# TEACHING CURVILINEAR COORDINATES WITH GOOGLE EARTH

Google Earth is a very interesting program with a lot of possibilities to be used in any classroom. The possibility of 3D visualisation of known places gives to the students a real perspective of the studied problems which is an important factor of motivation in the learning of sciences. In addition to the great deal of information about the natural landscape and human infrastructure on the Earth's surface, Google Earth also allows the study of some issues of physical sciences and mathematics. In this study, we present an analysis of the physical-mathematical model used by the Google Earth to calculate the distance between two points on the Earth surface. The analysis is based in the resolution of an inverse problem, i.e., it starts with the results and then calculates the causes. This investigation is based in the results given by the Google Earth, for some measures of the length of the arc connecting two points on the earth surface. These measures are used to predict the mathematical model used by the Google Earth. With that investigation was also developed a procedure to teaching spherical and oblate ellipsoid geometries and apply them to the study of planets.

On the other hand is well known that the geometry of the Earth is well approximated by an oblate ellipsoid, i.e., a slightly flattened sphere. Further are also analysed the distances given by Google Earth and geometrical models for the path between two points, on the Earth surface. The measures of the path between two points are used to determine the polar and equatorial radius of Earth, Moon and Marte, and then calculate the planets’ sphericity.