Vol.6, No 1, 2007 pp.
179-187
UDC
537.51+531.2(045)=111
THE FUNDAMENTAL CRITERION FOR ESTIMATION
OF THE REFERENCE ELLIPSOID ACCURACY
Bogoljub Marjanović
Higher Technical School, Serbia, 34000 Kragujevac, Kosovska 8
E-mail: boca@kg.ac.yu
Abstract.
The value of the semi-major axis a, and the value of the semi-minor axis b are the geometrical characteristics of the reference ellipsoid. The other important characteristic is the normal gravity g, which represents the magnitude of the gradient of the gravity potential with the ellipsoid as an equipotential surface.
This paper presents the fundamental criterion for estimation of accuracy of the reference ellipsoid, which stems from the Newton's second law. It has been proved, by the analysis of the motion of particle along a meridian of the reference ellipsoid, that the algebraic sum of works of gravitational attraction force and centrifugal force, excited by rotational ellipsoid around its axis, equals to zero. This is an indispensable term that the direction of gravity vector is everywhere perpendicular to the ellipsoid surface as an equipotential surface. This is what makes this criterion reliable and enables the obtaining of the quantitative evaluation of the ellipsoid's accuracy. Applying this criterion for estimation of accuracy of the ellipsoid, defined according to the Geodetic Reference System 1980 (GRS80), it can be concluded that the ellipsoid's semi-minor axis contains an error of about 599 m.
Key words:
the reference ellipsoid, semi-minor axis, gravitational attraction, GRS80
OSNOVNI KRITERIJUM ZA OCENU TAČNOSTI REFERENTNOG ELIPSOIDA
Veličina veće poluose a, i veličina manje poluose b su geometrijske karakteristike referentnog elipsoida. Druga bitna karakteristika je normalna gravitacija g, koja pretstavlja intenzitet gradijenta gravitacionog potencijala na ekvipotencijalnoj površini elipsoida.
U ovom radu je pretstavljen osnovni kriterijum za odredjivanje tačnosti referentnog elipsoida koji proističe is drugog Njutnovog zakona. Analizom kretanja materijalne tačke, duž meridijana referentnog elipsoida, je dokazano da je algebarski zbir radova sile gravitacionog privlačenja i centrifugalne sile, nastale obrtanjem elipsoida oko njegove ose, jednak nuli. Ovo je neophodan uslov da pravac vektora gravitacije bude svuda upravan na površinu elipsoida kao ekvipotencijalnu površinu. Zato je ovaj kriterijum pouzdan i omogućava da se dobije kvantitativna ocena tačnosti elipsoida. Primenjujući ovaj kriterijum za ocenu tačnosti elipsoida definisanog prema the Geodetic Reference System 1980 (GRS80), može se zaključiti da manja poluosa elipsoida sadrži grešku od oko 599 m.
Ključne reči:
referentni elipsoid, manja poluosa, gravitaciono privlačenje, GRS80
