Elliptic orbits
Focus and directrix construction of an ellipse
An ellipse is the set of points the same distance from a point S and a circle.
For the point P on the ellipse, segments SP and SQ have the same length, and the tangent line to the ellipse is the perpendicular bisector of SQ.
S is one focus of the ellipse, and the center of the circle, O, is the other focus.
The main claim to fame of Newton's calculus was a derivation of the motion of planets around the sun. Their orbits are elliptical, with the sun at one focus. The speed is not constant; in this diagram, the direction and size of the velocity are shown by the vector. Its length is the same as SI.
(The velocity vector in this diagram is not exactly the real life one, but it’s close.)
About the diagram:
- The slider makes point Q move around the circle, causing P to move around the ellipse. You can also use the animation button in the lower left.
- Some points can be dragged; try it. What changes?