1) Start with same data for uncollected hw1, and simulate an entire orbital period. 

2) Plot trajectories from both ODE45 and true anomaly solution (as before)

 
The difference is now at point 3 of the previous HW:

3) compute the true anomalies corresponding at each time step created by the ODE45, USING THE NUMERICAL APPROACH TO SOLVING KEPLER's EQUATION. (find theta/s given time/s)

4) At those theta values computed above, compute the velocity vector using the true anomaly parameterization .

5) Verify that the velocity vectors obtained with ode45 and the parametric method coincide.

6) Plot time vs true anomaly. What plot from the book does it remind you of? How would it look like for a circular orbit?

7) play with the value of initial velocity to obtain various eccentricities below 1, and observe the behavior of the above plot

8) try to resolve the whole exercise for a circular orbit