Engineering topics
Publications and source records attributed to Eichhorn, H..
Rigorous formulas are derived with which one can compute from three observed (coplanar) directions the proper-motion components and the product of parallax and radial velocity of an object (star) which moves uniformly with respect to the observer (earth). The errors of the determination of distance by parallactic acceleration are analyzed and the possibility of determining distances by this method is discussed.
It is shown that after treating a least-squares problem in the standard fashion, the imposition of stochastic restrictions on certain parameters can be accomplished essentially by inverting a matrix of an order no larger than the total number of restricted parameters, and that generally there is an explicit term for correcting the unrestricted to the restricted solution. In addition, any known type of nonstandard least-squares adjustment problem can be reduced to an equivalent standard linear problem, that is, one in which there is exactly one observation per condition equation and in which the observations are not correlated.
Least squares adjustment problems are considered in which the condition equations are nonlinear in both the observations and the adjustment parameters ('unknowns'). A solution algorithm is presented which takes into account the second (as well as the first) order derivatives in the adjustment residuals (observation errors) and the corrections to the initially available approximations to the adjustment parameters. The inclusion of second-order terms in the adjustment residuals is necessary whenever the adjustment residuals themselves cannot be regarded as negligible as compared to the adjustment parameters, i.e., whenever the linearized condition equations would no longer be practically equivalent to the rigorous ones. The consideration of second-order terms in the parameter corrections is completely independent of the second-order terms in the adjustment residuals.
Conference on astrometric photointerpretation methods for satellite geodesy and astronomical catalogs
The flying spot digitizer can measure the coordinates of star images on photographic plates in one pass with an accuracy of 4.8 microns r.m.s. error. A field of the size 50 x 100 square millimeters is measured in a few seconds. Suggestions are made as to how a better accuracy can be achieved through the way in which the measurements are arranged and by repetition of the measurements. It is suggested that the speed of photographic astrometric measurements can be improved by about two orders of magnitude, at no loss of accuracy, by proper use of the FSD.
The objective grating technique is discussed. From the investigation of actual material, it is established that the effect of coma varies significantly from plate to plate, also that a model linear in diameter and/or coordinate may be inadequate for its removal, and even introduce systematic errors. From this standpoint, the requirements of reference star systems are discussed.