积极 AI Logo 积极 AI

近极地轨道卫星

近极地轨道卫星
几何画板及绘图内容加载中，请稍等……
2016-02-04 21:46
圆变换参数方程
该范例演示了近极地轨道卫星的运行轨迹。涉及的核心数学概念包括圆的几何性质、参数方程和变换。通过使用GeoGebra命令如Rotate、Point、Circle等，可以动态展示卫星的轨道变化。适合高中及以上学生或教师使用。

GeoGebra 命令及参数

  1. Rotate(IntersectPath[Rotate[Plane[Line[centreearth, (x(centreearth) + 1, y(centreearth), z(centreearth))], Line[centreearth, (x(centreearth), y(centreearth) + 1, z(centreearth))]], ((-orbitinclination))°, Line[centreearth, (x(centreearth), y(centreearth) + 1, z(centreearth))]], Sphere[centreearth, radiusearth + altitude]], ((-15 * timeofday))°, Line[(0, 0, 0), (0, 0, 1)]) → orbit
  2. Point(orbit, orbitpos) → satellite
  3. Sphere(centreearth, radiusearth) → planet
  4. Segment(satellite, Intersect[Line[satellite, centreearth], planet]) → height
  5. Sphere(centreearth, radiusorbit + focallength) → a
  6. Intersect(Line[satellite, centreearth], a) → A, B
  7. OrthogonalLine(A, orbit) → c
  8. Point(c) → S1
  9. Point(c) → S2
  10. Intersect(Line[S1, satellite], planet) → E, F
  11. Intersect(Line[S2, satellite], planet) → G, H
  12. IntersectPath(Plane[(x(centreearth), y(centreearth), z(centreearth)), (x(centreearth) + 1, y(centreearth), z(centreearth)), (x(centreearth), y(centreearth) + 1, z(centreearth))], planet) → equator
  13. Segment((0, 0, radiusearth + (radiusearth * 0.2)), (0, 0, (-(radiusearth + (radiusearth * 0.2))))) → earthaxis
  14. PointIn(planet) → merideanpoint
  15. Circle(merideanpoint, (0, 0, (-radiusearth)), (0, 0, radiusearth)) → meridean
  16. Point(c) → S3
  17. Rotate(meridean, 45°, Line[(0, 0, 0), (0, 0, 1)]) → meridean45
  18. Rotate(meridean, 90°, Line[(0, 0, 0), (0, 0, 1)]) → meridean90
  19. Rotate(meridean, 135°, Line[(0, 0, 0), (0, 0, 1)]) → meridean135
  20. IntersectPath(Plane[(x(centreearth), y(centreearth), z(centreearth) + (radiusearth * sin(latitude°))), (x(centreearth) + 1, y(centreearth), z(centreearth) + (radiusearth * sin(latitude°))), (x(centreearth), y(centreearth) + 1, z(centreearth) + (radiusearth * sin(latitude°)))], planet) → parallel
  21. Intersect(Line[satellite, centreearth], planet) → C, D
  22. CircumcircleArc(E, C, G) → coverage
  23. Point(orbit, 0.25 + viewaltitude / 360) → viewpoint
  24. If((orbitpos ≥ 0) ∧ (orbitpos ≤ 0.5), true, false) → descending
  25. If(abs(orbitpos - latitudepos) ≤ miss, true, false) → pass