Pointing Angle Calculation and Aiming Accuracy Analysis of a Lunar Laser Ranging Retro-Reflector

Wuqi Pan; Zhien Cheng; Zhongping Zhang; Xinhao Liao

doi:10.3788/LOP240465

Laser & Optoelectronics Progress, Volume. 61, Issue 7, 0706018(2024)

Pointing Angle Calculation and Aiming Accuracy Analysis of a Lunar Laser Ranging Retro-Reflector

Wuqi Pan^1,2,3、*, Zhien Cheng^1、**, Zhongping Zhang¹, and Xinhao Liao^1,2

Author Affiliations

¹Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China

²School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China

³School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China

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Figures & Tables(10)

Fig. 1. Track of barycenter of Earth in ME reference system between 2020-01-01 and 2025-01-01

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Fig. 2. Diagram of rotation between moon center-ICRF equator system and lunar body-fixed coordinate system

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Fig. 3. Diagram of rotation between lunar body-fixed coordinate system and lunar topocentric coordinate system

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Fig. 4. Relation of angular deviation and bias of time

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Fig. 5. Diagram of Sun in topocentric coordinate system

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Fig. 6. Relation of angular deviation and bias of emplacement site. (a) Diagram of emplacement site and planned site; (b) plots of relation of angular deviation and bias of emplacement site for $R = 30 k m$ ;(c) plots of relation of angular deviation and bias of emplacement site for $R = 60 k m$ ; (d) plots of relation of angular deviation and bias of emplacement site for $R = 100 k m$

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Fig. 7. Relation of misalignment and bias of emplacement site

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Table 1. Emplacement angle of retro-reflector
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Table 1. Emplacement angle of retro-reflector
Emplacement site and time $A_{M E}$ $h_{M E}$ $A_{s u n}$ $h_{s u n}$ $θ$
A， $T_{1}$ $216.1$ $57.3$ 135.5 55.9 -80.6
A， $T_{2}$ 146.0 56.5 -70.1
B， $T_{1}$ $70.0$ $65.1$ 84.3 24.6 14.3
B， $T_{2}$ 86.4 30.1 16.4

Table 2. Permissible time of LRRR with different emplacement site and altitude of the sun

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Table 2. Permissible time of LRRR with different emplacement site and altitude of the sun

Longitude of emplacement site	Latitude of emplacement site	Altitude of LRRR	Calculated by Eq. （15）	Calculated by program^*
h_sun=20°
0°	20°	69.9°	58.9 h	60.1 h
20°	20°	61.9°	43.0 h	44.0 h
17.4°	10°	69.9°	116.1 h	89.6 h^**
h_sun=40°
0°	20°	69.9°	39.2 h	41.8 h
20°	20°	61.9°	28.5 h	30.3 h
17.4°	10°	69.9°	77.1 h	87.3 h
h_sun=60°
0°	20°	69.9°	16.7 h	18.2 h
20°	20°	61.9°	12.2 h	13.2 h
17.4°	10°	69.9°	32.9 h	40.2 h

Table 3. Misalignment caused by different month

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Table 3. Misalignment caused by different month

Emplacement month	$h_{s u n}$	Gnomon shadow angle set as
Emplacement month	$h_{s u n}$	15.27°^*	15.08°^*	15.36°^*	16.02°^*	16.86°^*	17.67°^*
Feb.	10°	0.75°	0.83°	0.71°	0.44°	0.08°	-0.26°
	20°	0.00°	0.08°	-0.04°	-0.32°	-0.67°	-1.01°
	30°	-0.88°	-0.80°	-0.92°	-1.19°	-1.55°	-1.89°
Mar.	10°	0.67°	0.75°	0.63°	0.35°	-0.01°	-0.34°
	20°	-0.08°	0.00°	-0.12°	-0.40°	-0.75°	-1.09°
	30°	-0.96°	-0.88°	-1.00°	-1.28°	-1.63°	-1.97°
Apr.	10°	0.78°	0.86°	0.74°	0.46°	0.11°	-0.23°
	20°	0.04°	0.12°	0.00°	-0.28°	-0.63°	-0.97°
	30°	-0.82°	-0.74°	-0.86°	-1.14°	-1.49°	-1.83°
May	10°	1.04°	1.12°	1.00°	0.72°	0.37°	0.03°
	20°	0.32°	0.40°	0.28°	0.00°	-0.36°	-0.69°
	30°	-0.52°	-0.44°	-0.55°	-0.83°	-1.19°	-1.53°
Jun.	10°	1.37°	1.46°	1.34°	1.06°	0.70°	0.36°
	20°	0.67°	0.75°	0.63°	0.36°	0.00°	-0.34°
	30°	-0.13°	-0.05°	-0.17°	-0.44°	-0.80°	-1.14°
Jul.	10°	1.70°	1.78°	1.66°	1.38°	1.03°	0.69°
	20°	1.01°	1.09°	0.97°	0.69°	0.34°	0.00°
	30°	0.24°	0.32°	0.20°	-0.08°	-0.43°	-0.77°

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Wuqi Pan, Zhien Cheng, Zhongping Zhang, Xinhao Liao. Pointing Angle Calculation and Aiming Accuracy Analysis of a Lunar Laser Ranging Retro-Reflector[J]. Laser & Optoelectronics Progress, 2024, 61(7): 0706018

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