Interactive Spreadsheets for Celestial Navigation
Solutions of the navigation triangle
1. Sight reduction using the intercept method
The spreadsheet intercept.xls solves the navigation triangle in accordance with the intercept method of Marcq Saint-Hilaire. Enter the latitude and longitude of the assumed position (AP) in cells A2, B2, the GHA and Declination (GP) in cells C2, D2, and the observed altitude (Ho) in cell E2. Cell F2 computes and displays the Local Hour Angle (LHA). If you have already determined LHA and want to use it as input, enter it in place of GHA (cell C2) and set the AP Longitude (in cell B2) to zero. The calculated altitude (Hc) at the AP is in cells A6, B6, C6 and the intercept distance (in nautical miles) is displayed in cells D6 and E6. The azimuth Zn toward the GP from the assumed position is in cell F6 This allows you to plot the line of position (LOP), along which the “true” position (TP) is located.
The following image shows the spreadsheet intercept.xls.
Summary for spreadsheet intercept.xls:
Input cells: A2, B2, C2, D2, E2
Output cells: A6, B6, C6, D6, E6, F6
Intermediate cell: F2
It is also possible to use this spreadsheet to solve great-circle sailing problems. Enter the coordinates of the origin in cells A2, B2, destination in cells C2, D2, and set Ho to 90º in cell E2. In cell C2 remember to flip the sign in order to convert longitude into equivalent GHA. Thus for Example 1 on pp. 348-349 of Bowditch (2002) we have A2 = -32, B2 = 116, C2 = -31 (or 329), D2 = -30, and E2 = 90. The resulting great-circle distance is D6 = 4247.6 nm and the initial great-circle course is F6 = 246.0. (This computed great-circle distance does not account for the oblateness of the Earth and therefore could differ somewhat from the exact result.)
2. The one-body fix
If both the azimuth (Zn) and the altitude (Ho) of a celestial body is known, then it is possible to obtain a fix for the “true” position (TP) from observing that one body alone. The spreadsheet one_body_fix.xls solves the navigation triangle in this scenario. The GP is characterized by its declination (cell A2) and Greenwich Hour Angle (B2). The azimuth (Zn) is entered in cell C2, and the observed altitude (Ho) goes into cell D2. The TP coordinates are displayed in row 6.
The following image shows the spreadsheet one_body_fix.xls.
Summary for spreadsheet one_body_fix.xls:
Input cells: A2, B2, C2, D2
Output cells: A6, B6, C6, D6, E6, F6
The data preset in this spreadsheet define an inverse problem to the one preset in intercept.xls.
