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地球轨道可能轨迹

地球轨道可能轨迹
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2020-04-09 21:40
向量解析几何
这个范例演示了地球周围发射物体可能的轨道轨迹。涉及的核心数学概念包括椭圆、几何和向量。通过使用GeoGebra命令如Ray、Line、Circle、Intersect等，可以构造出物体的可能轨迹。适合高中及以上学生或相关科研人员使用。

GeoGebra 命令及参数

  1. Ray(F, j) → vert
  2. Point(xAxis) → A
  3. Line(F, A) → b
  4. Circle(F, A) → Terre
  5. Intersect(Terre, vert) → H,
  6. Ray(H, j) → possible
  7. Point(possible) → M_0
  8. Distance(F, M_0) → r
  9. Line(M_0, xAxis) → horiz_0
  10. Point(horiz_0) → B
  11. Vector(M_0, B) → v
  12. Length(v) → lv
  13. Midpoint(F', F) → D
  14. Segment(D, M_0) → d
  15. Line(D, b) → c
  16. Ellipse(F, F', Distance[M_0, M'_0] / 2) → traj
  17. Intersect(Terre, traj) → I, J, ,
  18. Intersect(traj, c) → E, G
  19. Segment(D, G) → e
  20. Mirror(BB_1, F) → BB_2
  21. Intersect(Terre, Segment[BB_1, B_4]) → B_1,
  22. Intersect(Terre, Segment[BB_2, B_3]) → B_2,
  23. Polygon(B_1, B_2, B_3, B_4) → tour, b_1, b_2, b_3, b_4
  24. Distance(C, J) → aa
  25. If(Distance[C, J] < 0.25, 0, 1) → Vitesse
  26. CurveCartesian((x(D) + (e * cos((-i) + π / 2)), y(D) + (d * sin((-i) + π / 2))), i, 0, f) → g
  27. Distance(A, F) → R
  28. Sequence(CurveCartesian[(x(D) + (j * cos((-i) + π / 2)), y(D) + (d * sin((-i) + π / 2))), i, 0, f], j, 30, 250, 20) → l1
  29. Element(l1, A1) → B1
  30. Element(l1, A2) → B2
  31. Element(l1, A3) → B3
  32. Element(l1, A4) → B4
  33. Element(l1, A5) → B5
  34. Element(l1, A6) → B6
  35. Element(l1, A7) → B7
  36. Element(l1, A8) → B8
  37. Element(l1, A9) → B9
  38. Element(l1, A10) → B10
  39. Element(l1, A11) → B11
  40. Element(l1, A12) → B12
  41. Element(l1, A13) → B13
  42. Element(l1, A14) → B14
  43. Element(l1, A15) → B15
  44. Element(l1, A16) → B16
  45. Element(l1, A17) → B17
  46. Element(l1, A18) → B18
  47. Element(l1, A19) → B19
  48. Element(l1, A20) → B20
  49. Element(l1, A21) → B21
  50. Element(l1, A22) → B22
  51. Element(l1, A23) → B23
  52. Element(l1, A24) → B24
  53. Element(l1, A25) → B25
  54. Element(l1, A26) → B26
  55. Element(l1, A27) → B27
  56. Element(l1, A28) → B28
  57. Element(l1, A29) → B29
  58. Element(l1, A30) → B30
  59. Element(l1, A31) → B31
  60. Sequence((x(D) + (j * cos((-f) + π / 2)), y(D) + (d * sin((-f) + π / 2))), j, 30, 250, 20) → l2