# From projectile motion to orbits using Geogebra

I was inspired last night while watching the launch of the Mars Science Laboratory that instead of doing banked curve problems (which are cool, but take a considerable investment of algebra to get into) we would move on to investigating gravity.

The thing that took me a long time to wrap my head around when I first studied physics in high school was how a projectile really could end up orbiting the Earth. The famous Newton drawing of the cannon with successively higher launch velocities made sense. I just couldn't picture what the transition looked like. Parabolas and circles (and ellipses for that matter) are fundamentally different shapes, and at the time the fact that they were all conic sections was too abstract of a concept for me. Eventually I just accepted that if you shoot a projectile fast enough tangentially to the surface of the Earth, it would never land, but I wanted to see it.

Fast forward to this afternoon and my old friend Geogebra. There had to be a way to give my physics students a chance to play with this and perhaps discover the concept of orbits without my telling them about it first.