How to program 2D rocket physics? (calling all physicists)

Hey guys. I have been programming for a while now, but I decided to take a new challenge: program a 2D rocket simulator (just for reference, I am going for something similar to this http://venturebeat.com/2013/09/06/kerbal-space-program-like-simplerockets-brings-space-flight-to-mobile-devices/).

So essentially, I just need some help starting my project.How do you program celestial bodies/orbital mechanics? How do you program the basic physics that allow the rocket to work (newtonian dynamics, n-body, etc)? Also, what math will be involved (I assumed geometry, algebra, and calculus)?

I know these questions are very broad, but I really only need a place to start, so resources, guides, or tutorials would be extremely helpful. Thanks!

 

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Google kerball. They did a few presentations at various Unites about orbital mechanics.

 

Thanks.

 

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