laser sensor on August 3, 2018, 22:10 UTC, showing slant ranges (top) and fit residuals (bottom) with 1900 valid returns. TCA means the time of closest approach. The min. and max. distances to the target were 1083 and 1750 km, respectively.
Pass of CZ-2C R/B (NORAD 31114) registered by Polish laser sensor on August 3, 2018, 22:10 UTC, showing slant ranges (top) and fit residuals (bottom) with 1900 valid returns. TCA means the time of closest approach. The min. and max. distances to the target were 1083 and 1750 km, respectively.

Figure 3.

Pass of CZ-2C R/B (NORAD 28480) registered by Polish laser sensor on April 21, 2018, 20:04 UTC, showing slant ranges (top) and fit residuals (bottom) with 869 valid returns. TCA means the time of closest approach (TCA). The min. and max. distances to the target were 1176 and 1621 km, respectively.
Pass of CZ-2C R/B (NORAD 28480) registered by Polish laser sensor on April 21, 2018, 20:04 UTC, showing slant ranges (top) and fit residuals (bottom) with 869 valid returns. TCA means the time of closest approach (TCA). The min. and max. distances to the target were 1176 and 1621 km, respectively.

Figure 4.

RMPOS determined for object 28480. The dotted line separates observational slots for object 28480. Slots are described in Table 5. The results obtained for scenarios 1, 2, and 3 are shown by the colors green, orange, and red, respectively.
RMPOS determined for object 28480. The dotted line separates observational slots for object 28480. Slots are described in Table 5. The results obtained for scenarios 1, 2, and 3 are shown by the colors green, orange, and red, respectively.

Figure 5.

RMPOS determined for object 31114. The dotted line separates observational slots for object 31114. Slots are described in Table 5. The results obtained for scenarios 1, 2, and 3 are shown by the colors green, orange, and red, respectively.
RMPOS determined for object 31114. The dotted line separates observational slots for object 31114. Slots are described in Table 5. The results obtained for scenarios 1, 2, and 3 are shown by the colors green, orange, and red, respectively.

Figure 6.

The sample results show the range errors in the RSW system for Scenario sc1-1 (object 28480). The red broken line indicates the determined alert time.
The sample results show the range errors in the RSW system for Scenario sc1-1 (object 28480). The red broken line indicates the determined alert time.

Figure 7.

The alert times for objects 28480 and 31114
The alert times for objects 28480 and 31114

Figure 8.

The results of comparing the semi-major axis determined using TLE ephemeris and laser measurements
The results of comparing the semi-major axis determined using TLE ephemeris and laser measurements

Figure 9.

The results of comparing the eccentricity axis determined using TLE ephemeris and laser measurements
The results of comparing the eccentricity axis determined using TLE ephemeris and laser measurements

The observational statistics for objects 28480 and 31114 from the years 2016 to 2022

28480 31114
Laser ns ps ns ps
Passes 25 90 33 230
Avg. returns 597 321 860 548
Avg. pass RMS [cm] 24.98 2.16 22.97 2.60
Avg. RB [m] 30.88 24.95 −30.95 −24.79
Avg. TB [ms] −117.65 −120.01 6.78 3.34

RMSPOS, RMSVEL, and arc RMS determined for object 31114. Results for scenario No. 2 are highlighted with a gray background color.

NR SCE RMSPOS [m] RMSVEL [m/s] Full-rate meas. Arc RMS [cm]
1 sc1-1 519.72 1.2512 137 3.99
2 sc1-2 519.50 0.9371 1066 4.85
3 sc1-3 517.37 0.9515 1362 5.03
4 sc1-4 486.99 0.9245 1402 11.50
5 sc1-5 495.13 0.9658 897 12.85
6 sc1-6 523.72 0.9571 313 2.49
7 sc1-7 648.47 0.5640 1900 5.53
8 sc2-1 519.72 1.2513 137 3.93
9 sc2-2 251.68 0.8691 1066 5.02
10 sc2-3 356.22 0.7911 1362 5.01
11 sc2-4 335.00 0.8601 1402 15.33
12 sc2-5 495.10 0.9657 897 11.95
13 sc2-6 341.95 0.7307 313 2.46
14 sc2-7 453.61 0.3691 1900 5.53
15 sc3-1 519.72 1.2512 137 3.99
16 sc3-2 15.70 0.1132 1203 6.19
17 sc3-3 1.39 0.0112 2565 110.55
18 sc3-4 0.56 0.0041 3967 374.04
19 sc3-5 495.13 0.9658 897 12.85
20 sc3-6 41.84 0.1580 1210 14.45
21 sc3-7 2.02 0.0073 3110 131.05

