# Conic Sections

In physics, the paths that can be taken by an object under gravitational attraction are called the conic sections. In mathematics these curves are obtained by taking a slice from a cone at different angles. These shapes are the circle, the ellipse, the parabola and the hyperbola. The circle and ellipse are bound orbits (like planets around the sun), and the parabola and hyperbola are unbound (like a deflecting rocketship on a slingshot orbit).

**Figure 1:** Illustration of the four different conic sections.

To determine whether an object with mass 'm' will follow a bound or unbound trajectory, meaning it will orbit the object with mass 'M' or escape the gravitational influence of the object, it is useful to apply conservation of energy and calculate the kinetic and gravitational potential energy of the object in the gravitational field of mass 'M'.