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Modeling the Reptigan Union's Space
Posted: Posted July 24th
Edited July 27th by chiarizio
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Each little bit of Reptigan Union Space could be a rhombal dodecahedron, an Archimedean solid with twelve congruent rhombuses for faces, each of them with angles of sixty and 120 degrees, like two congruent equilateral triangles stuck together at the bases.
The reason for that figure is, it’s nearly a sphere; and if I close-packed some space by a face-centered-cubic close-packing of equal spheres, then expanded all the spheres identically to take up the empty space between them, I’d have tiled the space with rhombal dodecahedrons.

Label the center of each such dodecahedron with an ordered quartet of three-digit non-negative whole numbers, from 000 to 999.
Limit them to three degrees of freedom by requiring their sum to be 1,998.
Then the six extreme points of Union Space will have these coordinates:
[999;999;000;000]
[999;000;999;000]
[999;000;000;999]
[000;999;999;000]
[000;999;000;999]
[000;000;999;999]

Adpihi, the human capital/Capitol of the Reptigan Union, is near the center;
let’s just say it’s at
[500;500;499;499]

A given rhombal-dodecahedron “tile” will have twelve nearest-neighbors.
For instance [w;x;y;z] would have the following nearest-neighbors.
[w+1;x-1;y;z]
[w+1;x;y-1;z]
[w+1;x;y;z-1]
[w-1;x+1;y;z]
[w;x+1;y-1;z]
[w;x+1;y;z-1]
[w-1;x;y+1;z]
[w;x-1;y+1;z]
[w;x;y+1;z-1]
[w-1;x;y;z+1]
[w;x-1;y;z+1]
[w;x;y-1;z+1]

In other words, add one to one coordinate, and subtract one from another coordinate.

If one of a tile’s coordinates is 000 you can’t subtract one, and if one of them is 999 you can’t add one. So tiles on the boundary will have fewer than twelve nearest neighbors in Union Space.

My battery is running low. I sure as hell hope I can continue this tomorrow morning!



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There are 666,667,000 rhombal-dodecahedron “tiles” in Union Space.
Each has a diameter of about a light-year.
The distance between two of them can be calculated from their coordinates this way;
Suppose we want the distance between [a;b;c;d] and [w;x;y;z]
Take all the differences between corresponding coordinates;
a-w, b-x, c-y, and d-z.
Square each of those differences;
(a-w)^2, (b-x)^2, (c-y)^2, and (d-z)^2.
Sum all those squared differences;
Divide that sum by two (2);
And take the square root of that quotient.
The result will be the distance in light-years.
Each tile’s center will be about a light-year from the center of each of its nearest neighbors.
Each tile will be about a light-year across. (Ie in diameter).


Edited July 28th by chiarizio
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Union space itself will be about 999*squrt(2) light-years from each extreme point to the furthest opposite extreme point.

Almost all of the tiles will contain nothing.



Posted July 24th by chiarizio
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I was told long ago, and accepted as a working hypothesis for years, that in parts of our galaxy like Sol’s “neighborhood”, the average distance between a star-system and the nearest neighboring star-system was about 10 or 11 light-years.
But now Wikipedia says it’s actually about 5 light-years.

So I actually went and counted* the star-Systems within 500 light-years from Sol; and it works out to a density of about one star-system for every 3029 or 3030 cubic light-years. That’s consistent with an average distance between each star-system and its nearest neighboring star-system of a shade more than 8.9 light-years.
*really? That’s like 172,800 star-systems ! I must have taken a shortcut of some kind!

Anyway I figure Union space will be similar; about one star-system for every 3000-or-so cubic light-years, and about 9-or-so light-years between a star-system and its nearest-neighbor star-system.

For computer gaming-or-simulation-or-database-maintenance about Reptigan space, it makes better sense to keep a list of star-systems and record the coordinates of each of them, than to keep a three-dimensional matrix of 666,667,000 “tiles” and list the contents of each tile in the matrix. The matrix is very sparse because so much of space has no star-stuff in it.

