The force of gravity determines the trajectories of the celestial bodies. Mathematical analysis reveals that there are three types of trajectories possible for a body moving in a gravitational field determined by Newton’s law of gravity.

• If one of the bodies has very high speed relative to the other the moving body traces out a hyperbola. The equation for this is
  x ²/a² – y ²/b² =1
• If the speeds of the bodies are beelow a certain threshold value they move in an elliptical curve. x ²/a² + y ²/b² =1
• The limiting case between the hyperbola and the ellipse is the parabola. y=ax² 

Those geometrical objects can be illustrated by slicing the cone according to the figure above.