If, for instance, both the sun and the moon are simultaneously visible in the sky it is possible to obtain your position by finding the intersection of the two lines of position (LOP) obtained from each sight. Typically there are two distinct possible positions and it should be very easy to decide which one is the correct one.

The measured sextant altitude is corrected for index error, refraction, parallax, and semidiameter which results in the observed altitude (Ho).

The Universal Time (UT) of the sight is used to determine the Geographical Position (GP) with the help of an almanac. The declination and Greenwich Hour Angle (GHA) of the GP plus the Ho for the two sights are entered in row 3 of the spreadsheet. The solutions are displayed in rows 8 and 10.

Summary for spreadsheet lops.xls:

Input cells: A3, B3, C3, D3, E3, F3

Output cells: A8, B8, C8, D8, E8, F8, A10, B10, C10, D10, E10, F10

The problem preset in this spreadsheet is treated in The Celestial Navigation Mystery Solved by David Owen Bell on p. 79.

The spreadsheet two_body_fix.xls has the same interface as lops.xls and solves the same problem using a different method. Whereas lops.xls employs the techniques of spatial geometry (Van Allen paper), two_body_fix.xls applies the equations of spherical trigonometry (John Karl, Celestial Navigation in the GPS Age, pp. 78-79). The latter reference also discusses the applicability of this approach to finding the latitude without a meridian sight or knowledge of UT (the double-altitude method).