Figure 3a · Scanning telescope, Apollo 11 lunar orbit rev 30, 124:40:00 GET
The command module scanning telescope's view shortly after the LM lifted off from the Moon, recomputed from the 1969 inputs and compared with the 1972 printed figure.
Residuals: recreation vs. the TN D-6853 (1972) scan (at the figure's own inputs)
Body
Scan x, y (°)
Recreation x, y (°)
Δ (°)
Within 2°
Sirius
-45.59, 49.79
-46.40, 49.73
0.81
Yes
Rigel
-32.11, 30.88
-32.33, 30.61
0.34
Yes
Capella
25.47, 36.76
25.21, 36.99
0.36
Yes
Aldebaran
-5.09, 27.00
-5.12, 27.07
0.08
Yes
Venus
-1.89, 32.10
-2.00, 33.69
1.60
Yes
Mirfak
31.57, 17.47
31.23, 17.57
0.35
Yes
Menkar
-12.25, 1.60
-12.03, 1.68
0.23
Yes
Saturn
-1.89, -4.20
-1.88, -4.06
0.14
Yes
Navi
49.79, 0.78
49.37, 0.88
0.43
Yes
Earth
2.40, -22.71
2.89, -22.57
0.51
Yes
Alpheratz
26.99, -26.64
27.16, -26.43
0.27
Yes
Diphda
-22.77, -38.28
-22.11, -38.07
0.70
Yes
RMS 0.62°, max 1.60°. The plotting convention was chosen by fitting this figure, so this is a calibration, not an independent test (RMS ≤ 1° and max ≤ 2°: met).
How this was made
Time. 124:40:00 ground elapsed time after the 13:32:00 UTC range zero on 16 July 1969 is 18:12 UTC on 21 July.
Stars. The 148 stars of the note’s own RTCC catalogue (Besselian 1970) were transcribed by OCR; 22 rows the OCR could not read were read from the page images. Every row’s printed position was checked against the Yale Bright Star Catalog to within 0.05°. The 37 navigation stars use the unit vectors stored in the Apollo 11 command module computer.
Earth and planets. Positions for that minute come from astronomy-engine, seen from the Moon’s center and rotated into the same B1970 frame.
Spacecraft attitude. The stars are rotated through the Lunar lift-off REFSMMAT, then the gimbal angles I = 49.1°, M = 0°, O = 0°, in the order the guidance computer’s CALCGA routine uses, and then the 32.5° optics mounting (NB1NB2).
Projection. The telescope looks along its shaft axis (trunnion 0°). The view is plotted as an azimuthal-equidistant (“fisheye”) projection ±50° across, with up toward increasing trunnion.
Comparison. The 1972 figure was scanned at 300 dpi, registered to its ±50° frame, and each labeled body’s position was measured.
Limits
The plot is drawn from the command module’s reconstructed position: the Apollo 11 Mission Report’s trajectory table, propagated from the nearest tabulated state (the note under the plot says which). From there the Moon is 131° from the telescope’s axis, well out of view, as on the original. The residuals table uses the Moon’s center as the observer, as registered for the validation; the difference moves Earth by under 0.3°.
The −0 to −50 scale along the reticle’s vertical line is drawn as it appears on the figures. Neither document explains it.
The program drew the 37 navigation-star names on the microfilm itself (TN D-6853, appendix), so they are always shown; the 1972 print re-lettered them. Planet and Earth names, the header and the axis titles were added to the published figures, and the Labels switch shows or hides that layer. The boxes around planet names follow the 1969 note’s version of this figure (69-FM-197 Fig 9.3-8); the 1972 print has none.
Venus sits 1.6° from its printed position, the largest difference. The offset lies along Venus’s own daily motion, which suggests the 1969 program’s planetary ephemeris rather than the geometry.