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Comparison of the coordinate systems used by the Soviet lunar missions and modern coordinate systems


   Since the preparation of the launch of "Luna-15", coordinate the provision of lunar missions relied on a lunar map LAC [Lunar Chart (LAC) Series], perhaps the best cartographic product of the time (Fig. 1). Today we have an opportunity to find out a degree of the Soviet coordinate data distinction 40 or 50 years ago (table. 1) from modern coordinate systems and even to get an idea about the accuracy of the "drive" the SPACECRAFT's aim point on the moon in the middle of the last century.
Table 1. The coordinates of the artifacts of the Soviet lunar program on the moon's surface.
* - the difficult landing of the spacecraft, the mission was not carried out.

Spacecraft Date Latitude, ° Longitude, ° Landing site
Luna 15*
Aiming point
21.07.1969 + 12.109° + 12.109° Sea Of Crises
Luna 16 21.09.1970 - 0°41' +56°18' Sea Of Abundance
Luna 17 2.09.1971 +38°17' - 35°00 ' Sea Of Rains
Luna 18* 2.09.1971 +3°41' 56°30' The continental region between the Sea of Plenty and the Sea of Crises
Luna 20 21.02.1972 +3° 32' +56°33' The continental region between the Sea of Plenty and the Sea of Crises
Luna  21 16.01.1973 +25° 51' +30° 27' Sea of Clarity (Crater le Monnier)
Luna 23* 6.11.1974 +12°41' +62°17' Southern part of the Sea of Crises
Luna  24 18.8.1976 +12°45' +62°12' Southern part of the Sea of Crises

   By the time of mission LRO (Lunar Reconnaissance Orbiter) the international community has developed two completely new precise lunar coordinate system Mean Earth/Polar axis (ME) and Principal axis (PA). Coordinate system IU is used to handle transmission of images of the lunar surface derived from LRO). It takes into account time variations of the position of the earth's polar axis. Work with physical instruments in lunar orbit and astronomical instruments on Earth (e.g., VLBI), a more useful coordinate system PA, associated with the principal axes of inertia of the lunar body [1, 2].
In MexLab were considered individual aspects of the problem that has arisen because of uncertainties in the coordinate data sets of the Soviet space objects (artifacts), delivered to the lunar surface in the 60-70 years of the last century (Fig. 2). An attempt was made to correlate this coordinate information of the twentieth century (the Soviet Union(XX century)) with the coordinates of the artifacts obtained in the latest lunar coordinate system ME (Mean Earth / Polar Axis). A direct comparison of the coordinate data of the two systems (tab. 2), which was further confirmed by calculation of communication parameters of these systems and follow-up (control) by transforming a set of coordinates of the system IU the system of the USSR (the twentieth century).
Table 2. The differences between coordinates of space objects (artifacts) in modern ME, and earlier applied in the USSR coordinate systems.

Spacecraft The difference between the coordinates of the spacecraft in the systems ME (LRO) and the Soviet Union (XX century)
Latitude, ° Longitude, ° Radius-vector, km
Luna 16 0.1697 0.0642 -0.555
Luna 17 -0.0416 0.0028 -1.669
Luna 18 0.1930 0.1550 -2.095
Luna 20 0.2568 0.0745 -1.188
Luna 21 0.1527 -0.0422 -2.480
Luna 23 -0.0169 -0.1320 -2.869
Luna 24 -0.0361 0.0131 -2.874
СКО 0.151° 0.087° +2.15

   The results of the coordinate systems mapping suggest that horizontal coordinates (latitude and longitude) system of the USSR(the twentieth century) is consistent with the coordinate values obtained in the system ME within (0,10-0,12)O. the Absolute height (radius-vectors) in the coordinate system of the USSR(the twentieth century) differ significantly (up to 2.8 km) from the values obtained from the data of laser altimeter LOLA. Also obtained the first idea about the magnitude of the shift along the respective coordinate axes and angles of their mutual reversal (table. 3).
Table 3. The communication parameters of two lunar coordinate systems obtained in MIIGAiK.

Parameter Value Accuracy estimate
Scale 1.0019536 0.0008808
The shift along the X-axis, km -1.005 3.762
The shift along the Y-axis, km -1.633 2.340
The shift along the Z-axis, km 1.002 5.175
Turn around the X-axis 0°12`46”.648 0°05`32”.210
Turn around the Y-axis -0°00`57”.636 0°14`43”.021
Turn around the Z-axis 0°02` 37.089 0°06`43”.077

[1] «A Standardized Lunar Coordinate System for the LRO and Lunar Datasets, LRO Project and LGCWG White Paper, Version 5», 2008 October 1 (Version 5), Goddard Space Flight Center, Greenbelt, Maryland, NASA // http://lunar.gsfc.nasa.gov/library/LunCoordWhitePaper-10-08.pdf
[2] Baldwin, RB 1963. The Measure of the Moon. University of Chicago Press.

Лист карты LAC 77 масштаба 1:1 000 000

Fig. 1. The LAC map sheet 77 scale 1:1 000 000

Места посадки советских лунных миссий.

Fig. 2. Landing sites of Soviet lunar missions

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