Simplified Expansions of Common Latitudes with Geodetic Latitude and Geocentric Latitude as Variables

Using the symbolic calculation program Mathematica and based on power series expansions of common latitude with geodetic as a variable, geocentric variable are derived. The coefficients two groups formulas ellipsoid eccentricity e third flattening n, which make more uniform. Taking CGCS2000 an example, numerical analysis is applied to verify accuracy reliability derived expansions. By analyzing calculating truncation error ellipsoidal n expansion different orders, we obtain simplified, practical for that satisfy requirement geodesic accuracy. Moreover, show formula has higher efficiency easier dissemination, enriches theory map projection, provides basis better display remote sensing images.