MathPlotAI Logo MathPlotAI

Lagrange Points V1.1

Lagrange Points V1.1
Loading the math board and drawing, please wait…
2019-05-14 12:21
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the geometric construction of Lagrange points. Key mathematical concepts include geometric transformations and loci. Using GeoGebra commands such as Circle, Point, Rotate, Line, and Segment, the positions of L1 to L5 Lagrange points relative to Earth and the Sun can be constructed. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Circle(Origin, 3.14) → orbit
  2. Point(orbit) → Earth_{01}
  3. Rotate(Earth_{01}, angle_{01} + 64°, Origin) → L_{4}
  4. Rotate(Earth_{01}, angle_{01} + 180°, Origin) → L_{3}
  5. Rotate(Earth_{01}, angle_{01} + 296°, Origin) → L_{5}
  6. Rotate(Earth_{01}, angle_{01}, Origin) → Earth_{02}
  7. Line(Origin, Earth_{02}) → f
  8. Point(f) → L_{2}
  9. Point(f) → L_{1}
  10. Segment(Origin, L_{4}) → g
  11. Segment(Origin, L_{3}) → h
  12. Segment(Origin, L_{5}) → i
  13. Segment(Origin, Earth_{02}) → j
  14. Circle(Origin, L_{1}) → Circle_{L1}
  15. Circle(Origin, L_{2}) → Circle_{L2}
  16. Rotate(L_{1}, angle_{01}, Origin) → L1_B
  17. Rotate(L_{2}, angle_{01}, Origin) → L2_B