Comparisons Between Gauss and Gnomonic Projectionsin Polar Regions

To overcome the singularity of traditional formulae of Gauss projection on the sphere in po-lar regions,the traditional formulae were improved and lastly nonsingular formulae of Gauss projec-tion in polar regions were carried out with introduction of colatitude.Based on the nonsingular formu-lae,equations of meridian and parallel were got.Compared with gnomonic projection,analysis oflength deformation and meridian deviation angle of Gauss projection were done.It’s showed thatwhen the colatitude was small,Gauss projection was similar to gnomonic projection,in other words,graticules of the two projections were approximate.Length deformation of Gauss projection was smal-ler than gnomonic projection’s,and the largest meridian deviation angle of Gauss projection from gno-monic projection is 2.468 8°in polar circles,while the largest value above the line of latitude=80°is0.438 6°.The nonsingular formulae in polar regions could satisfy the need for continuous polar projec-tion and provide theoretical basis for polar charting.