Bode’s Law
Bode’s Law was a mathematical concept developed for predicting planetary distances in this solar system. The formula a concept of Johann D. Titus, a German Mathematician in 1766, provides a formula for predicting the orbits of most planets, but has exceptions. The formula goes astray when determining the distance of the outer planets Neptune & Pluto, and their orbital paths. Also, it does not address the yet undiscovered 12th planet, which will become visible to large observatory telescopes in the late 2001-early 2002, and to the occasional amateur astronomers in mid-to-late 2002 on, but dismissed as a lens flare.
Bode’s Law is a formula based on a series of “3”, which doubles starting at zero with the number 4 added to each number then the total divided by 10. The result is an orbital distance in astronomical units. One astronomical unit (AU) is equal to the distance between the Earth and the Sun or approximately 93 million miles.
The following table shows a
widening discrepancy between Bode’s Law and actual scientific orbital
measurements in (AU) for the outer planets.
Series: 0, 3, 6, 12, 24, 48, 96,
192, 384, 768,…
Bode’s
Law
Actual Distance (AU)
(0 + 4)/10 = .4 .39 Mercury
(3 + 4)/10 = .7 .72 Venus
(6 + 4)/10 = 1.0 1.00 Earth
(12 + 4)/10 = 1.6 1.62 Mars
(24 + 4)/10 = 2.8 varied Asteroids
(48 + 4)/10 = 5.2 5.2 Jupiter
(96 + 4)/10 = 10.0 9.5 Saturn
(192 + 4)/10 = 19.6 19.2 Uranus
(384 + 4)/10 = 38.8 30.0 Neptune
(768 + 4)/10 =
77.2
39.3 Pluto
Solar systems develop from a state of equilibrium between the forces of gravity and repulsion. Planetary orbital formation is truly a random and chance event in the universe. The dominant stellar object captures free-floating cosmic objects within its zone of gravitational influence. The mass of the cosmic objects and their chance placement near the dominant stellar object determines the distance between orbits. The size of the mass in any orbit dictates placement of surrounding orbital paths. The greater an exterior planetary mass, the tighter the interior orbital paths will ride closer to the Sun, and the orbits of the all the outer planets will fan out due to a larger repulsion generated from the same mass.
Titus was correct that a planet at one time did exist between Mars and Jupiter. His formula predicts it even though he did not know that several planets once resided in the zone now populated by the asteroid belt. The planets varied in size from a small moon to a planet similar in size to Neptune. Some were destroyed by cascading collisions, others were captured as trailing moons behind the 12th planet, or, expelled from orbit by a massive hit and the subsequent cascading collisions. In the past, the Sun’s mass was larger, the repulsion force generated from it was greater fanning out the present orbits of the planets in this solar system. During that time frame, the 12th planet’s periodic 3,600-year transit through the solar system intersected the zone of the current asteroid belt. At some stage in the past, the orbital passage of the 12th planet and its trailing moons passed through the asteroid belt. Gravitational attraction from one of the planetary objects orbiting in the asteroid belt during a near pass, ripped away and collided with one of the trailing moons of the 12th planet. This occurrence set into motion a chain of events resulting in the odd orbits of asteroids around the Sun, comets, and the remnant planetary chunks between Mars and Jupiter.
Johann D. Titus experimented with many formulas until he found one that closely fit the orbital profile of our solar system. It was a great achievement for his time, but does not accurately predict all planetary orbits in this, or other solar systems throughout of the universe.
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