Instrumental and atmospheric corrections for the reduction of photographic plates taken with sidereally driven satellite cameras

To obtain the direction of a vector from the earth towards a satellite with an accuracy of 0″.2 or better, some typical instrumental and atmospheric influences can no longer be ignored or neglected when reducing photograms taken with sidereally driven satellite cameras. The wobbling error and the permanent error of the camera pole axis, the starting delay and the systematic alternations of the rotation velocity as well as the influences of changes in the amount and in the direction of the astronomical refraction are discussed. Generally all these errors produce deformations of the satellite trail itself and in its relation to the background stars. However instrumental investigations and computations allow numerical corrections of the measured data and the elimination of all error influences, even with old data. The suggestions given refer to every model of a sidereally driven camera.     

TRIGONOMETRICAL HEIGHTS AND THE COEFFICIENT OF TERRESTRIAL REFRACTION

Abstract

Mr. A. J. Morley has contributed a series of articles in the Review (E.S.R., iv, 23, 16; iv, 25, 136 and vi, 40, 76) on the adjustment of trigonometrical levels and the evaluation of the coefficient of terrestrial refraction with a view to ascertaining how other Colonies and Dominions deal with these problems. This object is very commendable as several problems concerning both the observational and theoretical sides arise in height determinations, regarding which there is not much guidance in the usual treatises on the subject.     

THE TRANSVAAL-SOUTHERN RHODESIA GEODETIC CONNEXION

Abstract

In the original geodetic series in Southern Rhodesia—completed by Mr Alexander Simms in 1901—the geographical coordinates of all stations were referred to the point SALISBURYas origin. The coordinates of SALISBURY were fixed by interchange of telegraphic signals with the Royal Observatory at the Cape for longitude, combined with astronomical determinations of time, latitude, and azimuth (see Vol. III, “Geodetic Survey of South Africa”).     

天文测量中减弱大气折射影响的方法

大气折射是对天文测量精度影响较大的因素之一，至今无法将其完全消除，只能尽量减弱。因此，处理好大气折射改正，是提高天文测量精度的一项重要任务。文中分析了大气折射的特点．介绍了传统天文测量对大气折射的处理方法；研究并实现了新的处理大气折射的方法，给出了具体解算公式。新方法的应用，使天文测量的效率、精度都得以大大提高。     

The accuracy of astronomic azimuth determinations

Astronomic azimuths are used in classical geodesy, through the Laplace equation, to control the orientation of geodetic networks. The method most commonly used by the United States National Geodetic Survey for the determination of astronomic azimuth is often referred to as the “direction method”, and is based on observations of Polaris at any hour angle. We have analyzed repeat determinations, by analysis of variance (ANOVA) techniques, to derive realistic estimates of the expected accuracy of typical astronomic azimuths to be used in the readjustment of the North American Datum. We found that the dominant errors are systematic in nature, with a very important source being observer bias, or “personal equation”. We were unable to decompose the remaining systematic error, which presumably consists primarily of instrument biases, anomalous refraction, and setup errors. We found, from an analysis of determinations that were first corrected for observer bias, an increase in the variance of repeat azimuth determinations as a function of latitude that agrees reasonably well with theoretical expectations.     

THE LEVELLING OF A THEODOLITE

Abstract

A Fully equipped theodolite is provided with plate levels, an alidade level, and a striding level. An instrument not so equipped has no title to be considered a “Universal Instrument”, that is to say, an instrument designed for every kind of both terrestrial and celestial measurement. Without a striding level, for example, nothing beyond relatively rough astronomical measures can be expected in general. Modern instruments, capable of giving considerable refinement in terrestrial measures, are frequently not furnished with a striding level; and it is sometimes assumed, with the tacit approval of the makers, that such instruments are equally capable of giving refined astronomical results. On the older type of instrument a striding level—rarely not supplied—could have been, and sometimes was, extemporized; it seems as if ignorance of astronomy of position has led, at least in part, to the construction of theodolites in such a manner as actually to render such extemporization difficult.     

ANGULAR CORRECTIONS FOR THE LAMBERT ORTHOMORPHIC CONICAL PROJECTION

Abstract

In E.S.R., viii, 56, 70, Brigadier K. M. Papworth has given expressions for the angular corrections, known as (t – t) corrections, in the Lambert NO.2 Projection, derived from empirical considerations based on actual detailed calculations. Apparently some difficulty has been experienced in offering a proof. In view of the widespread use of the Lambert Projection in World War II, it is hoped that the following proof will be found to be of more than academic interest.     

