Estimability of astronomical longitude and latitude only from theodolite observations within three-dimensional networks of terrestrial type

Summary From a two-dimensional network adjustment it is well understood that the one orientation unknown of a theodolite frame is estimable, once the orientation datum parameter, e.g., one azimuth, is fixed. In three-dimensional networks the problem of estimability of three orientation unknowns inherent in a theodolite frame is more complex. Here we prove that not only the classical horizontal orientation unknown is estimable (up to the datum degrees of freedom), but also astronomical longitude and astronomical latitude which can be considered as two additional orientation unknowns of the theodolite frame moving with respect to an earth-fixed equatorial frame of reference. Thus the theodolite instrument can be considered—at least theoretically—a gradiometer measuring the variation of the directional parameters of the gravity vector from one point to another. Or up to the datum degrees of freedom astronomical longitude and astronomical latitude can be determined from only theodolite observations between exclusively terrestrial points. M?nicke (1982), has shown that despite the refraction problem the method works sufficiently well in practice.