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Orbit around the Planets 2a: Multi-body Motion and Geometric Construction

Orbit around the Planets 2a: Multi-body Motion and Geometric Construction
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2020-06-27 08:28
CircleVectorCoordinate GeometryTransformationSlider Animation
This example demonstrates orbital motion around multiple planets, using dynamic geometry to visualize celestial trajectories and related geometric relationships. Core mathematical concepts include circles, conic sections, coordinate geometry, vector translation, and subtraction, while also incorporating statistical elements such as distributions and binomial distribution, though the primary focus remains geometric construction and motion simulation. Construction highlights: GeoGebra commands such as Point, Segment, Polygon, Slope, Circle, Area, PointIn, Line, Intersect, Name, Midpoint, Vector, and Translate are used to build multiple points, segments, polygons, circles, and vector objects, with sliders or parameters controlling orbital changes. Suitable for middle or high school mathematics or physics classes to demonstrate planetary motion, geometric transformations, and coordinate relationships, as well as to explore intersections between conic sections and statistical distributions.

GeoGebra Commands & Parameters

  1. Point(b) → A
  2. Point(c) → B
  3. Segment(C, A) → d
  4. Segment(C, B) → f
  5. Point(c) → D
  6. Segment(B, D) → i
  7. Point(Circle[A, 1.4142135623730951]) → F
  8. Segment(A, F) → g
  9. Segment(A, F) → h
  10. Polygon(B, C, D) → poly1, d_1, b_1, c_1
  11. Segment(C, D) → d_h
  12. Point(c) → E
  13. Point(c) → G
  14. Segment(B, G) → τ
  15. Segment(F, G) → n
  16. Slope(n) → m
  17. Slope(d_h) → m_1
  18. Circle(C, A) → k
  19. Area(k) → e
  20. PointIn(k) → Pointk
  21. Line(H, f) → j
  22. Intersect(k, j, 2) → I
  23. Segment(C, I) → l
  24. Line(I, b) → p
  25. Intersect(p, d) → J
  26. Segment(C, J) → q
  27. Segment(J, I) → s
  28. Point(s) → K
  29. Segment(C, K) → t
  30. Segment(I, F) → a_1
  31. Segment(J, A) → e_1
  32. Polygon(C, I, F, G, B) → poly2, c_2, i_1, f_1, g_1, b_2
  33. Name(o) → A1
  34. Name(u) → B1
  35. Name(a) → C1
  36. Point(k) → L
  37. Circle(M, N) → h_1
  38. Point(h_1) → O
  39. Point(h_1) → P
  40. Midpoint(O, P) → Q
  41. Segment(M, O) → j_1
  42. Segment(z_1, z_2) → k_1
  43. Vector(T, U) → v
  44. Translate(z_1, v) → z_3
  45. Translate(z_2, v) → z_4
  46. Segment(z_3, z_4) → l_1
  47. Point(l_1) → V
  48. Segment(V, W) → n_1
  49. Segment(V, Z) → p_1
  50. Segment(V, A_1) → q_1
  51. Segment(V, B_1) → r_1
  52. Segment(V, C_1) → s_1
  53. Segment(V, D_1) → t_1
  54. Segment(V, E_1) → a_2
  55. Segment(V, F_1) → d_2
  56. Segment(V, G_1) → e_2
  57. Point(j_1) → H_1
  58. Circle(H_1, I_1) → f_2
  59. Circle(H_1, J_1) → g_2
  60. Circle(H_1, K_1) → h_2
  61. Circle(H_1, L_1) → k_2
  62. Circle(H_1, M_1) → p_2
  63. Circle(H_1, N_1) → q_2
  64. Circle(H_1, O_1) → r_2
  65. Point(h_1) → P_1
  66. Circle(H_1, P_1) → s_2
  67. Segment(V, Q_1) → i_2