Problem 1. Consider the one-particle Kepler's problem k -+ k > 0. (1) 1. Prove that the Laplace-Runge-Lenz vector A = pxl_kur (2) is a constant of motion, where p and are the linear and angular momentum of the particle, respectively. Since A is a vector and A/ǝt = 0, we have here three first integrals of motion. 2. Show that the equation of the orbit (1/r as a function of 0) can be easily derived from dA = 0. 3. Find 5 independent integrals of motion of the problem.