The list of observations of objects 28480 and 31114 taken into orbital computations

Slot No. Date [mm.dd.yyyy] UTC time Duration of meas. [mm:ss] No. of Full-rate meas. TB [ms] RB [m] Pass RMS [cm]
Object 28480
1 04.18.2018 21:19 00:38 56 −116.94 39.42 2.93
04.19.2018 20:53 02:49 459 −129.48 −14.10 2.86
04.20.2018 20:28 04:41 755 −110.38 −32.80 4.64
04.21.2018 20:04 04:27 869 −104.93 11.28 2.61
04.21.2018 21:44 01:39 146 −106.76 28.70 1.80
2 10.10.2018 20:26 02:54 592 −137.14 102.96 2.24
10.11.2018 20:02 05:18 305 −130.51 21.83 1.89
10.12.2018 19:38 03:38 184 −121.54 10.15 2.62
Object 31114
3 05.29.2018 20:51 02:02 137 −18.57 41.76 3.37
05.29.2018 22:28 05:39 1066 0.77 −89.60 2.23
05.30.2018 22:09 05:11 1362 −19.37 −42.73 3.60
05.31.2018 21:50 07:35 1402 8.09 −3.52 3.43
4 08.01.2018 21:05 06:38 897 41.16 −15.75 3.53
08.02.2018 22:29 03:52 313 23.33 −17.54 1.98
08.03.2018 22:10 05:12 1900 −23.51 −10.13 4.62

The basic parameters of the lasers used by the BORL sensor

Laser EKSPLA PL-2250 Continuum Surelite III
Stand Optical table Optical table
Pulse width 60 ps 3–5 ns
Repetition rate 10 Hz 10 Hz
Pulse energy 0.05 J 0.45 J
Average power 0.5 W 4.5 W

Basic physical and orbital parameters of CZ-2C’s 28480 and 31114

Object CZ-2C R/B CZ-2C R/B
NORAD 28480 31114
COSPAR 2004-046B 2007-010B
Semi-major axis [km] 7187 7207
Eccentricity 0.01447029 0.0058965
Inclination [deg] 98.05 98.37
Height [m] 8.4
Mass [kg] 3800
Avg. cross section [m2] 26.51

Observational statistics for CZ-2C's 28480 and 31114 from 2017 to 2018

NORAD 28480 31114
Year Passes Returns Normal points Mean pass RMS [cm] Passes Returns Normal points Mean pass RMS [cm]
2017 36 17,830 259 8.67 56 49,335 502 9.37
2018 39 12,424 227 2.45 116 74,287 959 3.89

The list of models and parameters used in orbital calculations

Force and measurement models

Earth gravity field: EGM2008 120 × 120

Earth tides: IERS conventions 2003

Ocean tide model: GOT99.2

Third-body gravity: Moon, Sun, and planets: DE403

Solar radiation pressure coefficient: CR = 1.00 (default value)

Drag coefficient: CD = 2.3 (default value, one coefficient per 24 h)

Tidal constants k2, k3, and phase k2: 0.300, 0.000, 0.093

Earth albedo

Dynamic polar motion

Relativistic corrections

Atmospheric density model: MSIS-86

Tropospheric refraction: Mendes–Pavlis model

Measurements: full-rate format from BORL7811 station

Laser pulse wavelength: 532 nm

Center of mass correction: not used
Reference frame

Inertial reference frame: J2000.0

Coordinate reference system: true of date defined at 0.0 h of the reference epoch for each satellite

Station coordinates: SLRF2014 for epoch 2010.0

Precession and nutation: IAU 2000

Polar motion: C04 IERS

Tidal uplift: Love model H2 = 0.609, L2 = 0.0852

Pole tide
Estimated parameters
Input state vector (six components + their deviations) determined at the beginning of the orbital arc-both Cartesian and Keplerian elements
Numerical integration

Integration: Cowell’s method

Orbit integration step size: 1 s

Arc length: from 1 to 4 days (depending on the scenario)

The alert time and the 3-sigma range error of RSW components for object 28480. Results for scenario No. 2 are highlighted with a gray background color.

