Solar System Model

Goals

• To render a (semi)realistic model of our solar systems major bodies (the sun, the observed planets, the natural planetary satellites [a/k/a the moons])
• Self-contained workflow
  • acquire required data without many external inputs

Data Sources

• Planetary Data - The Solar System OpenData
• Formulae
  • Semi Major Axis
    • The data source, The Solar System OpenData does not provide semiminorAxis data for planets (but does for moons). Since we use the parametric equation to form the orbital ellipse, we use a standard formula to derive the semiminorAxis from the known semimajorAxis and eccentricity values.

    • each planet's orbit about the Sun is an ellipse. The Sun's center is always located at one focus of the orbital ellipse. The Sun is at one focus. The planet follows the ellipse in its orbit, meaning that the planet to Sun distance is constantly changing as the planet goes around its orbit.

    • citation keplers laws

      • Deriving the semi-minor-axis from semi-major-axis & eccentrity values

        • The eccentricity (e) of an ellipse is a number that quantifies how elongated the ellipse is. It equals 1 - (perihelion)/(semi-major axis). Circles have an eccentricity = 0; very long and skinny ellipses have an eccentricity close to 1 (a straight line has an eccentricity = 1). The skinniness an ellipse is specified by the semi-minor axis. It equals the semi-major axis × Sqrt[(1 - e2)].

        • citation: Astronomy Notes

          • 
  • Orbital Rotation
    • Orbital rotation, representing a planets travel around the sound in a elliptical shapes
      • 
        • a is the semiMajor Axis, and b is the semiMinorAxis
        • t is generated by normalizing the frame value between 0 and 2pi

                                            

     

• Angular Rotation Calculations       From a top down view, given the imaginary lines drawn by the distances between objects:
  • a) orbitingBody(x,y) <-> radiusLen(0,y) (side a)
    • the distance from (0,0) to (0,planetsAverageRadius)
  • b) sunCenter(0,0) <-> orbitingBody(x,y) (side b)
    • the distance from (0,0) to the orbitingBody
  • c) sunCenter(0,0) <-> radiusLen(0,y) (side c)

                     

     

• The angle(alpha) is derived by:

  • not if:
    • y==0 && x==semiMajorAxis || y==0 && x==-semiMajorAxis
    • y==semiMinorAxis && x==0 || y==-semiMinorAxis && x==0
  • if [ ( x > 0 && x < semiMajorAxis ) && ( y > 0 && y < semiMinorAxis )] (Quadrant I)
    • 
  • if [ ( x > -semiMajorAxis && x < 0 ) && y > 0 && y < semiMinorAxis ] (Quadrant II)
    • 
  • if [ ( x > -semiMajorAxis && x < 0 ) && y > 0 && y < semiMinorAxis ] (Quadrant III)
    • 
  • if [ ( x > -semiMajorAxis && x < 0 ) && y > 0 && y < semiMinorAxis ] (Quadrant IV)
    • 

• Frame Normalization

def normalized_frame(mini= 0.0, maxi = math.pi*2):
    """
    mini: float (Min. value for normalize frame)
    maxi: float (Max. value for normalize frame)
    Returns normalized value for current frame between `mini` and `maxi` values
    """
    mini = float(mini)
    maxi = float(maxi)
    frame = float(bpy.context.scene.frame_current)
    print(f"frame value: {frame}")
    # use standard normalization function with frame values
    print(f"({maxi} - {mini}) * ({frame} - {mini}) / (float(frames()) - 1.00) + {mini}")
    return float(
        (maxi - mini) * (frame - mini) / (float(frames()) - float(1)) + mini
    )