Did you see that movie "The Martian"? It was not too bad but since the movie came out, there has been quite a lot of information provided on the planet but what math is required to get us there?
If you want to build interest in doing some of the math, start with this wonderful article which looks at the real life science of the craft and the mission in the movie.
If you want to show how important precision is when planning a mission, because a small error can cost a huge amount of money. According to an article in the LA Times some engineers forgot to convert standard measurements to metric and the $125 million Mars Climate Orbiter was lost.
The JPL navigation team did their calculations in metric while the Lockheed Martin chose to do their calculations in standard English measurements such as inches and feet.
Unfortunately, the error caused the craft to miss Mars. Just a small error can have far reaching results.
This 10 page pdf has some wonderful information on orbits, planning to get a spacecraft from the earth to mars along with the mathematical equations used for the trip. It introduces Kepler's laws which deal with the planetary travel, Newton's laws of motion, and includes lots of illustrations to help people see what is happening.
Another good site is the Rocket and Space Technology page on orbital mechanics which also looks at the mathematics involved such as conic sections, orbital elements, types of orbits, uniform circular motion, the motions of planets and satellites, the math involved in the launch of a space vehicle, along with orbit tilt, rotation, and orientation.
Furthermore, it takes time to explore position in the elliptical orbit. orbital maneuvers, and so much more material. Each topic has a good explanation with the math. This might be good for a trigonometry class because many of the equations use trig. I think I'm going to spend a couple of days just showing them these equations so they see the real life applications of tangent functions.
For classes that are not quite as high mathematically, Teach Engineering has a lovely lesson to look some of the forces and such that engineers must consider when planning to send a spacecraft to Mars. It gives the background on what is needed, has pictures, and provides thrust for various engines. Although it does not give as many equations, it does provide data, so students can calculate force, etc.
This would be a cool cross curricular unit with the science department. What do you think.