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Elliptical Orbit Animated by Mean Anomaly

Elliptical Orbit Animated by Mean Anomaly
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2016-04-12 03:44
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the varying speed of a planetary body moving along an elliptical orbit, visualized through mean anomaly animation. Key mathematical concepts include ellipse, mean anomaly, eccentricity, rotation, and geometric constructions. The construction leverages GeoGebra commands like Ellipse, Axes, Intersect, Circle, Point, Angle, Rotate, and more. It is suitable for high school students and enthusiasts studying orbital mechanics and applied mathematics.

GeoGebra Commands & Parameters

  1. Ellipse(S', S, Q) → ELLIPSE
  2. FirstAxis(ELLIPSE) → axis_1
  3. SecondAxis(ELLIPSE) → axis_2
  4. Intersect(axis_1, axis_2) → C
  5. Intersect(ELLIPSE, axis_1) → A', A
  6. Intersect(ELLIPSE, axis_2) → B', B
  7. Circle(C, A) → c_{CA}
  8. Point(c_{CA}) → M'
  9. Angle(A, C, M') → M
  10. Eccentricity(ELLIPSE) → e
  11. Rotate(A, E_M, C) → E'
  12. Angle(A, C, E') → E
  13. OrthogonalLine(E', axis_1) → E'_⊥
  14. Intersect(ELLIPSE, E'_⊥) → P_2, P_1
  15. If(M < π, P_1, P_2) → P
  16. Segment(S, P) → SP
  17. Angle(A, S, P) → θ
  18. Segment(C, M') → CM'
  19. Segment(C, E') → CE'
  20. FirstAxisLength(ELLIPSE) → a
  21. SecondAxisLength(ELLIPSE) → b