—————


—————

Stars’ tendencies to be in multi-star systems depend on their spectral class, surface temperature, and mass, all of which are correlated.

—————

The mean and median and mode number of planets a star has is probably in the range of two to six.
The mean and median and mode number of planets-in-the-Goldilocks-Zone is probably in the range one to three.
These last two statements might apply especially to class M stars.

—————

The heaviest F stars — the F0s —— and the lightest A stars — the A9s —— are right at Chandrasekhar’s limit. (1.38 to 1.44 Solar masses).
They might, and anything heavier will, go supernova eventually.

—————

———





Edited August 11th by chiarizio
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I was told long ago, and accepted as a working hypothesis for years, that in parts of our galaxy like Sol’s “neighborhood”, the average distance between a star-system and the nearest neighboring star-system was about 10 or 11 light-years. But now Wikipedia says it’s actually about 5 light-years.


Out of curiosity was the 10ly hypothesis counting only easily visible (I guess main line?) stars, or dwarf were dwarf stars included as well? There aren't many OBAFGK stars within about 16ly from the Sun (I count 10); and, apart from Centauri, the next closest are 9 and 10ly away. Whereas dwarf stars are in the 4, 6, 7 and 8ly ranges.
https://www.space.com/18964-the-nearest-stars-to-earth-infographic.html
If Nemesis turns out to be an actual star, it would likely be a dwarf of some colour and also rather closer than either 5 or 10ly distance. ;)


Posted July 24th by elemtilas
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@elemtilas:

Out of curiosity was the 10ly hypothesis counting only easily visible (I guess main line?) stars, or dwarf were dwarf stars included as well? There aren't many OBAFGK stars within about 16ly from the Sun (I count 10); and, apart from Centauri, the next closest are 9 and 10ly away. Whereas dwarf stars are in the 4, 6, 7 and 8ly ranges.


I suspect there’s some such explanation.
I’m sure they included yellow dwarfs, and probably also most of the orange dwarfs we know about now. And they included the red dwarfs they knew about; but they probably knew about many fewer red dwarfs then than they know about know.
They didn’t know about brown dwarfs, so they didn’t include any of them. I’m not intending to include them either; at least not in my posts up til now. Our model may have lots of brown dwarfs, but I doubt brown-dwarf systems are going to have permanent populations in the myriads.

https://www.space.com/18964-the-nearest-stars-to-earth-infographic.html


Thanks!





Posted July 25th by chiarizio
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I doubt brown-dwarf systems are going to have permanent populations in the myriads.


They might be a garden spot, for some kinds of folks!

Posted July 25th by elemtilas
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@Xhin:
I can access this thread if not logged in. I can’t access it if logged in.

They might be a garden spot, for some kinds of folks!


@elemtilas:
What do you mean?

Posted July 25th by chiarizio
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I can access this thread now when logged on.
I still can’t fix the apostrophe thing.


Posted July 25th by chiarizio
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I don’t expect a binary star with a planet or planets orbiting just one of its stars in the Goldilocks zone, to also have a planet orbiting the entire pair in the pair’s Goldilocks zone.
Either any orbit close enough to either star to orbit just that star rather than the pair, is too hot for water to remain liquid, instead of boiling away;
or any orbit distant enough from both stars to orbit them both as a pair, is too cold for water to remain liquid, instead of freezing;
or there is no stable Goldilocks orbit.

But I do want people (human and/or non-human) to settle the systems of solitary F and G and K and M stars,
and to settle in the systems of binary FF FG FK FM GG GK GM KK KM MM star-pairs.

I’m going to assume that life in a three-or-more star-system is too complex and dangerous for a large permanent settlement of intelligent inhabitants.
But maybe there’ll be small-to-medium quasi-permanent research stations etc. there, near some of them, that occasionally have to be temporarily shut down and evacuated because of stellar weather, and that nobody raises a family in.

The same might be true of some systems containing one or two class A stars.



