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

Lejba, Paweł

doi:10.2478/arsa-2023-0010

Figures & Tables

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.

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 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.

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 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.

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 alert times for objects 28480 and 31114

The results of comparing the semi-major 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: C_R = 1.00 (default value)
Drag coefficient: C_D = 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

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

Figures & Tables

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.