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Planets Retrograde Curve

Planets Retrograde Curve
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2020-01-06 16:37
Coordinate GeometryParametric EquationGeometric Construction
This example demonstrates the retrograde curve of planets. It involves basic concepts from astronomy and parametric equations. Using GeoGebra commands like CurveCartesian, users can construct the motion trajectories of planets. Suitable for high school students or astronomy enthusiasts.

GeoGebra Commands & Parameters

  1. CurveCartesian(x(B) + (2.2 * cos(((2 * π) * (t - i) / 2) - π / 2)) - (3.5 * cos(((2 * π) * (t - i) / 4) - π / 2)), y(B) + (2.2 * sin(((2 * π) * (t - i) / 2) - π / 2)) - (3.52 * sin(((2 * π) * (t - i) / 4) - π / 2)), i, 0, 4.29) → Mercure
  2. CurveCartesian(x(D) + (3.19 * cos(((2 * π) * (t - i) / 1.9))) - (2.07 * cos(((2 * π) * (t - i) / 1.108))), y(D) + (3.19 * sin(((2 * π) * (t - i) / 1.9))) - (2.07 * sin(((2 * π) * (t - i) / 1.108))), i, 0, 13.52) → Venus
  3. CurveCartesian(x(H) - (0.62 * cos(((2 * π) * t) - i)) - (4.85 * cos(((2 * π) * (t - i) / 60))), y(H) - (0.62 * sin(((2 * π) * t) - i)) - (4.85 * sin(((2 * π) * (t - i) / 60))), i, 0, 66) → Saturne
  4. CurveCartesian(x(G) - (0.76 * cos(((2 * π) * (t - i) / 5))) - (4.6 * cos(((2 * π) * (t - i) / 60))), y(G) - (0.76 * sin(((2 * π) * (t - i) / 5))) - (4.6 * sin(((2 * π) * (t - i) / 60))), i, 0, 60) → Jupiter
  5. CurveCartesian(x(C) + (R * cos(((2 * π) * (t - i) / aa))) - (r * cos(((2 * π) * (t - i) / bb))), y(C) + (R * sin(((2 * π) * (t - i) / aa))) - (r * sin(((2 * π) * (t - i) / bb))), i, 0, t) → c
  6. CurveCartesian(x(A) + (3.8 * cos(((2 * π) * (7.62 - i) / 7.6))) - (1.93 * cos((((2 * π) * 7.62) - i) / 0.067)), y(A) + (3.8 * sin(((2 * π) * (7.62 - i) / 7.6))) - (1.93 * sin((((2 * π) * 7.62) - i) / 0.067)), i, 0, 7.62) → Mars

AI Drawing Prompt Reference

Draw the retrograde curves of Mercury, Venus, Mars, Jupiter, and Saturn. Start with Mercury's curve using x(t) = 2.2 * cos(2π(t - i)/2 - π/2) - 3.5 * cos(2π(t - i)/4 - π/2), y(t) = 2.2 * sin(2π(t - i)/2 - π/2) - 3.52 * sin(2π(t - i)/4 - π/2), i from 0 to 4.29. Then draw Venus's curve with x(t) = 3.19 * cos(2π(t - i)/1.9) - 2.07 * cos(2π(t - i)/1.108), y(t) = 3.19 * sin(2π(t - i)/1.9) - 2.07 * sin(2π(t - i)/1.108), i from 0 to 13.52. Next, draw Mars's curve using x(t) = R * cos(2π(t - i)/7.62) - r * cos(2π(t - i)/0.067), y(t) = R * sin(2π(t - i)/7.62) - r * sin(2π(t - i)/0.067), i from 0 to 7.62. After that, draw Jupiter's curve with x(t) = 0.76 * cos(2π(t - i)/5) - 4.6 * cos(2π(t - i)/60), y(t) = 0.76 * sin(2π(t - i)/5) - 4.6 * sin(2π(t - i)/60), i from 0 to 60. Finally, draw Saturn's curve using x(t) = -0.62 * cos(2πt - i) - 4.85 * cos(2π(t - i)/60), y(t) = -0.62 * sin(2πt - i) - 4.85 * sin(2π(t - i)/60), i from 0 to 66.
The prompt above was compiled from the original drawing commands and is for reference only.