Edited July 25th by chiarizio
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They might be a garden spot, for some kinds of folks!

What do you mean?




Worlds orbiting brown dwarf stars might be rather appealing to some folks...



Posted July 25th by elemtilas
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@elemtilas:
“Beautiful” does not imply “comfortable”; nor even “safe”, nor “relaxing”.
But I’ll grant you having a magenta-colored almost-star dominating your sky would be pretty.


Posted July 25th by chiarizio
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The “Space Centipedes”’ homeworld should be one of those 3-Earth-mass “super-habitable” planets orbiting a class K orange dwarf.
They’re the first non-human interstellar-spacegoing sapients the Reptigan/Adpihi encounter, except for the AIs.
So I’m dithering about whether their home world should be at about [333;333;666;666] or [249;250;749;750].

[333;333;666;666] is about 243.35 ly away.
[249;250;749;750] is about 500.001 354.26 ly away.


Edited July 31st by chiarizio
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“Beautiful” does not imply “comfortable”; nor even “safe”, nor “relaxing”.






Posted July 25th by elemtilas
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@elemtilas:

Worlds orbiting brown dwarf stars might be rather appealing to some folks...




They might have peak seasonal populations of about 10,000 humans, about 90% of whom are tourists (like Vermont’s and Maine’s “leaf-peepers”), with the permanent human population being more like 1,000.

Whatcha think?






Posted July 27th by chiarizio
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They might have peak seasonal populations of about 10,000 humans, about 90% of whom are tourists (like Vermont’s and Maine’s “leaf-peepers”), with the permanent human population being more like 1,000.

Whatcha think?


Sounds about right.



Posted July 28th by elemtilas
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@elemtilas:
What’s a “season” in the context of our last several posts?


Posted July 29th by chiarizio
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What’s a “season” in the context of our last several posts?




Presumably some sort of slightly arbitrary division of time on this kind of world that corresponds to the "peak" and "off-peak" divisions of tourism dominated countries and planets all through the known polyverse.

Depending on the given world's climatic situation, there may be dreadful times of year that only natives and hardy immigrées could ever want to stand --- that would be the off season. Other times of year, the weather might be nice and folks that really enjoy a baleful red landscape will flock in droves --- that would be the peak season.



Posted July 29th by elemtilas
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On brown dwarfs, it rains iron. Is it possible that there’s a rainy season?

Posted July 30th by chiarizio
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@elemtilas:
@Black Yoshi:
Since there are so many more K stars than G stars, and since they last longer, and their planets may be more hospitable to life, I’d think that there’d be more intelligent, technological, maybe advanced and space-going, species whose home star-systems are solitary K stars, than solitary G stars.
In a way, that might mean there are many more Space-Centipedes than Humans in Union space.
Maybe, since the SCs outmass humans on the average, and their home planets’ gravity is stronger, it takes them longer to mature to reproductive age, longer to gestate, and more time between offspring?
Might that make their numbers more like the Humans’?

—————

Anyway, according to their founding agreement (when “Union Space” was only one or two eighths or twenty-sevenths as big as it is in Latest Reptigan), the SCs give the Humans any otherwise-habitable planet orbiting a K star, that’s too small or lightweight for their tastes.
And if the Humans find an otherwise-habitable planet orbiting a G star, that’s too massive for their tastes, they’ll give it to the Space Centipedes.

So both of those species will probably about double their rate of expansion, from the time they reach this agreement, until they meet a third species they want to admit to the Union.


Edited July 31st by chiarizio
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Posted July 31st by chiarizio
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On brown dwarfs, it rains iron. Is it possible that there’s a rainy season?



I don't see why not. If there's surface water and the geographical conditions prove favourable.


Posted July 31st by elemtilas
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Anyway, according to their founding agreement (when “Union Space” was only one or two eighths or twenty-sevenths as big as it is in Latest Reptigan), the SCs give the Humans any otherwise-habitable planet orbiting a K star, that’s too small or lightweight for their tastes. And if the Humans find an otherwise-habitable planet orbiting a G star, that’s too massive for their tastes, they’ll give it to the Space Centipedes.


