III. Bodes' Law

            In 1766, a German mathematician named Johann D. Titius developed an arithmetical relationship between the approximate distances of the planets from the Sun. Although it wasn't until 1772, when it was published by a man known as Johann E. Bode that it attracted attention. Today it carries his name and it's known as Bodes' Law.

            The law states the relationship between the planets can be expressed by adding 0.4 to each term in the progression - 0 , 0.3 , 0.6 , 1.2 , 2.4 , 4.8 , 9.6 , etc. ( in which each number is double the preceding one). Each term in the sequence is given in astronomical units, or A.U. ( 1 A.U. = 93 million miles, the mean radius of Earths distance from the Sun).9

            This is shown in the table below.

Table 1
Distance Mercury Venus Earth Mars Asteroid Belt Jupiter Saturn Uranus Neptune Pluto
Predicted

0.4

0.7

1

1.6

2.8

5.2

10

19.6

38.8

78
Actual

0.39

0.72

1

1.52

2.1-3.5

5.2

9.5

19.2

30.1

39.6

            At the time of the discovery of Bodes' Law, only six planets were known and the numbers closely fitted the observable facts with over 95% accuracy. However, as you can tell, with the discovery of the planets Neptune and Pluto, it seemed to bring the fatal blow to this theory and today is generally regarded as being merely a coincidence.

            However, if you select the last planet that fits this law, Uranus discovered in 1781 with its mean radius from the sun at 19.2 A.U. or approximately 1,785,600,000 miles. Followed by the planet Neptune at 30.1 A.U. ( 2,799,300,000 miles ) and Pluto at 39.6 A.U. ( 3,682,800,000- miles). You can tell there is still an arithmetical ( harmonic ) series at work. Each planet starting from Saturn, with a mean distance from the Sun of 9.5 A.U. ( 886,200,000 miles) and proceeding planet to planet. Continuing, out to Plutos' average orbit, reveals each of the planets has an average distance separating them of approximately 9 - 10 A.U.. As predicted by Bodes' law, it gives this close at 9.6 A.U. The importance of this observation will become apparent later.

            At this point, I'd like you to take notice of the other separating distances between the planets as predicted by Bodes' law. Starting at the planet Mercurys' mean radius point ( 0.4 A.U.) out to the planet Venuss' radius point ( 0.7 A.U.). You'll find the difference of 0.3 A.U. ( 27,900,000 miles) then between the planets Venus ( 0.7 ) and Earth ( 1 ) it remains 0.3 A.U..This planetary spacing then doubles between Earth and Mars to 0.6 A.U. and continues to double out to the planet Uranus. Clearly a harmonic series, and just to keep things straight I've constructed the following table.

Table 2
Planets Mercury Venus Earth Mars Asteroid Belt Jupiter Saturn Uranus Neptune Pluto
Bode's

0.4

0.7

1

 1.6 2.8 5.2 10 19.6 30.1 39.6

<Difference in A.U.>

          0.3

      0.3

    0.6

    1.2

         2.4

       4.8

      9.6

       9.6

         9.6

Table 3
0.3 A.U. =   27,900,000 miles Solar Dia. x 25 =    27,680,000 miles
0.6 A.U. =   55,800,000 miles Solar Dia. x 26 =    55,360,000 miles
1.2 A.U. = 111,600,000 miles Solar Dia. x 27 =  110,720,000 miles
2.4 A.U. = 223,200,000 miles Solar Dia. x 28 =  221,440,000 miles
4.8 A.U. = 446,400,000 miles Solar Dia. x 29 =  442,880,000 miles
9.6 A.U. = 892,800,000 miles Solar Dia. x 210 = 885,760,000 miles
( Solar Diameter = 865,000 miles ) ( 1 mile = 1.6 kilometers )

( Diagram 1 )

( Diagram 2 )


            I've taken the liberty of adding my own revisions to Bodes' law in the above ( Table 2 ), by placing Neptune and Plutos' mean radius numbers on the table. After all the two planets weren't discovered until after Bodes death and in spite of the fact it really isn't even his law! If Mr.Titius had even known of the two planets (Neptune, Pluto) existence, he might have made the additions himself. ( The right half of the lower Table 3 was added to show an observation that will be made clear later in this paper.)


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