Refactoring the Accretion Disk Theory

On the Technological and Market Feasibility of Introducing Martian ores of Elements and Minerals into the General Marketplace

by C.K. Komrik

Part K: Pure Science Contributions to Interstellar Space Flight

— Refactoring the Accretion Disk Theory

[redacted] is a privately held corporation incorporated in the State of DE with its combined, interested conglomerate assets exceeding 50 billion USD. Its primary mode of business is marine [redacted] for the petroleum industry. As of 2011, [redacted] has earned over 12 billion USD in the sale of [redacted]. An innovative paradigm shifter, [redacted] continually seeks heterodox ventures with the potential for large reward.

This is one of several documents whose purpose is to provide the Business and Technical Requirements for a set of Reference Design models. One of the questions this project immediately raised when power levels for the power plant design were specified was, given such a high power, could this same propulsion technology be applied to interstellar space flight. Of course, in terms of energy, power, distance and time it certainly can. We determined that a trans-stellar burn of about 3 months with a stellar insertion burn of the same duration would be required using Reference Design Twenty-One Castle Mike (Thin Film Electromagnetic Fusion).

It quickly became obvious that navigation for such a mission would represent the next greatest hurdle to overcome, in particular as regards collision avoidance in the interstellar medium. While seldom given much thought, this represents a serious lacunae of knowledge and experience and at speeds at appreciable fractions of the speed of light it becomes a serious navigational puzzle. In order to understand this problem more clearly, the academic literature was consulted as regards what is known about this medium. As it turns out very little is known about it and we have therefore set about to better understand, as a first-order approximation to the overall problem, the formation of star systems in hopes that discoveries well in advance of the development of a navigational strategy and associated system will make this effort easier and more cost-effective.

In examining the current state of the art it was found that the formation of star systems is based on a rather dated theory known as the “Accretion Disk Theory” which frames the formation of star systems as having started out as disks of gas/particulate that “coalesced” into stars and planets. Having no stake in the academic disuptes over theories, we noted that recent advances in our understanding of the formation of extrasolar systems implies one of two things:

1.) Either the Accretion Disk Theory is completely unusable and must be discarded for a new model made of whole cloth OR

2.) The Accretion Disk Theory was adequate in the main but was presently incomplete.

After studying the matter I’ve concluded that the Accretion Disk Theory is incomplete and I will remedy its defects here.

The key problem with the theory, as its detractors claim, is that modern observations are showing that other star systems (outside the solar system) do not obey the assumptions that go into the Accretion Disk Theory; namely that,

1.) All planetary orbits will lie at or near a single ecliptic.

2.) All star systems would preferentially contain something like an asteroid belt observed here.

3.) All star systems would more likely have large gaseous planets in their outer orbits and heavier elements in their inner orbits.

4.) Binary star systems would not likely have planets about them.

I believe this is in fact all due to a misunderstanding, or incomplete understanding, of to what a prolonged accretion event would lead.

Assumption

A star system always begins as a cloud of gas/particulate obeying the Second Law of Thermodynamics (it is geometrically irregular and misshapen and of virtually uniform density).

Then what follows is a full remedy.

Let a test observer k1 be placed within this cloud, call it ð, and let k1 be placed just inside the outer edge of ð. It shall be sufficient for our purposes to simply say that k1 is sufficiently close to the inner edge of ð. Then we construct the following free body diagram:

A trio of three basis axes, |i1|, |j1| and |k1| whose origin lies coincident with k1 the fundamental metric tensor of General Relativity, provided adequate operators for centrifugal forces are provided with a deliberate neglect of the other three forces of nature.

Let a test observer k2 be placed within ð but closer to the ð’s cg than that of k1.

A trio of three basis axes, |i2|, |j2| and |k2| whose origin lies coincident with k2, the fundamental metric tensor of General Relativity, provided adequate operators for centrifugal forces are provided with a deliberate neglect of the other three forces of nature.

