286 PUBLICATIONS OF THE ELECTROMAGNETIC WAVES IN THE SOLAR* SYSTEM By C. O Connor During a great part oí his life Johann Kepler, one of the principal founders of modern astronomy, sought a basis for the Pythagorean concept of the music of the spheres. He believed one of his greatest discoveries was that of the regularity of planetary distances shown in the approximate ratio he found through the five regular solids. He said of this achievement : The intense pleasure I have received from this discovery can never be told in words. His labors were richly rewarded, however, through the discovery of the three fundamental astronomical laws forever associated with his name. He thought these laws were physically related to magnetism or vortical motion. In his time the velocity of light was unknown and planetary distances were known only relatively. The laws of electromagnetism were to be discovered much later. But with the additional knowledge at our command it can be shown now that the harmonic relationships he so diligently sought do actually exist. Planetary Mean Distances from the Sun in Miles (approx.) Mercury... 36,000,000 Venus 67,000,000 Earth 93,000,000 Mars 141,000,000 Orbital Velocities (miles per sec.) 29.8 21.8 18.5 14.9 Periods of Revolution in Seconds 7,600,000 19.400.000 31.500.000 59,200,000. Jupiter. Saturn. Uranus Neptune Pluto*. 483,000,000 ~ 885,000,000 8.1 6 373.000. 928.000. 1.780.000. 4.3 2.643.000. 0 2.850.000. 3.7 5.186.000. 0 3.800.000. 2.8 7.980.000. 0 * The planetary distances and periods used in this paper are approximations. The latest determination of Pluto s mean distance from the Sun is about 3,680,000,000 miles and the period of revolution about 247.697 years. The velocity of light is a statistical mean; the figure now accepted is about 186,324 mile/seconds.
ASTRONOMICA!. SOCIETY OF THE PACIFIC 287 The problem of planetary regularity has interested astronomers ever since Kepler s time. Titius, Bode, and many others have proposed different ratios, but no physical explanation of the phenomenon has been offered. Dr. Fernando Sanford of Stanford University in 1921 wrote that the regularity could be shown through a series of simple numbers. +5 +5 +5 +5 4-5 The squares of 3, 4, 5, 6,.. 11.. 16.. 21.. 26.. 31 i.e., 9,16,25,36, 121 256 441 676 961 when multiplied by appropriate length units (4 million miles or 6.4 million kilometers) are roughly as planetary mean distances from the Sun. Physicists have found that the characteristic line spectra of all atoms follow a similar progression of the squares of simple numbers, and the Bohr model of the atom is like a miniature solar system. Through a simple formula involving the velocity of light, it can be shown that planetary distances closely follow a common series of wave frequencies. The wave serial numbers are : Wave Serial Numbers Derived Planet Numbers through Formula Mercury 36 36 Venus 64 67 Earth 96 93 Mars 144 141 Vesta 216 Planetoid 324 Jupiter 486 483 Saturn... 7... 910 885 Uranus 1820 1780 Neptune 2730 2850 Pluto 4096 3800 These numbers, multiplied by appropriate length units (1 mil- lion miles or 1.6 million kilometers) are as planetary mean distances from the Sun.
