text: The orbiting body's initial position() and velocity() are known
  The ellipse lies within the XY-plane
  The fourth assumption can be made without loss of generality because any three points (or vectors) must lie within a common plane.   Under these assumptions the second focus (sometimes called the "empty" focus) must also lie within the XY-plane:  .
  Using vectors
  The general equation of an ellipse under these assumptions using vectors is:
  where:
  is the length of the semi-major axis.
  is the second ("empty") focus.
  is any (x,y) value satisfying the equation.
  The semi-major axis length (a) can be calculated as:
  where  is the standard gravitational parameter.
  The empty focus () can be found by first determining the Eccentricity vector:
  Where  is the specific angular momentum of the orbiting body:
  Then
  Using XY Coordinates
  This can be done in cartesian coordinates using the following procedure:
  The general equation of an ellipse under the assumptions above is:
  Given:
  the initial position coordinates
  the initial velocity coordinates
  and
  the gravitational parameter
  Then:
  specific angular momentum
  initial distance from F1 (at the origin)
  the semi-major axis length
  the Eccentricity vector coordinates
  Finally, the empty focus coordinates
  Now the result values fx, fy and a can be applied to the general ellipse equation above.