Conics and Orbits

In a first look at the motion of an object under the influence of gravity, one often makes the simplifying assumption that while an object is in motion near the surface of the earth the force of gravity is constant. Under this assumption, the equations for acceleration, velocity and distance are simple polynomials in time which are easily solved with high school algebra. In particular, the resulting equation of motion is a quadratic equation in time meaning that the path of the object's motion is a parabola. How close is this parabolic path to the actual (gravity varying with distance from the center of the earth) path?

Conics and Orbits is a paper that I worked on in 2013 to address this question. It first takes a Geometric look at Conics in which the basic properties of Conics are developed directly from their definitions as sets of points with a fixed ratio of distances to a fixed point and a fixed line. It then examines the fundamentals of Orbits to show that their paths are conics. At the end it gives a quantitative answer to how good the approximation of a parabola is to the true path (very good for moderate initial velocities)!

In case link does not work, copy this address in browser:
https://drive.google.com/file/d/0B9grE0MhdrFLRHYwV29FWDNzejA/view?usp=sharing