New form of geodetic coordinate system taking two length quantity as coordinate parameters

Abstract

A new form of geodetic coordinate system based on geodesic coordinates instead of geodetic longitude and latitude was proposed. The vertical and horizontal geodesic coordinates measured with length were defined as coordinate parameters, but the two families of coordinate curves were still meridians and parallel circles. The first fundamental form on the ellipsoidal surface and its three coefficients were deduced by the geodesic coordinate. The formula for the latitudinal scale factor of length for geodetic parallel lines was derived, by which the obtained result conformed to that standard value calculated from geodetic latitude, and it is applicable in the range of 400 km from north to south. Therefore, it lays the foundation for establishing the differential equation and differential relationship based on this type of coordinate parameters; and consequently, it is convenient and accurate enough to operate on the ellipsoidal surface in this new form of geodetic coordinate system.

Keywords

geodetic coordinate system / meridian and parallel circle / coordinate parameter / the first fundamental form on the ellipsoidal surface / latitudinal scale factor of length

References

[1] Kneissl M. Mathematisch Geodäsie (Landevermessung), Die geodätischen Berechnungen auf der Kugel und auf dem Ellipsoid. Jordan-Eggert-Kneißl. Handbuch der Vermessungskunde, Band Ⅳ, 10. Auf J. B. Metzlersche,Verlagsbuchhandlung, Stuttgart:1959: 704-753, 1067-1093

[2] Grossmann W. Geodaetische Rechnungen und Abbildungen in der Landesvermessung, Dritte, Verlag Konrad Wittwer in Stuttgart, 1976: 31-56, 127-136

[3] Heck H. Rechenverfahren und Auswertemodelle der Landesvermessung. 3rd ed. Herbert Wichmann, Heidelbe: Springer, 2003: 123-152, 187-204

[4] Shi Yimin, Feng Yan. Establishment and application of another form of geodesic coordinate system on the earth ellipsoid. Journal of Tongji University (Natural Science), 2001, 29(11): 1282-1285 (in Chinese)

[5] Shi Yimin, Zhu Ziyang. The differential equations and differential relationship of geodesic lines in the geodesic coordinate system. Journal of Tongji University (Natural Science), 2003, 31(1): 40-43 (in Chinese)

Acknowledgements

The project was supported by the National Natural Science Foundation of China (Grant No. 40471114).

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg