Mathematics

6.1.1 Solve for vx2 + vy2 to second order to show that vnew = v0. 6.1.2. Integrate vx and vy to show that x2 + y2 = r02 6.1.3. For the constraint that mg = mv02/r, compute v0 if the acceleration due to gravity is g = 9.8 m/sec2 and r is the radius of the earth. 6.1.4. Show that 2πrearth/v0 = Torbit = 84.4 minutes, the period of a Shuler pendulum. 6.2.1. Use the Excel spreadsheet (attached above) to plot graphs, which should be pasted into a single Word or pdf file, that illustrate all of the features listed in slide 4 of this sub-module. 6.2.2. Explain why the moon’s orbital period is 28 days, in apparent violation of Kepler’s third law.