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Solar System Simulation

Solar System Simulation
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2015-05-17 03:25
VectorSolid GeometryGraphing
This example demonstrates the 3D graphic of Earth and an arbitrary Planet X orbiting the Sun in the ecliptic plane. It involves core mathematical concepts such as ellipse, plane figures, vectors, rotation, and locus. The construction utilizes GeoGebra commands and objects like Ellipse, Rotate, Angle, Ray, Intersect, Circle, Line, Point, Vector, Translate, Segment, Sphere, Tangent, Plane, OrthogonalLine, and IntersectPath. Suitable for high school and above students to learn about celestial motion and geometric relationships.

GeoGebra Commands & Parameters

  1. Ellipse(A, B, C) → c
  2. Rotate(C, α, A) → C'
  3. Angle(C, A, C') → β
  4. Ray(A, C') → a
  5. Intersect(c, a) → D,
  6. Circle(A, Segment[A, E]) → d
  7. Rotate(E, γ, A) → E'
  8. Angle(E, A, E') → δ
  9. Line(A, E') → b
  10. Point(b) → G
  11. Rotate(G, ε, E') → G'
  12. Angle(G, E', G') → ζ
  13. Ray(E', G') → g
  14. Rotate(C, 257.1*°, A) → C'_1
  15. Angle(C, A, C'_1) → η
  16. Line(A, C'_1) → h
  17. Rotate(C, 83.4*°, A) → C'_2
  18. Vector(D, A) → u
  19. Translate(D, u) → D'
  20. Point(Circle[A, k]) → J
  21. Segment(A, J) → l
  22. Rotate(J, γ, A) → J'
  23. Angle(J, A, J') → ι
  24. Point(Circle[A, m]) → K
  25. Segment(A, K) → n
  26. Rotate(K, γ, A) → K'
  27. Angle(K, A, K') → κ
  28. Ellipse(A, K', J') → p
  29. Rotate(C, θ, A) → C'_3
  30. Angle(C, A, C'_3) → ξ
  31. Line(A, C'_3) → i
  32. Rotate(A, ε, K') → A'
  33. Angle(A, K', A') → μ
  34. Ray(K', A') → q
  35. Rotate(p, Tilt, i) → p'
  36. Rotate(K', Tilt, i) → K''
  37. Rotate(A', Tilt, i) → A''
  38. Ray(K'', A'') → q'
  39. Intersect(q', p') → M, N
  40. Segment(D, M) → r
  41. Vector(D, A) → v
  42. Translate(D, v) → D'_1
  43. Translate(M, v) → M'
  44. Segment(D'_1, M') → r'
  45. Sphere(D'_1, k) → o
  46. Ray(D'_1, M') → s
  47. Intersect(s, o) → O, P
  48. Tangent(D, p') → t, a_1
  49. Intersect(t, p') → Q, R
  50. Intersect(a_1, p') → S, T
  51. Intersect(c, xAxis, 1) → U
  52. Intersect(c, xAxis, 2) → V
  53. Point(c) → W
  54. Point(c) → Z
  55. Point(c) → Z_1
  56. Point(c) → C_1
  57. Point(c) → E_1
  58. Intersect(c, h, 2) → A_1
  59. Point(c) → B_1
  60. Point(c) → D_1
  61. Point(c) → F_1
  62. Point(c) → G_1
  63. Point(c) → H_1
  64. Point(c) → I_1
  65. Point(c) → J_1
  66. Point(c) → K_1
  67. Plane(F_1, B_1, J_1) → w
  68. Rotate(w, 23.4*°, h) → w'
  69. OrthogonalLine(D'_1, w') → b_1
  70. IntersectPath(w', o) → c_1
  71. Intersect(q, q') → H
  72. Intersect(q, q') → I
  73. Intersect(q, q') → F
  74. Intersect(q, q') → L
  75. Intersect
  76. Intersect(p, p') → L_1, O_1, ,
  77. Intersect(p, q) → M_1, N_1
  78. Rotate(b, Tilt, i) → b'
  79. Intersect(zAxis, b') → R_1
  80. Point(h) → U_1
  81. Ray(R_1, U_1) → h_1
  82. Point(h_1) → V_1
  83. Vector(U_1, V_1) → u_1
  84. Intersect(h_1, c, 1) → W_1

AI Drawing Prompt Reference

Create a 3D simulation of a solar system, including the Sun, Earth, and an arbitrary planet X orbiting the Sun. Start by drawing the elliptical orbits of Earth and the arbitrary planet X around the Sun. Then rotate Earth and the planet X, calculate the angles, and draw their trajectories. Next, add other celestial bodies like Earth's satellite, and finally combine all the bodies and their orbits to form a complete solar system model.
The prompt above was compiled from the original drawing commands and is for reference only.