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Gaussian Gravitational Field Model

Gaussian Gravitational Field Model
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2018-07-29 02:13
FunctionCoordinate GeometrySlider Animation
This example demonstrates the distribution of a Gaussian gravitational field. Key mathematical concepts include the Gaussian function and standard deviation. Using GeoGebra commands, the model constructs the Gaussian gravitational field, including objects A, x_0, σ_x, y_0, σ_y, fg, CR, CG, CB, CO, α, r, B, etc. Suitable for high school physics and mathematics education.

GeoGebra Commands & Parameters

  1. Numeric A(-8.07)
  2. Numeric x_0(0)
  3. Numeric sigma_{x}(2)
  4. Numeric y_0(0)
  5. Numeric sigma_{y}(2)
  6. fg(x, y) = (A * exp((-((x - x_0)^(2) / ((2 * sigma_{x}^(2))) + (y - y_0)^(2) / ((2 * sigma_{y}^(2)))))))
  7. Numeric CR(0.92)
  8. Numeric CG(0.6)
  9. Numeric CB(0.34)
  10. Numeric CO(0.48)
  11. Angle α(5.061454830783556)
  12. Numeric r(1.9)
  13. (x_0 + (r * cos(α)), y_0 + (r * sin(α)), fg(x_0 + (r * cos(α)), y_0 + (r * sin(α))))