Pyramid Science

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Monday, February 22, 2010

Orbit Distance With Time Relationship

The orbital distance (r) of any planet from the Sun has a definite relationship with the time it takes to circumnavigate the star. Considering the time (comparatively in P days) taken for a planet's 'year' and the distance from the central star either in millions of kilometres (mkm) or AU (Astronomical Units), a constancy is apparent.

Orbital Period (P days)

Mercury
  • P = 88, P2 = 7744
Venus
  • P = 224.7, P2 = 50490
Earth
  • P = 365.25, P2 = 133408
Mars
  • P = 686.9, P2 = 471832
Asteroid Belt
   
Jupiter
  • P = 4331.87, P2 = 18765098
Saturn
  • P = 10760.27, P2 = 115783411
Uranus
  • P = 30684.65, P2 = 941547746
Neptune
  • P = 60189.55, P2 = 3622781929
The Asteroid Belt is spread over a wide distance

Planetary distance (r) from the Sun (mkm, AU)

The respective planetary values below are for r, r3, AU, AU3

Mercury
  • 57.9, 194105, 0.387, 0.058
Venus
  • 108.2, 1266723, 0.723, 0.378
Earth
  • 149.6, 3348072, 1.000, 1.000
Mars
  • 227.9, 11836764, 1.523, 3.533
Asteroid Belt

Jupiter
  • 778.3, 471455918, 5.203, 140.852
Saturn
  • 1427, 2905841483, 9.539, 867.978
Uranus
  • 2871, 23664622310, 19.190, 7066.835
Neptune
  • 4497, 90942871470, 30.060, 27162.324

According to Kepler's third law

The respective planetary values below are for P2/r3, P2/AU3

Mercury 
  • 0.0399, 133517
Venus
  • 0.0399, 133571
Earth
  • 0.0398, 133408
Mars
  • 0.0399, 133550
Asteroid Belt                            

Jupiter
  • 0.0398, 133226
Saturn
  • 0.0398, 133394
Uranus
  • 0.0398, 133235
Neptune
  • 0.0398, 133375

Average
  • 0.0398, 133410
In both cases the constancy is clearly demonstrated and shows a relationship between a 2D quantity (function2) and a 3D quantity (function3).
    • A planet's 'year' will be completed after P days and it will travel through 360°. Relative to Mercury as the innermost planet and consequently the fastest moving, each of the other seven planets will move through less than this full circle. In the time taken for one complete orbit of Mercury (360°), the planet Venus will have moved only 88/224.7 * 360 = 140.99° and Earth by 88/365.25 * 360 = 86.735° and so on.
    Note: the ellipticity of a planet's orbit is ignored
    for the sake of this empirical argument

    Orbital Period (P days), Orbital (Circular) Angle °)

    Mercury
    • P = 88, θ = 360.00°
    Venus
    • P = 224.7, θ = 140.99°
    Earth
    • P = 365.25, θ = 86.735°
    Mars
    • P = 686.9, θ = 46.12°
    Asteroid Belt
           
    Jupiter
    • P = 4331.87, θ = 7.313°
    Saturn
    • P = 10760.27, θ = 2.944°
    Uranus
    • P = 30684.65, θ = 1.032°
    Neptune
    • P = 60189.55, θ = 0.526°
    The following values are derived from P and θ:
    • θ2 = 129600.00, AU3 = 0.058, θ2 * AU3 = 7516.80
    • θ2 = 19878.18, AU3 = 0.378, θ2 * AU3 = 7513.95
    • θ2 = 7522.96, AU3 = 1.000, θ2 * AU3 = 7522.90
    • θ2 = 2127.05, AU3 = 3.533, θ2 * AU3 = 7514.87
    • θ2 = 53.48, AU3 = 140.852, θ2 * AU3 = 7532.76
    • θ2 = 8.667, AU3 = 867.978, θ2 * AU3 = 7522.77
    • θ2 = 1.0658, AU3 = 7066.835, θ2 * AU3 = 7531.83
    • θ2 = 0.2767, AU3 = 27162.324, θ2 * AU3 = 7515.82
    In all cases the constancy is clearly demonstrated and again shows a relationship between a 2D quantity (function2) and a 3D quantity (function3).