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Stellar Parallax Demonstration

Stellar Parallax Demonstration
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2015-10-24 19:47
VectorTrigonometryCoordinate GeometryGeometric Construction
In collections MalinC's GeoGebra-book
This example demonstrates the stellar parallax phenomenon, showing how the apparent position of a star changes as Earth orbits the Sun. It involves core mathematical concepts like trigonometry, vector operations, complex numbers, and coordinate geometry. The construction uses GeoGebra commands and objects such as Point, OrthogonalLine, Ray, Intersect, Vector, Translate, Segment, Polygon, Circle, and CurveCartesian to model celestial bodies and geometric shapes. Suitable for high school and above students learning about astronomical parallax measurements and geometric modeling applications.

GeoGebra Commands & Parameters

  1. Point(yAxis) → Star0
  2. Point(yAxis) → A
  3. OrthogonalLine(A, yAxis) → a
  4. Ray(Earth0, Star0) → b
  5. Intersect(b, a) → B
  6. Vector(A, C) → u
  7. Translate(B, u) → B'
  8. Vector(Star0, B') → v
  9. Segment(Earth0, B) → c
  10. OrthogonalLine(Rect1, yAxis) → d
  11. Point(d) → Rect2
  12. OrthogonalLine(Rect2, d) → e
  13. Point(e) → Rect3
  14. Polygon(Rect1, Rect2, Rect3, Rect4) → poly1, rect1, rect2, rect3, rect4
  15. Translate(pic1, u) → pic1'
  16. Circle((0, 0), 1) → SunCircle
  17. CurveCartesian(((earthOrbit * cos(t)) * 1.5), ((earthOrbit * sin(t)) * 0.9), t, 0, 6.283185307179586) → ell
  18. Translate(pic2, v) → pic2'