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Dynamic Solar System with Elliptical Orbits

Dynamic Solar System with Elliptical Orbits
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2013-02-21 04:16
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates a dynamic simulation of a solar system with elliptical orbits. It involves core mathematical concepts such as ellipses, unit circles, power functions, trigonometry, reflections, and polygons. The construction utilizes GeoGebra commands like Intersect, Circle, Rotate, Angle, Ray, Ellipse, Point, OrthogonalLine, Segment, and Polygon. It is suitable for high school and above students to learn about celestial motion and geometric constructions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → Sun
  2. Circle(Sun, 1.0) → c
  3. Intersect(d, xAxis) → B, C
  4. Rotate(C, n°, Sun) → C'_1
  5. Angle(C, Sun, C'_1) → α
  6. Ray(Sun, C'_1) → a
  7. Intersect(d, a) → D,
  8. Circle(D, 0.1) → e
  9. Rotate(C, n + 10.0°, Sun) → C'_2
  10. Angle(C, Sun, C'_2) → β
  11. Ray(Sun, C'_2) → b
  12. Rotate(C, 1.2 * n + 45.0°, Sun) → C'_3
  13. Ray(Sun, C'_3) → i
  14. Rotate(C, 0.8 * n + 45.0°, Sun) → C'_4
  15. Ray(Sun, C'_4) → j
  16. Rotate(C, 0.8 * n°, Sun) → C'_5
  17. Angle(C, Sun, C'_5) → γ
  18. Ray(Sun, C'_5) → k
  19. Intersect(h, k) → F,
  20. Circle(F, 0.2) → p
  21. Rotate(C, 0.9 * n°, Sun) → C'_6
  22. Angle(C, Sun, C'_6) → δ
  23. Ray(Sun, C'_6) → g
  24. Intersect(f, g) → E,
  25. Circle(E, 0.15) → q
  26. Rotate(C, 0.7 * n°, Sun) → C'_7
  27. Angle(C, Sun, C'_7) → ε
  28. Ray(Sun, C'_7) → l
  29. Intersect(r, l) → G,
  30. Circle(G, 0.17) → s
  31. Rotate(C, 0.5 * n° + 35.0°, Sun) → C'_8
  32. Angle(C, Sun, C'_8) → ζ
  33. Ray(Sun, C'_8) → m
  34. Intersect(t, m) → A,
  35. Rotate(C, 0.3 * n° + 70.0°, Sun) → C'_9
  36. Angle(C, Sun, C'_9) → η
  37. Ray(Sun, C'_9) → a_1
  38. Intersect(d_1, a_1) → H,
  39. Circle(H, 0.3) → e_1
  40. Rotate(C, 0.3 * n° + 73.0°, Sun) → C'_{10}
  41. Rotate(C, 0.3 * n° + 73.0°, Sun) → C'_{11}
  42. Angle(C, Sun, C'_{11}) → θ
  43. Ray(Sun, C'_{11}) → b_1
  44. Intersect(d_1, b_1) → I,
  45. Rotate(C, 0.3 * n° + 67.0°, Sun) → C'_{12}
  46. Angle(C, Sun, C'_{12}) → ι
  47. Ray(Sun, C'_{12}) → f_1
  48. Intersect(d_1, f_1) → J,
  49. Rotate(C, 0.3 * n° + 75.0°, Sun) → C'_{13}
  50. Angle(C, Sun, C'_{13}) → κ
  51. Ray(Sun, C'_{13}) → g_1
  52. Intersect(d_1, g_1) → K,
  53. Ellipse(J, I, K) → h_1
  54. Circle(A, 0.45) → c_1
  55. Rotate(C, 0.2 * n° + 20.0°, Sun) → C'_{14}
  56. Angle(C, Sun, C'_{14}) → λ
  57. Ray(Sun, C'_{14}) → i_1
  58. Intersect(k_1, i_1) → L,
  59. Circle(L, 0.3) → p_1
  60. Rotate(C, 0.1 * n°, Sun) → C'_{15}
  61. Angle(C, Sun, C'_{15}) → μ
  62. Ray(Sun, C'_{15}) → j_1
  63. Intersect(q_1, j_1) → M,
  64. Circle(M, 0.25) → r_1
  65. Rotate(C, 2.0 * n°, Sun) → C'
  66. Angle(C, Sun, C') → ν
  67. Ray(Sun, C') → l_1
  68. Intersect(s_1, l_1) → N,
  69. Circle(N, 0.15) → t_1
  70. Point(l_1) → O
  71. Point(l_1) → P
  72. OrthogonalLine(O, l_1) → m_1
  73. OrthogonalLine(P, l_1) → n_1
  74. Point(m_1) → Q
  75. Point(m_1) → R
  76. Segment(N, Q) → a_2
  77. Polygon(N, Q, P, R) → poly1, n_2, q_2, p_2, r_2

AI Drawing Prompt Reference

Draw a dynamic solar system with elliptical orbits. Start with two intersecting axes to create a sun at the center, then draw a unit circle around it. Create multiple elliptical orbits by rotating and drawing rays, determining each planet's path through intersection points. Represent each planet as a small circle on its respective orbit. Adjust the angles and sizes of the orbits to simulate the planets moving around the sun, showcasing celestial motion and elliptical paths.
The prompt above was compiled from the original drawing commands and is for reference only.