Imagine the Earth moving around the unit circle. We shoot a satellite into space, planning to have it reach a planet in another orbit in a specified time ( time = 5). The motion of the point M shows how to achieve this. You can do this same work on a graphics calculator, plotting in polar coordinates. Let r1=1, r2=2/(1+.5*cos(theta-1) (in radians), and r3=r1+(r2-r1)*theta/5.