Write parametric equations for a two circle model as described above. Find he slope of the tangent to the motion as a function of time. B (t ) a(t ) Suggestions Choose the center of the big circle as (0, 0), and let's call its ra- dius R. Find the parametric equations for the rotating point on the small circle, of radius r, as x(t), y(t), rotating around the center which is it- self rotating on the big circle (let's call this "rotating center's" coordinates (a* (t), y*(t))). You will notice that the horizontal and vertical coordinates on the two circles simply add. We will also assume that the circular mo- tions happen with a constant angular velocity, that is a(t) = at, B(t) = Bt (that's ", where T is the period of the rotating point), which was also a constant assumption (planets on elliptical orbits do not move at a con- stant angular velocity, but follow Kepler's second law). For definiteness, consider a = 27 (one round trip per unit of time, which would presumably be "years"), and B = 367 (a full round trip around the smaller circle in 1/18 of unit time, as in 18 revolutions per year), R = 10, r = 1 as an artificial case. We can ssume, for definiteness, that (x(0), y(0)) = (r + R, 0). Here is a graph of the result: 16 -12 416 Ptolemy, but it has been argued that, since Hellenistic astronomers were fully aware that the solar system rotated around the Sun, and not the Earth, Ptolemy was reporting a calculation device to predict planetary motions not an actual physical model. In fact, using modern math ("Fourier Series") it can be shown that any periodic motion can be represented by the superposition of a sufficient number of circular motions