Geodetic model for teaching motion on the Earth’s spheroidal surface

Abstract

We explore the forces that shape our spheroidal earth and the forces that govern the motion of a puck that slides without friction on its surface. The earth s stable spheroidal shape (apart from small-scale surface features) is determined by balancing the gravitational forces that hold it together against the centrifugal forces that try to tear it apart. The motion of a puck on its surface differs profoundly from motion on a sphere because the earth s spheroidal deformations neutralize the centrifugal and gravitational forces on the puck, leaving only the Coriolis force to govern the motion. Yet the earth s spheroidal deformations are small and difficult to see in scale drawings. To assist students in exploring the crucial role of these deformations for motion on the earth s surface, we develop a model of uniformly rotating homogeneous earth-like planets with arbitrary eccentricities and arbitrary angular speeds of rotation, derive equations of motion for a puck sliding on the frictionless surface of such a planet, and introduce CorioVis software for visualizing this motion. By construction, this model replicates the rotational properties of the reference spheroid that is used in terrestrial cartography, geodesy, and the global positioning system.