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 planet of Neptune and its orbital distance. Observations of extra solar planets orbiting stars yield orbital distances that do not conform with this theory, how could they when the base distance is the Earth to Sun measurement.

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 set orbital distances 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,…

### Planetary Orbital Mean Distances from the Sun

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                                               Asteroid Belt

(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

So Lets Examine Orbital Spacing

Planetary  orbital distances within the 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. If that same large mass in the middle of the same inner planets the planet to the inside would be pushed closer to the Star and the planets to the outside would ride outwards of their original positions.

Titus was correct that a large planet at one time did exist between Mars and Jupiter. His formula predicted a planet, he did not know that several planets( info on planets residing in the what is now a remnant asteroid belt provided by Zetatalk) once resided in the zone now populated by the asteroid belt. The planets varied in size from a small moons to a water 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. With the absence of mass more ejected to other areas of the solar system, Jupiter's orbit closed thus capturing planets on the outer edge of the newly created asteroid belt as moons. The move inward affected some orbital paths of the asteroids by forcing them inward and the Sun repulsing a slow oscillating process.

Johann D. Titus and Bode experimented with many formulas until they 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 any other solar system in the universe. It was a mathematical representation of what he observed in his point in time. The orbital distance of planets and their solar masses is an interrelationship of gravity, repulsion, random placement, the planetary mass, orbital position and if their orbit is shared by a similar mass are the basic factors in determining orbits at specific point in time. This changes as the solar mass decreases due to the fusion rate of the star and out gassing through the solar winds and flares, thus over time planetary orbits as a whole would shift inward. The use of math to validate theories has always been used in Physics, as a computation in most cases will somewhat fit what is occurring by shuffling numbers, but if the theory is wrong, the set of equations are useless and stagnation within the field will occur as progress to expand knowledge slows to a crawl.