There are two factors of Mars exploration explored by this activity:

1. The time between launches to Mars. (Relative positions of Earth and Mars is important.)
2. The time required to travel to Mars after “leaving” Earth.

The Euler-Cromer method can be used to compute the orbits. Thus, this activity is accessible to introductory physics students who have already modeled constant force motion. However, the activity can be extended for students in intermediate mechanics who might compute the motion of the rocket during launch.

Finding the day to launch and the initial direction to launch requires trial and error. It is possible to change parameters and re-run the simulation. However, it may be desirable to have an interface by which one can adjust the parameters and more easily rerun the simulation. This GlowScript simulation trip-to-Mars shows how you can use a second window to interactively set the initial velocity of the rocket using your mouse to adjust an arrow. Then, you can click a button on the day of launch. However, this kind of interactivity is not built into the attached template and sample code.

JPL’s Horizons web interface can be used to obtain initial velocity and position of Mars and Earth on today’s date. If you do not wish to obtain new data, you can use data obtained on Aug. 29, 2015.

variable | value
--- | ---
r⃗ M a r s r→M a r s | 1000<−1.181709819034665 E+08,2.135080519845017 E+08,0>1000<−1.181709819034665 E+08,2.135080519845017 E+08,0> m
v⃗ M a r s v→M a r s | 1000<−2.028048448328753 E+01,−9.673026032986073,0>1000<−2.028048448328753 E+01,−9.673026032986073,0> m/s
r⃗ E a r t h r→E a r t h | 1000<1.371047699606275 E+08,−6.350801741095807 E+07,0>1000<1.371047699606275 E+08,−6.350801741095807 E+07,0> m
v⃗ E a r t h v→E a r t h | 1000<1.202828172495448 E+01,2.690745455098789 E+01,0>1000<1.202828172495448 E+01,2.690745455098789 E+01,0> m/s

Exercise 1 leads students through the exercise of obtaining this data for whatever date they want.

In Exercise 3, a very important point to make to students is that our initial velocity of the rocket is specified relative to Earth. However, its velocity in the simulation must be relative to the Sun. Therefore, the initial velocity of the rocket when launched is

v⃗ r o c k e t r e l a t i v e S u n=v⃗ r o c k e t r e l a t i v e E a r t h+v⃗ E a r t h r e l a t i v e S u n.(1)