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Inner Planet Phases Simulation

Inner Planet Phases Simulation
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2015-06-14 18:14
CircleTrigonometryGeometric ConstructionLocus
This example demonstrates the phases of inner planets like Mercury and Venus as observed from Earth. It involves core mathematical concepts such as circles, rotations, and loci. The construction utilizes GeoGebra commands like Circle, Rotate, Locus, and Vector. Suitable for high school students studying astronomy and geometry to understand planetary motion and phase changes.

GeoGebra Commands & Parameters

  1. Circle(A, f) → f_1
  2. Rotate(B, α, A) → B'
  3. Rotate(B, γ, A) → B'_1
  4. Ray(A, B'_1) → g
  5. Intersect(f_1, g) → C,
  6. Segment(C, B') → j
  7. Circle(A, m) → p
  8. Intersect(p, yAxis) → I, J
  9. Intersect(p, xAxis) → K, L
  10. CircumcircleSector(F, K, I) → e_1
  11. Area(e_1) → s_1
  12. Angle(C, B', A) → ε
  13. Circle(A, e) → q
  14. Intersect(q, yAxis) → D, E
  15. Ellipse(D, E, F) → s
  16. Area(s) → t_1
  17. Area(s') → w_1
  18. Angle(A, C, B') → ζ
  19. Angle(B, A, B') → β
  20. Circle(A, B) → c
  21. Circle(B', a) → d
  22. Tangent(B', c) → b,
  23. Angle(B, A, B'_1) → δ
  24. Circle(C, h) → k
  25. Tangent(C, f_1) → i,
  26. Segment(A, B') → l
  27. Area(p) → n
  28. PointIn(p) → Punktp
  29. Area(s) → o
  30. PointIn(s) → Punkts_1
  31. If(ε ≥ 90°, x = u, x = t) → a_1
  32. Intersect(a_1, xAxis) → G
  33. Sphere(B', a) → b_1
  34. OrthogonalPlane(B', l) → c_1
  35. CircumcircleSector(F, L, I) → d_1
  36. Angle(g, l) → λ
  37. Circle(H, 0.5, xOyPlane) → g_1
  38. Angle(l, g) → η
  39. Locus(M, α) → Ortslinie1
  40. Vector(O, N) → u_1
  41. Point(u_1) → P
  42. Vector(P, Q) → v_1
  43. Tangent(C, c) → h_1, i_1
  44. Angle(h_1, i_1) → θ
  45. OrthogonalLine(R, xAxis) → j_1
  46. OrthogonalLine(S, v_1, xOyPlane) → k_1
  47. Segment(H, C) → l_1
  48. Point(Ortslinie1) → T
  49. OrthogonalLine(T, v_1, xOyPlane) → m_1
  50. Point(m_1) → U
  51. Segment(U, V) → n_1
  52. Point(m_1) → W
  53. Segment(W, V) → p_1
  54. Locus(V, α) → Ortslinie2
  55. PointIn(e_1) → Punkte1
  56. PointIn(s) → Punkts
  57. PointIn(s') → Punkts'