ON PERIODIC POLAR ORBITS IN THE ARTIFICIAL-SATELLITE PROBLEM

We compute periodic orbits in the Artificial Satellite Theory. We fix our attention on the Earth case where we considered a zonal gravitatio nal model for the potential. In a rotating frame attached to the Earth we have found sixteen polar orbits that are periodic after different number of revolutions. The altitude of each orbit remains almost const ant and varies from about 263 km for the sixteen-revolutions orbit to about 35,830 km for the one-revolution orbit. All the orbits are linea rly stable and their period is exactly 24 hours.