Now you do not specify the number of steps, but only a tolerance on how much change in the angle of the velocity vector you will allow in one step. In this way the algorithm is adapted to the problem. The Runge-Kutta was given 200 steps but ran off the screen before the calculation was completed. The adaptive algorithm did the job in 119 steps, with the step-size controlled to keep the rotation of the velocity vector below .1 radian per step. To carry out the entire calculation at this step size would have required over 5000 steps.
More eccentric orbits require tighter control on the velocity vector rotation.
Taking rotation tolerance .01 does the job. The looser tolerance does not allow a correct approximation of the solution. Newton's laws 2. Euler's method 3. The Runge-Kutta algorithm 4.