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Kepler's Problem

Kepler's Problem
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2015-10-07 03:06
Coordinate GeometrySolid GeometryGeometric Construction
In collections On Sphere
This example illustrates Kepler's problem, involving concepts such as cylinder, sphere, volume difference, and slope. Using GeoGebra commands like Plane, Sphere, IntersectPath, Point, etc., the geometric shapes in Kepler's problem can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Plane(A, xOyPlane) → a
  2. Plane(A1, a) → b
  3. Sphere((0, 0, 0), 3) → c
  4. IntersectPath(a, c) → d
  5. IntersectPath(b, c) → e
  6. Point(d) → B
  7. Segment(A, B) → r
  8. Mirror(B, (0, 0, 0)) → B'
  9. Segment(A1, B') → j
  10. Segment(B, B') → k
  11. Mirror(B, A) → B'_1
  12. Mirror(B', A1) → B''
  13. Segment(B, B'') → l
  14. Segment(A, B'_1) → n
  15. Segment(A1, B'') → p
  16. Intersect(n, c, 2) → C
  17. Segment(C, B') → q
  18. Segment(A, A1) → s
  19. Intersect(k, s) → O
  20. Cylinder(A, A1, r) → f, h, t, i
  21. Segment(D, D1) → a_1