LONG LINES ON THE EARTH: THE DIRECT PROBLEM

Abstract

19. Formulae.—In Nos. 6, vol. i, and 9, vol. ii, pp. 259 and 156, there has been described a new method for dealing with long geodesics on the earth's surface. There the so-called “inverse” problem has claimed first attention: given the latitudes and longitudes of the extremities of a geodesic, to find its length and terminal azimuths. It remains to discuss the “direct” problem : a geodesic of given length starts on a given azimuth from a station of known latitude and longitude; to find the latitude and longitude of its extremity and the azimuth thereat. The solution of this direct problem demands a certain recasting of the formulae previously given. In order of working the several expressions now assume the forms below.     

LAPLACE POINTS IN MODERATE AND HIGH LATITUDES

Abstract

A method of applying azimuth control to a survey is given in which the precision with which the astronomical position must be determined is proportional to tan (altitude) instead of tan (latitude) as in the orthodox method. By using the method with stars of low altitude the observational difficulties are greatly reduced, especially in high latitudes. Methods of observation and reduction are discussed which make it possible to avoid altogether special observations to determine the astronomical position.     

EVALUATION OF THE COEFFICIENT OF TERRESTRIAL REFRACTION

Abstract

In two previous articles (E.S.R., vol. iv, nos. 23 and 25) it was shown that, at the time of maximum diurnal temperature in the tropics, a definite relationship exists in the lower layers of the atmosphere between the magnitude of the coefficient of terrestrial refraction at a point and the height of that point above plain level, provided the weather is fine and clear. In fact the coefficient K increases with the height h, within certain limits which are probably defined by the condensation layer.     

Regional geopotential model improvement for the Iranian geoid determination

Spherical harmonic expansions of the geopotential are frequently used for modelling the earth’s gravity field. Degree and order of recently available models go up to 360, corresponding to a resolution of about50 km. Thus, the high degree potential coefficients can be verified nowadays even by locally distributed sets of terrestrial gravity anomalies. These verifications are important when combining the short wavelength model impact, e.g. for regional geoid determinations by means of collocation solutions. A method based on integral formulae is presented, enabling the improvement of geopotential models with respect to non-global distributed gravity anomalies. To illustrate the foregoing, geoid computations are carried out for the area of Iran, introducing theGPM2 geopotential model in combination with available regional gravity data. The accuracy of the geoid determination is estimated from a comparison with Doppler and levelling data to ±1.4m.     

An evaluation of some systematic error sources affecting terrestrial gravity anomalies

Terrestrial free-air gravity anomalies form a most essential data source in the framework of gravity field determination. Gravity anomalies depend on the datums of the gravity, vertical, and horizontal networks as well as on the definition of a normal gravity field; thus gravity anomaly data are affected in a systematic way by inconsistencies of the local datums with respect to a global datum, by the use of a simplified free-air reduction procedure and of different kinds of height system. These systematic errors in free-air gravity anomaly data cause systematic effects in gravity field related quantities like e.g. absolute and relative geoidal heights or height anomalies calculated from gravity anomaly data. In detail it is shown that the effects of horizontal datum inconsistencies have been underestimated in the past. The corresponding systematic errors in gravity anomalies are maximum in mid-latitudes and can be as large as the errors induced by gravity and vertical datum and height system inconsistencies. As an example the situation in Australia is evaluated in more detail: The deviations between the national Australian horizontal datum and a global datum produce a systematic error in the free-air gravity anomalies of about −0.10 mgal which value is nearly constant over the continent     

Gravimetric and astro-geodetic geoids and mean free-air anomalies in India

A preliminary gravimetric geoid with respect to the International Spheroid and the latest astro-geodetic geoid computed on the Everest and International Spheroids are given in the form of undulation maps over the Indian Sub—continent. 1⁰x1⁰ mean free-air anomalies (modified) on the Geodetic Reference System, 1967 (GRS-67) are also given for the whole country in the form of a chart. For the purpose of computing the gravimetric geoid, 5⁰x5⁰ mean free-air anomalies were used outside the area bounded by latitudes 0⁰ to 40⁰ N and longitudes 60⁰ to 100⁰ E and 1⁰x1⁰ mean free-air anomalies within these limits. The anomalies partly computed by Survey of India and mostly collected from other sources (such as B.G.I.) were utilised for this purpose. The astro-geodetic geoid is based on the astronomical data observed in India up to 1978.     

