Welcome to mars!

Here is a picture of the rocket as it is orbiting our friend the red planet.

This picture shows the orbits of the three main bodies, the earth is in blue, mars is in red and the rocket has a yellow trail.

As you can see in the following image, the perigee of mars orbit is 3.414e6, and the equatorial radius of mars is 3.396e6. This shows that at its closest point the rocket is orbiting a mere 18 km above the martian surface!!!
For this project there was a significant investment in mathematical modeling which had to be augmented as simulations were run. In an ideal Hohmann transfer the velocity for a shift to an elliptical orbit can be calculated, but in our simulation there was a problem. The earth keeps following the rocket!!! because of this, the rocket is continuously decelerated through it's elliptical trajectory while inside the earth's sphere of influence. In order to compensate for this fact we modified the rocket's trajectory (read: strapped more rockets on with duct tape), and were able to model a more realistic Hohmann transfer. Finally, we had issues with Mars being in the same place we predicted it to be, so we defined a variable to represent Mar's theta for the initial conditions.
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If you look carefully at the second image, you will notice that mars is approximately 70-80 degrees out of phase with the earth, and this is absolutely essential. A Hohmann transfer has a very specific mission time associated with it, and once this is calculated it is a simple process to calculate how much out of phase the earth and mars must be in order to complete the transfer. Over all, this process was both challenging mentally and computationally, and I wish the rest of you good luck. I hope you are all looking forward to compensating for the effects of Jupiter and modeling rocket behavior!