I always thought this made a lot of sense. Much smarter than hoarding worlds in a strictly spatiographical fashion.

Posted July 31st by elemtilas
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I don't see why not. If there's surface water and the geographical conditions prove favourable.


Of course there won’t be any surface water on the brown dwarf.

And of course there is some on any habitable planet orbiting the brown dwarf in its Goldilocks zone. And water-rain, too.

But on the brown dwarf itself, and in its atmosphere, iron can be liquid on the surface, can evaporate into the atmosphere, can condense into clouds, and can rain ☔️ as liquid iron back onto the surface.

I was wondering whether sight-seers on the planet could watch the rain on the star.

And as you know, Solar “weather” has a roughly 11-year cycle, and sunspot activity waxes and wanes. Brown dwarfs are mostly not convective —— I think —— so their weather-cycles won’t be like the Sun’s; but several of the Sun’s planets have weather cycles, some of which can be observed from Earth, (though of course not with the naked eye!).

I was wondering whether people might come to the brown dwarf’s habitable planet to watch the iron storms on the brown dwarf.


Posted August 1st by chiarizio
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Of course there won’t be any surface water on the brown dwarf.


Correct. The red or brown dwarf under consideration is the star around which our prospective planet is orbiting. The image I quoted above is an artist's conception of a (watery) planet orbiting a red dwarf star.


And of course there is some on any habitable planet orbiting the brown dwarf in its Goldilocks zone. And water-rain, too.




But on the brown dwarf itself, and in its atmosphere, iron can be liquid on the surface, can evaporate into the atmosphere, can condense into clouds, and can rain ☔️ as liquid iron back onto the surface.



I wouldn't want to be caught out in a shower of iroain!


I was wondering whether sight-seers on the planet could watch the rain on the star.



Hm. You may not actually be able to see the rain itself (too far distant to focus on iroain drops?) but you might be able to see the weather:



And as you know, Solar “weather” has a roughly 11-year cycle, and sunspot activity waxes and wanes. Brown dwarfs are mostly not convective —— I think —— so their weather-cycles won’t be like the Sun’s; but several of the Sun’s planets have weather cycles, some of which can be observed from Earth, (though of course not with the naked eye!).



Right. Jupiter's weather can be seen with a telescope --- cloud bands and the amazing appearing and disappearing Red Spot.


I was wondering whether people might come to the brown dwarf’s habitable planet to watch the iron storms on the brown dwarf.



I don't see why not, though they might require specialist equipment to do so. And if some consortium is able to construct a suitably sturdy craft, they might be able to get up close to at least some of the upper level weather!


Edited August 3rd by elemtilas
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I’ve been trying to come up with iron rain lyrics for “I Bless The Rains Down In Africa” ( by Toto?) But I cant get anywhere. https://m.youtube.com/watch?v=FTQbiNvZqaY

Posted August 5th by chiarizio
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@elemtilas:

The image I quoted above is an artist's conception of a (watery) planet orbiting a red dwarf star.


The artist may have made an error.
Red dwarves look white; brown dwarves usually look red.
Maybe that star is being seen through the planet’s atmosphere at sunset or sunrise; if so that could explain its color.
But if the planet’s atmosphere is not responsible for the color, that’s probably a brown dwarf instead of a red dwarf.
Although most brown dwarfs appear red, there are some whose own atmospheres or coronas, have absorption lines that absorb all green light, leaving the sub-star or almost-star to appear magenta.

Also note that a planet in the Goldilocks zone of a red dwarf, and especially of a brown dwarf, is likely to be tide-locked, so that there is no such thing as sunrise or sunset on that planet.

———

No matter what that artist intended, and whether or not they made an error, still, a scene like that might be frequently visible from the surface of a habitable planet of a deuterium-fusing brown-dwarf quasi-star. I happen to think magenta is a pretty color!
So thanks for the image!

Posted August 12th by chiarizio
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