Uniquely and overdetermined geodetic boundary value problems by least squares

Least-squares by observation equations is applied to the solution of geodetic boundary value problems (g.b.v.p.). The procedure is explained solving the vectorial Stokes problem in spherical and constant radius approximation. The results are Stokes and Vening-Meinesz integrals and, in addition, the respective a posteriori variance-covariances. Employing the same procedure the overdeterminedg.b.v.p. has been solved for observable functions potential, scalar gravity, astronomical latitude and longitude, gravity gradients Г_xz, Г_yz, and Г_zz and three-dimensional geocentric positions. The solutions of a large variety of uniquely and overdeterminedg.b.v.p.'s can be obtained from it by specializing weights. Interesting is that the anomalous potential can be determined—up to a constant—from astronomical latitude and longitude in combination with either {Г_xz,Г_yz} or horizontal coordinate corrections Δx and Δy, or both. Dual to the formulation in terms of observation equations the overdeterminedg.b.v.p.'s can as well be solved by condition equations. Constant radius approximation can be overcome in an iterative approach. For the Stokes problem this results in the solution of the “simple” Molodenskii problem. Finally defining an error covariance model with a Krarup-type kernel first results were obtained for a posteriori variance-covariance and reliability analysis.     

LEAST-SQUARE ADJUSTMENTS OF TRIANGULATION DIRECTIONS VERSUS ANGLES

Abstract

IT has been assumed in the past that because angles for triangulation are usually observed by the direction method, therefore it must be more correct theoretically to perform the least-square adjustments by directions rather than by angles. It is fairly obvious that an adjustment of the same figure by directions will not give the same result as an adjustment by angles: the unknowns in each case are different and the number of directions is usually about 25 per cent. greater than the number of angles for the same figure. Strictly, the least square method is only applicable to observations from which all systematic errors have been eliminated, and in which the remaining errors are truly accidental. It is generally safe to assume that most survey errOlS consist of a random and a systematic part. Rarely, if ever, is it possible to state that all systematic error has been eliminated, strive how we may to take all precautions against it.     

CONVENTIONS AND GENERALIZED FORMULAE FOR THE ASTRONOMICAL TRIANGLE

Abstract

In the October 1953 issue of this Review (E.S.R. xii, 90, 174), Mr. J. G. Freislich has written of the difficulties of a southern hemisphere computer attempting to use astronomical formulae from a textbook prepared for use in the northern hemisphere. He proposes a solution in which different conventions are adopted in the two hemispheres, leading to different formulae for the two cases, a solution which the present writer does not favour.     

PRACTICAL APPLICATION OF THE LAPLACE LONGITUDE-AZIMUTH RELATION TO CONTROL OF GEODETIC ANOMALIES

Abstract

1. In geodetic work a ‘Laplace Point’ connotes a place where both longitude and azimuth have been observed astronomically. Geodetic surveys emanate from an “origin” O, whose coordinates are derived from astronomical observations: and positions of any other points embraced by the survey can be calculated on the basis of an assumed figure of reference which in practice is a spheroid formed by the revolution of an ellipse about its minor axis. The coordinates (latitude = ?, longitude = λ and azimuth = A) so computed are designated “geodetic”.     

Stability of the determination of earth rotation parameters (ERP) from VLBI

The observations of theIRIS network are used to study the stability of the determination ofERP fromVLBI. It is concluded that the uncertainties in the initial values ofERP, the errors of other parameters and analyst noise are at the same level as the formal errors in the determination ofERP. The geometric effect on the determination ofERP is important and gives rise to systematic errors. The geometric effect on polar motion is greate than onUT1, and much greater for the continental network. The stability of the determination ofERP fromVLBI can be improved either by creating new stations at reasonable locations in a network or by creating new networks. At last a comparison is provided between the determinations ofERP from theIRIS andTEMPO networks.     

THE STEREOGRAPHIC SOLUTION OF THE SPHERICAL TRIANGLE

Abstract

In the course of his stimulating and suggestive paper in your recent issue, No. ro, pp. 226–38, Mr. A. J. Potter writes on p. 233 “but there is no simple construction by which X can then be found”, and again on p. 237 “a direct construction, if there be such”. This cheerful challenge invites the construction of a circle centred on a given line, passing through a given point thereon, and touching a given circle, and I have found the lure of Mr. Potter's gauntlet as irresistible as its recovery has proved delicate. In order to shoulder responsibility and by no means to claim highly improbable originality, let me confess that the problem is new to me and the two constructions I offer are my own; I venture to hope that Mr. Potter may consider one or other of them not unworthy of his epithet “simple”, though I freely admit the aptitude of his empiric procedure to its purpose. The proofs are not long, but for fear of overshooting my welcome I offer them to anyone for the asking; and for the same reason my diagrams are small and therefore mere.