Secrets your physics textbook didn't reveal.  Compiled by Donald
E. Simanek  Is the path of a trajectory a parabola or an
ellipse?  Many physics textbooks tell you, in the early
chapters, that the path of a trajectory is a parabola. Indeed,
all of the mathematical formulae and calculations dealing with
trajectors of objects falling, thrown or propelled support that
interpretation. But in later chapters, when earth satellites and
ballistic missiles are discussed, the textbook may reveal that
their orbits are portions of ellipses. Later, when the orbits of
planets and comets are discussed, they are all elliptical, or,
in the case of non-periodic comets, hyperbolic.  Transforming an
ellipse to a parabola.  So what's going on here? What is the
mathematical shape of a trajectory?  It depends on your
coordinate system. When dealing with trajectories of short range
and near the earth's surface, we use a coordinate system in
which one axis is "horizontal" and one axis is "vertical". We
treat it as a cartesian coordin