Spherical Ellipse

Spherical Ellipse Construction

spherical ellipse const 001
Spherical Ellipse Construction, with Tangent

Leave text as is. (You may add that F1 is the north pole or that the sum of the distances from Q to F1 and F2 equals the radius of the circle - same definition as in the plane.)

  1. Let there be a fixed circle C with center F1 (north pole) on a sphere.
  2. Let there be a fixed point F2 inside the circle, not coincide with F1.
  3. Let P be a point on C.
  4. Let t be a line perpendicular to line[P, F2] and intersect midpoint[P, F2]
  5. Let Q be the intersection[line[F1,P], line[t]]
  6. As Q move about, Q traces out an ellipse, and t is its tagent at Q.

Note: t is a great circle. F1 and F2 are the foci.

Also, distance[Q, F1]+distance[Q, F2] equals the radius of the circle. This is similar to the definition of ellipse in the plane.

Spherical Ellipse 001

Spherical Ellipse with Osculating Circles

spher ellipse osculatin 001
Spherical Ellipse with osculating circles, the locus of their center is its evolute
Spherical ellipse normals 82801
Spherical ellipse normals in red

Spherical Ellipse with Different Eccentricies

spher ellipse expanding 001
spher ellipse with different eccentricies
spherical ellipse tube 07608
spherical ellipse, rendered as tube

Spherical_Ellipse.pdf