Whilst we are thinking about orbital mechanics, I want to comment that there is

Question

Whilst we are thinking about orbital mechanics, I want to comment that there is an interesting relationship between the Solar System planet's semi-major axis and a simple numerical series. The relationship states that the semi-major axis of planets in our Solar System conforms to (where 10 = 1AU): a = 4 + n Where a = semi-major axis n = 0, 3, 6,12, 24, 48... n, with the exception of the first step, has each value is twice the previous value. Thus the 3rd planet from the Sun (Earth) has a semi-major axis (a) = 4+6 = 10, or 1AU. A. Compare this relationship to the actual distances of the planets in our Solar System. Computer their percentage difference from reality.

Explanation / Answer

a = 4+n(AU)            actual distance(AU)                 percentage difference

    0.4                         0.387                                   3.35

    0.7                           0.723                                    3.181

1                            1.000                                     0

     1.6                             1.524                                   4.987

      2.8                          5.203                                  46.185

     5.2                           9.537                                 45.476

    10                             19.191                               47.892

     19.6                        30.069                                 34.816

     38.8                        39.482                                1.727

    

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