Alerttime [s] SCE 3-sigma range error R [m] 3-sigma range error S [m] 3-sigma range error W [m]
77,160 sc1-1 3105.67 56,194.05 210.34
75,540 sc1-2 472.38 18,206.11 138.15
76,080 sc1-3 459.26 25,574.61 753.82
76,020 sc1-4 305.54 4150.10 1016.30
77,160 sc1-5 2366.66 42,412.72 414.71
69,000 sc1-6 927.51 20,229.23 287.22
86,400 sc1-7 184.05 6558.61 676.77
69,180 sc1-8 647.79 16,555.54 1231.71
77,160 sc2-1 3100.32 56,100.60 210.12
76,080 sc2-2 1833.24 81,233.78 3107.26
76,440 sc2-3 1304.10 39,701.68 7863.85
76,320 sc2-4 1270.35 37,543.63 2969.35
77,400 sc2-5 2717.97 40,404.66 605.94
69,000 sc2-6 927.51 20,229.23 287.22
75,600 sc2-7 2356.37 102,477.05 5203.18
75,660 sc2-8 1376.67 64,128.16 8125.32
77,100 sc3-1 3095.06 56,285.17 214.53
148,200 sc3-2 418.69 15,744.07 685.10
69,960 sc3-3 222.22 7889.42 652.46
68,940 sc3-4 336.70 7815.63 853.14
63,480 sc3-5 347.78 7830.87 1106.28
69,000 sc3-6 929.04 20,281.01 292.12
68,100 sc3-7 757.92 10,287.96 943.96
63,600 sc3-8 1175.77 10,441.24 1052.57

The alert time and the 3-sigma range error of RSW components for object 31114. Results for scenario No. 2 are highlighted with a gray background color.

Alert time [s] SCE 3-sigma range error R [m] 3-sigma range error S [m] 3-sigma range error W [m]
78,180 sc1-1 112.61 4386.70 164.48
75,780 sc1-2 293.66 35,828.80 782.60
79,500 sc1-3 157.70 1525.23 610.29
75,660 sc1-4 15960.54 431,936.22 17,428.61
76,260 sc1-5 4164.90 171,254.88 2219.53
75,240 sc1-6 158.07 7147.91 492.29
62,880 sc1-7 198.07 1214.40 955.42
83,700 sc2-1 207.15 3329.70 181.66
78,240 sc2-2 202.01 3894.75 913.07
78,360 sc2-3 132.43 4515.85 780.22
75,720 sc2-4 6517.98 266,437.84 13,800.13
76,200 sc2-5 6280.38 231,564.70 3208.94
76,440 sc2-6 542.69 20,509.42 1561.46
57,180 sc2-7 200.46 1144.53 983.61
78,180 sc3-1 112.62 4385.22 164.49
75,120 sc3-2 400.59 21,401.25 7262.87
74,940 sc3-3 254.22 11,002.82 585.79
57,180 sc3-4 2621.07 12,134.63 586.38
76,260 sc3-5 4164.94 171,255.84 2219.54
77,760 sc3-6 803.40 14,323.83 9480.79
70,860 sc3-7 706.13 13,450.79 805.29

RMSPOS, RMSVEL, and arc RMS determined for object 28480. Results for scenario No. 2 are highlighted with a gray background color.

NR SCE RMSPOS [m] RMSVEL [m/s] Full-rate meas. Arc RMS [cm]
1 sc1-1 528.98 1.3812 56 2.69
2 sc1-2 503.00 1.0179 459 2.67
3 sc1-3 512.91 0.9687 755 5.88
4 sc1-4 528.11 0.9378 869 4.04
5 sc1-5 547.04 1.2799 146 2.40
6 sc1-6 506.83 1.0249 592 2.28
7 sc1-7 507.84 0.9830 305 6.29
8 sc1-8 527.77 0.9595 184 3.31
9 sc2-1 528.98 1.3812 56 2.69
10 sc2-2 186.48 1.0086 459 2.66
11 sc2-3 242.63 0.5520 755 5.90
12 sc2-4 328.32 0.7299 869 4.08
13 sc2-5 360.28 1.1822 146 3.12
14 sc2-6 506.83 1.0249 592 2.28
15 sc2-7 371.21 0.8089 305 5.41
16 sc2-8 238.79 0.6121 184 3.34
17 sc3-1 528.98 1.3812 56 2.69
18 sc3-2 89.78 0.5765 515 2.98
19 sc3-3 5.04 0.0387 1270 176.99
20 sc3-4 1.18 0.0066 2139 54.52
21 sc3-5 0.62 0.0026 2285 94.33
22 sc3-6 506.83 1.0249 592 2.28
23 sc3-7 23.86 0.0943 897 5.75
24 sc3-8 8.08 0.0256 1081 27.30
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