288 PUBLICATIONS OF THE The formula is : Planetary distance \ Velocity of light / = Number. E.g., Earth : Radius of Sun \ 2 Velocity of light / / 149,000,000 km \ 298,000 km/sec. / 691,200 km \ 298,000 km/sec. - = 93 2 A related series of numbers shows direct correspondence between the velocity of light and the cube roots of planetary periodic times, in seconds : Planets Venus Earth Distance numbers 64 96 Periodic time numbers 256 324 Cubic roots of periodic time.. 268 316 Mars Vesta Planetoid Jupiter 144 216 324 486 384 486 576 729 390 480... 722 The periodic time serial numbers are as the square roots of the distance serial numbers multiplied alternately by 32 and 33, e.g. : V64 X 32 = 256; V96X 33 = 324; \/Ï44 X 32 = 384 ; V2Ï6 X 33 = 486, etc: Through the foregoing relationships the following formula is found : Planetary \ / Square of cube root of planetary \ orb. vel. / \\ periodic time in seconds / Velocity ; = of light Square root of planetary distance number (approx.) E.g., Earth : 29.7 km/sec. (31,500,000 sec.) V8 301,000 km/sec. The wave-frequency series heretofore mentioned is :
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290 PUBLICATIONS OF THE The planetary numbers extended from left to right progress as (3/2), (3/2) 2, (3/2) 3, etc.; extended from right to left they are as (2/3), (2/3) 2, (2/3) 3, etc. The square roots of the numbers, taken in reverse order, and multiplied by appropriate length/time units (1 mi/sec or 1.6 km/sec) are as mean orbital velocities of the planets. It will be seen that the serial numbers are paired, i.e., products of the pairs are constant : numbers for Mercury and Saturn; Venus and Jupiter; Earth and Planetoid; Mars and Vesta. Orbits of Uranus, Neptune, and Pluto would pair with possible orbits between Mercury and the Sun. That corresponding planetary numbers are derived through a formula involving the velocity of light as shown heretofore, leads to the inference that planetary distances and motions are regulated by electromagnetic waves radiated by the Sun. This inference is supported by the direct correspondence shown between the velocity of light and the cube roots of planetary periodic times (in seconds). Periodic Time Cubic Roots of Planet Numbers Periodic Time Mercury 192 197 Venus 256 268 Earth 324 316 Mars 384 390 Vesta 486 480 Planetoid 576 Jupiter 729 722 Saturn 972 975 Uranus 1380 1383 Neptune 1728 1735 Pluto 2048 2000 These serial numbers are paired also, i.e., products of pairs are constant : Mercury and Saturn ; Earth and Planetoid ; (192 X 972) (324 X 576) Venus and Jupiter; (256 X 729) Mars and Vesta. (384 X 486)
ASTRONOMICAL SOCIETY OF THE PACIFIC 291 The constant product is 186,624, which when multiplied by appropriate length/time units (1 mi/sec or 1.6 km/sec) equals the velocity of light. From the foregoing figures the conclusion may be drawn that frequencies of the solar electromagnetic waves are as the cube roots of planetary periodic times ; these frequencies and the velocity of light determine the wave lengths (c/fà = À). The initial amplitude of the waves would be as the radius of the Sun, and the electromagnetic intensity (equivalent to gravita- tional mass) would be proportional to the square of the wave amplitude. The space between Mars and Jupiter would correspond to a region of wave interference, affecting the orbits of Mercury and Saturn and contributing to orbital ellipticities. A characteristic of wave motion is that interference is pro- duced by the coincidence of multiples of given wave lengths. In the solar system wave series the fundamental frequency (and wave length) is found between Mars and Vesta and is as the geometrical mean of the pair (i.e., square root of the constant product 186,624, or 432). The serial number corresponding to the major diameter of Mercury s elliptical orbit is 42.8+; periodic time (frequency) number is 33 X +42.8 = 216; wave length 186,624/216 = 864 or twice the fundamental wave length. The serial distance number corresponding to the minor diameter of Saturn s elliptical orbit is 729; periodic time (frequency) number is 32 X V?29 = 864; wave length 186,624/864 = 216, or half the fundamental wave length. Similar wave elements can be computed for all planet-satellite systems, in conformity with Keplerian laws. Kepler s intuition of relationship between his laws and magnetism is borne out. His search for Pythagorean harmonies is also justified. The planetary serial numbers 64, 96, 144, 216, 324, 486 are as the actual vibrational frequencies in music of C, G, D, A, E, B The periodic times serial numbers 192, 256, 324, 384, 486, 576, 729, 972 are as frequencies of the notes... G, C, E, G, B, D, G, B. Burlingame, California August 1938