Operate the tensor over a time interval, t, sufficiently large until such time as variances in density impart suffcient (see context) spin to ð. k1 and k2may have the same or different orbital chirality. It is further not required that orbital velocity vector components x|i1| = x|i2|; y|j1| = y|j2| or z|k1| = z|k2|; [assume an adequate coordinate rotation exists].

Here we assume for illustration a variability in mass throughout ð such that these values are in fact, not equal:

x|i1| NOT= x|i2|; y|j1| NOT= y|j2| or z|k1| NOT= z|k2|; ∀ t element of R.

[assume an adequate coordinate rotation exists].

Thus orbits corresponding to the radial motion of k1 and k2 are generated as gas/particulate continues to spin and “fall” to the cg, each orbit denoted φ1 and φ2, respectively. The first thing we notice is that both k1 and k2 are not just “falling” to the center, they are being dragged by the gravitational forces acting between neighboring gas/particulate masses: as mass closer to the center “falls” to the center it and its local neighborhood drag mass in higher orbits down with it. The effect of this is to spiral the “orbits” in which the spiral begins at the center and works its way outward. Though inclined at different angles, and though one’s orbits are contained within the other’s, spirals corrersponding to both k1 and k2 are produced, each one terminating at the center.

For illustrative purposes we can section the two spirals, denoting that linear spiral section nearest the center (and attacehd to it) as A, and proceeding lexicographically outward to Z, the outermost spiral section of our interest. As more material is channeled to the center by this action the mass at the center increases. The gravitational field there likewise increases and the “downward” spiral speeds up. This tugging action places tension in the spiral since section Z, being the outermost section, is compelled to spin faster than A by virtue of the spirals geometry. This is best represented using a mathematical tensor, but the point is simple. When sufficient tension is placed at the dividing line between spiral sections Y and Z, section Z will “snap” and break off, turning outward to a wider orbit and, given sufficient time, will coalesce into a sphere of elements of the Periodic Table. Eventually, Y will also exceed a threshold radial velocity in which the centrifugal force created exceeds the sum of the gravitational force of the center and the spiral acting on Y. Thus Y, likewise, will next “snap” as well, repeating the process as Z. The process will repeat and the number of sections that “break off” will depend on the geometry, mass and constituency of the gas/particulate cloud ð. Eventually, B remains and coalesces as either a star, planet or asteriod belt. This process, viewed fundamentally, is simply the very essence of how a particulate organization can achieve orbital equilibrium and it shows that most of the “lost” material is taken up at the center, which finally coalesces with sufficient mass to ignite by fusing its lightest available elements.

This remedies all defects in that:

1.) Any number of “layers” correspoding to k, that is, any kn, can exist, which means that any combination of orbital inclinations, n, in a star system can exist, with decreasing probability of the configuration as the number n increases. This can be predicted and tested using this model and the probability of 2 or 3 inclinations is non-negligible (though orbital periods will likely differ considerably due to the initial geometry just described).

2.) The distribution of asteriod belts is purely random in this model.

3.) In this model the elemental composition preference planet by planet would depend on inclination; where a different inclination exists, this rule need not follow.

4.) Binary star systems in the remedy are merely larger accretions of mass sufficient to fuse, at minimum, the lightest nuclei.

Fortunately this didn’t take too much time to work out as it doesn’t help us much. The hope was that this might tell us more about, for example, the Oort Cloud. However, further work using this model might be able to help. I recommend more work on this in the future. It is believed, given the sheer volume of the space involved, that collision avoidance should be straightforward. The problem however, is that even the smallest mass would be catastrophic at the velocities considered and no amount of shielding will help.

My current reommendation is to specify a phased array, very high power celestial forward search radar coupled by computer control to hydrazine powered control inputs. Calculations regarding maximum range required to detect masses over the range of concern, radar capabilities and feasible lateral translation speed (automated) need to be performed to validate.

– kk

An artist's conception of a supermassive black...

An artist’s conception of a supermassive black hole and accretion disk. (Photo credit: Wikipedia)

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