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Earth's Orbit and Seasonal Changes

Earth's Orbit and Seasonal Changes
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2019-04-12 03:32
CircleTransformationLocus
In collections GeoGebra 3D & AR: Geometry Resources & Challenges
This example demonstrates the Earth's orbit around the Sun and its impact on seasonal changes. Key mathematical concepts include circles, transformations, and loci. Using GeoGebra commands such as Circle, Rotate, and IntersectPath, the dynamic orbit of the Earth around the Sun is illustrated. Suitable for middle school students to learn Earth science and geometric constructions.

GeoGebra Commands & Parameters

  1. Circle((0, 0, 0), 25, zAxis) → c
  2. Sphere((-25, 0, 0), 5) → b
  3. Rotate(b, SPIN, (0, 0, 0), zAxis) → b'
  4. Center(b') → A_1
  5. Line(A_1, B_1) → f
  6. IntersectPath(xOyPlane, b') → d
  7. Surface(-25 + (sqrt(25 - ((5 * cos(u)))^(2)) * cos(v)), (sqrt(25 - ((5 * cos(u)))^(2)) * sin(v)), (5 * cos(u)), u, 0, (2 * π), v, 0, (2 * π)) → k
  8. Surface(-25 + ((5 * cos(u)) * sin(v)), ((5 * sin(u)) * sin(v)), (5 * cos(v)), u, 0, π, v, 0, π) → i
  9. Rotate(i, π / 2, xAxis) → i'
  10. Rotate(i, ((-π)) / 2, xAxis) → i'_1
  11. Sphere((0, 0, 0), 7) → a
  12. Line(A_1, A_1 + (1, 0, 0)) → j
  13. Rotate(i', SPIN, (0, 0, 0), zAxis) → i''
  14. Rotate(i'_1, SPIN, (0, 0, 0), zAxis) → l
  15. Rotate(i'', (23.5 * π / 180), A_1, Line[A_1, A_1 + (1, 0, 0)]) → i'''
  16. Rotate(d, (23.5 * π / 180), A_1, Line[A_1, A_1 + (1, 0, 0)]) → d'_4
  17. Rotate(l, (23.5 * π / 180), A_1, Line[A_1, A_1 + (1, 0, 0)]) → l'
  18. Rotate(f, (23.5 * π / 180), A_1, Line[A_1, A_1 + (1, 0, 0)]) → f'
  19. Segment((-25, 0, 0), (25, 0, 0)) → g
  20. Segment((0, -25, 0), (0, 25, 0)) → n