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Geometri Gymnasiematematik(high school math) matematik 2c

Conical sections

280px-Conic_section_-_clean

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/b=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=ax

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