Five easy assignments for an Advanced Honors Seminar on analytic mechanics , Spring , 2005

Geodesy is the science of measurement or mapping of the properties of the Earth’s surface. A good example of an interesting problem in geodesy is the gravitation acceleration g(λ) on earth as a function of the latitude λ = π/2 − θ. (The angle θ in spherical coordinates is sometimes called the co-latitude angle.) For background, also read Marion # 10-7 and 10-20. Newton already suggested in Principia (1687) that the Earth, because of its rotation about its own axis, is roughly an oblate spheroid with the polar radius Rp = b less than the equatorial radius Re = a. He therefore proposed that