Teaching Kepler's laws as more than empirical statements

At the pre-college and first-year college level of physics instruction, Kepler's laws are generally taught as empirical laws of nature. Introductory physics textbooks only derive Kepler's Second law of areas. It is possible to derive all of Kepler's laws mathematically from the conservation laws, employing only high-school algebra and geometry. Moreover, a treatment of Kepler's Third law can naturally proceed from the general elliptic orbit to the special case of a circular orbit. Consequently, a study of Kepler's Third law need not be restricted to circular orbits.