DOI: 10.5593/SGEM2016/B22/S09.054

METHODS FOR CALCULATING THE LENGTH OF THE GEODESIC SPHERE

Thursday 8 September 2016

References: 16th International Multidisciplinary Scientific GeoConference SGEM 2016, www.sgem.org, SGEM2016 Conference Proceedings, ISBN 978-619-7105-59-9 / ISSN 1314-2704, June 28 - July 6, 2016, Book2 Vol. 2, 421-426 pp

ABSTRACT
We consider the approximation on Earth in a sphere of radius R, or we can consider reduced sphere (globe) radius Ro. On this point we consider M (ϕ,λ) şi M1(ϕ + Δϕ, λ + Δλ), where ϕ it is up to M, λ it’s longitude M, and Δϕ but Δλ is the difference in latitude longitude respect of M1 as against M. In this article we present two methods of calculating the length of the geodesic MM1 using the classical theory of Euclidean geometry and some related items spherical geometry. The geodesic line MM1 is the shortest way around the globe between M and M1 and it will be determined by cutting a sphere with a plane passing through M,M1, and O (center of the sphere) thus obtaining the length of the geodesic arc length MM1 before a large circle (circle of radius R). If I know the extent of this arc m(MM1) = v = m∡(MOM1) then in radians l(MM1) == vR and the reduced scope l(MM1) = vRo.

Keywords: spherical geometry, geodesic line, circle of spring

PAPER DOI: 10.5593/SGEM2016/B22/S09.054, METHODS FOR CALCULATING THE LENGTH OF THE GEODESIC SPHERE