Simplex Solar Hierarchies: Problem Specification

Solar Hierarchy in PISES

The “Solar Hierarchy” of a solar system in PISES describes how the various stars of an N-ary solar system arrange themselves. PISES currently does generate solar hierarchies, but they’re not always realistic. In this post, we’ll specify what we’d like our solar hierarchies to look like and identify the group of problems we’d like to solve. But first, let’s talk about where the “Solar Scope” lies in the architecture of PISES.

The Scopes of PISES

PISES, at the moment, has three different scopes: the Galactic Scope, the Solar Scope and the Planetary Scope.

As its name might reveal, the Galactic Scope is the view in which the observer is able to traverse and visualize the entire modeled galaxy.

The Solar Scope is the view in which the observer is able to traverse and visualize the contents of the solar system.

The Planetary Scope is still not visualized in PISES: it consists of a vast, megalithic text-dump of planetary logs that I will not bore you with here. However, our work on the icospherical world model is the beginning of our quest to visualize the planetary view.

Generating Solar Hierarchies

The “Solar Hierarchy” of a solar system in PISES describes how the various stars of an N-ary solar system arrange themselves. If this seems like it might be an unsolvable, n-body gravitational problem that would require warehouses full of supercomputers to model with even vague realism, it absolutely is. However, it turns out that most N-ary solar systems arrange themselves in such a way that can be simplified to a series of very manageable, idealistic 2-body problems.

We will not go into great detail about how PISES currently generates its solar hierarchies, mostly because it’s wrong. PISES is able to generate realistic solar hierarchies, but if it does so, it’s by accident. About 40% of the time, PISES generates unrealistic solar hierarchies.

What we want PISES to generate (at least for now) are orbital hierarchies known as Simplex Systems.

Simplex Systems and Multiplex Systems

A Binary system is quite easy to wrap our minds around: in a Binary star system, two stars orbit about their mutual barycenter (their center of mass).

In the first case, the two stars are of near-similar mass. The white X denotes their barycenter.

In this second case, the two stars are of notably different mass.

In either of these cases, the stars orbit their mutual center of mass (their barycenter).

Things get interesting when we introduce a third star to the system. There are two possibilities:

In the case on the left, all three stars orbit their mutual barycenter. This case is known as a Multiplex System.

In the case on the right, the two blue stars orbit a mutual barycenter. These two stars, for all intents and purposes, behave like a single keplerian body. This “single body” orbits its mutual barycenter with the red star at the right. In essence, this system behaves like a pair of two-body systems: the “hierarchy 1” 2-body system and the “hierarchy 2” two-body system. This case is known as a Simplex System.

As it turns out, most N-ary systems in our galaxy are simplex systems. This is because multiplex systems are unstable. As you can see in our crude multiplex example above, multiple stars may occupy a similar orbital plane and therefore interact, creating chaotic 3, 4, n-body scenarios that are not cyclical.

Over megayears, systems often stabilize into cyclical, generally predictable simplex arrangements, like our example above and on the right.

Adding more and more nodes to our simplex systems creates some very interesting and non-intuitive orbital structures. Here is a symmetrical simplex octal system, accompanied by a “mobile diagram” of the orbital hierarchy.

Try to imagine a sky with Eight Suns.

N-Ary systems don’t have to be “symmetrical” like the system above, however. N-Ary systems can be asymmetrical, like this quaternary solar system:

An “asymmetrical” quaternary simplex system.

And finally, just to fully define a multiplex system, A multiplex system is a system in which there exists an orbital node with more than two children.

A Multplex Trinary System.

Some N-Ary systems like the examples above are as small as 10 AU in diameter. For scale, Mars is about 1 AU from Earth (at its minimum orbital intersection distance). Imagine if we humans had been born into such a solar system, with seven different star systems in our backyard, all within reach? Imagine being born into a solar system with eight as many chances to generate intelligent life. Would our brief foray into space have ended at the moon in the 70s, a half century ago? The stories practically write themselves.

Alas, these few lonely worlds are all we have.

The Goal for PISES

Currently in PISES, the Solar Scope only displays a “mobile” view of solar systems. Additionally, the solar hierarchy backing the display is not always accurate. We want PISES to be able to do the following:

  1. Generate an Abstract Solar Hierarchy, which will be an element of the SolarSystem class. For now, only Simplex systems.
  2. On request, generate Keplerian orbital elements from the Abstract Solar Hierarchy.
  3. Provide two different display options for the solar system: Mobile and Orbital, with the option to toggle between the two.
  4. Provide three scale options for the solar system: Linear, Logarithmic and True Scale, with the option to toggle between the three.
  5. In the orbital display, “propagate” planets along their elliptical paths.

In the next post, we will dive into the Abstract Solar Hierarchy.

Recommended Reading

  1. Nightfall by Isaac Asimov is one of my favorite short SF stories of all time. The setting, a planet named Lagash, belonging to a 6-ary star system, is constantly illuminated by one of its six suns, and the society there has no concept of “night.” The story begins on the eve of a very rare, 2,000 year event in which Lagash’s moon, normally invisible due to the constant light of the six suns, makes a total eclipse while all six suns are near conjunction. As you might imagine, it gets dark.
Vintage Science Fiction coverart is a low key passion of mine

2. The Three Body Problem by Liu Cixin contemplates life in an unstable (multiplex!) Trinary system, in which an Earthlike planet suffers repeated planet-wide extinction events due to the volatility of its solar system.

The book also dives deeply into the Cultural Revolution and has an incredible sense of cold-war mystique, SETI intrigue (the first half of the book really keeps you in the dark) and some cool Cyberpunk undertones. It was also the first Asian novel to ever win the prestigious Hugo Award.

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