Interactive Spreadsheets for Celestial Navigation
Lunar distance
1. Lunar distance clearing and UT recovery




The lunar distance technique allows you to determine Universal Time (UT) in case you cannot rely on a chronometer.  This method is not all that accurate by modern standards but it is rigorous and can serve as a viable backup option.  The spreadsheet lunar_distance.xls clears the lunar distance and then performs the interpolation that yields an improved UT.  Start by entering your best estimate of UT in row 3.  Select Time1 and Time2 instants on opposite sides of this estimate  and enter the corresponding GPs of the Moon and the other body in rows 7 and 12.  The apparent and observed altitudes go to row 17.  Enter the observed lunar distance (corrected for index error only) into cell B22.  The objects’ semidiameters are placed in cells C22 and E22 (enter near-limb values as positive, and far-limb values as negative).  The computed UT is displayed in cell C30, which is Time1 + T_add (i.e. the sum of cells A7 and B30).  Verify that the interpolation factor IntF (cell A30) lies between 0 and 1.  If that is not the case then the two instants Time1 and Time2 do not “bracket” the “true” UT and need to be changed accordingly.

The following image shows the spreadsheet lunar_distance.xls.





Summary for spreadsheet lunar_distance.xls:

Input cells: row 3, A7-E7, A12-E12, B17, C17, E17, F17, B22, C22, E22
Output cells: A30, B30, C30
Intermediate lunar distance cells: F7, F12 (computed), F22 (centered), E27, F27 (cleared)

The method and example preset in this spreadsheet can be found in Celestial Navigation in the GPS Age by John Karl, pp. 93-95.





2. Precomputed lunar distance

The spreadsheet ld_comp.xls allows the calculation of the center-to-center (i.e. no semidiameter) geocentric lunar distance (cells A10, B10, C10) from almanac data (row 2).  The topocentric result in cells D10, E10, F10 includes the effect of Moon’s parallax on the lunar distance, when observed from an assumed position (cells E6, F6).  While these results do not include the effects of refraction, they are close enough for your sextant to be preset to an angle that is sufficiently close to the actual observed value.  The values are preset for a Sun lunar on January 8, 2011, UT = 22:00:00.

The following image shows the spreadsheet ld_prec.xls.





Summary for spreadsheet ld_prec.xls:

Input cells: A2, B2, C2, E2, F2, E6, F6
Output cells: A10, B10, C10, D10, E10, F10


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