kelianmao

Animations of Lumar's 12 moons

26 posts in this topic

Let us consider how we might keep the moons in their fancy geostationary orbits. Theoretically, a moon could be made to orbit along an offset circle if there was some thrust (like a rocket) that redirected the gravitational force to point horizontally towards the axis rather than the center of the planet. And hey, we might actually have a source of this reaction force, the spores that fall from the moon to the planet!

Unfortunately, if we assume Relativity exists and the speed of light is the same in the Cosmere, the maths of this does not really work out (it's even worse without Relativity btw). See this document for the full working out: https://drive.google.com/file/d/1zcYDzYe0BqoEZV8jbL-mENzBdcScNyjs/view?usp=sharing

In summary, for an Earth mass planet with 24 hour days, in order to keep a moon at 52.6 degrees (the upper flat-topped orbit), the moon would lose half its mass in ~21.4 years if the spores were ejected at 50% the speed of light or ~261 years if they were ejected at 99% c. 

These timescales are way too short for astrophysical systems, which generally last millions to billions of years. Furthermore, ejecting spores at such high speeds essentially creates deadly particle beams that would wreak destruction in their path rather than sedately falling down to Lumar. Thus, purely relativistic momentum is insufficient.

Unsurprisingly, the conclusion reached is that Investiture must be involved to keep these moons in their orbits. We know Investiture can be used to impart energy and momentum, e.g. steelpushing, or conjoiner fabrials like spanreeds. 

So, is momentum being imparted via Investiture to the spores being ejected, amplifying the force they exert, keeping the system sustainable for orders of magnitude time longer? Or, if the spores are also formed / grown out of Investiture, perhaps the moon wouldn't even have to lose mass.

Alternatively, perhaps it is more like the entanglement mechanism of spanreeds, locking the 12 moons together into a rigid structure. Since the icosahedron is symmetric, a rigid structure would theoretically support itself: the northern moons pushing on the southern moons and vice versa would provide a corrective force. Unfortunately, simply pairing opposite moons would not work, as conservation of angular momentum and minimizing rotational energy would lead to the pairs realigning to orbit the equator; it would require all 12 moons (or at least two groups of 6) to be fully coupled to each other in 3d. Or maybe there could be Aluminium shenanigans that decouple the different force components, like for Rysn's chair.

Another possibility is manipulating gravity directly, like the lashings of Windrunners / Heavenly Ones, changing the direction gravity is acting on the moons. These latter two methods would not require any reaction mass, only a constant source of Investiture.

I personally find concept of the moons being supported by the constant stream of Invested spores they're ejecting being the coolest, satisfying Brandon's Zeroth law.

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Also we assume that these are actually moons.  It could be that they are clumps of Investiture grown to Moon size.  Perhaps the Shard for this system used these to manufacture the stream of Aether spores.

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Posted (edited)

I think you should change the name of the topic. I believe that Brandon has asked all info about the project be kept from people who don't want to know it and technically the planet's name counts and I saw the planet's name from the general page listing all of the forums.

Edited by DougTheRug
adding a thought to prevent double posting
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Posted (edited)

6 hours ago, DougTheRug said:

I think you should change the name of the topic. I believe that Brandon has asked all info about the project be kept from people who don't want to know it and technically the planet's name counts and I saw the planet's name from the general page listing all of the forums.

iirc there was a post shortly after the secret projects came out where someone wanted to hide the feed coming from this forum for that specific reason, and iirc again they were able to accomplish it fairly easily with a custom feed once they figured it out.

maybe biased, but if you have the option to hide them, i think the posts on this forum should be able to have thoroughly descriptive names like this one.  coming to this site to begin with is already treading on spoiler territory XD

edit - if i remembered right and that thread exists, maybe pin it somewhere or make a post letting people know how to do so?

edit 2 - @kelianmao, is that pfp from Worm?  was too distracted by the awesome animations to process it lol

Edited by Anomander Rake
a word and an "o"
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13 hours ago, Brgst13 said:

Also we assume that these are actually moons.  It could be that they are clumps of Investiture grown to Moon size.  Perhaps the Shard for this system used these to manufacture the stream of Aether spores.

True, I've definitely wondered what these moons could be, e.g. if they're made of spores too or they just produce spores. Especially with the statement that the moons are 'Big enough to fill a full third of the sky', which seems either impossible (12 x 1/3 = 400% the area of the sky is moons?), or Hoid is exaggerating in his storytelling. Or maybe this means the angle subtended is 1/3 of the horizon (i.e. 1/3 of 180 degrees = 60 degrees), which translates to an area of 6.7% of the sky per moon, meaning the 12 moons together cover 80% of the sky, still pretty extreme.

However, the orbits I've drawn and the timescale calculations don't actually care about the mass or composition of the moon, only of the planet.

2 hours ago, Anomander Rake said:

edit 2 - @kelianmao, is that pfp from Worm?  was to distracted by the awesome animations to process it lol

It's the primary mirror of the JWST! I've heard great things about Worm but haven't gotten around to reading it yet.

4 hours ago, DougTheRug said:

I think you should change the name of the topic. I believe that Brandon has asked all info about the project be kept from people who don't want to know it and technically the planet's name counts and I saw the planet's name from the general page listing all of the forums.

I get where you're coming from, but I'm not sure what I could name it without making it completely unclear what the post is about. I could change Lumar to SP1, but surely the fact that the SP1 planet has 12 moons is more 'spoilery' than the fact that its called Lumar. And if I remove 12 moons, then the title is barely descriptive of the content...

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33 minutes ago, kelianmao said:

It's the primary mirror of the JWST! I've heard great things about Worm but haven't gotten around to reading it yet.

Ah!  totally see that now, thats a neat one.  Thats funny though - one plot arc in worm is very closely related with the color gold and separated hexagons like that, and was the immediate connection i made

def give it a shot!  its a great casual read compared to something like stormlight where you need to juggle dozens of plotlines, but still has some great scope by doing similar interludes from new PoVs.  very refreshing if you're at all a fan of superhero stories too, some sick powers from the author, and even better imo is the incredibly clever use of simple ones

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What if the congregation of so many of such invested bodies combined with some other factor caused a perpendicularity of unique nature to form. The image I form in my head is of a pulsar or neutron star(shown below if you don't get the concept). I believe it has been confirmed, and I may edit this post with a WOB if I have time to find it, that investiture causes gravitational fields or something of the like, thus the beams of radiation from the pulsar are replaced with perpendicularities that create and axis of rotation that the moons all rotate around.

Disclaimer: I don't have an astrophysics degree, so I may be completely missing the mark, but I do think I understand enough to hand-wavy magic the physics of investiture to work.

neutron-stars.jpg

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2 hours ago, Ta'veren Kaladin said:

What if the congregation of so many of such invested bodies combined with some other factor caused a perpendicularity of unique nature to form. The image I form in my head is of a pulsar or neutron star(shown below if you don't get the concept). I believe it has been confirmed, and I may edit this post with a WOB if I have time to find it, that investiture causes gravitational fields or something of the like, thus the beams of radiation from the pulsar are replaced with perpendicularities that create and axis of rotation that the moons all rotate around.

Interesting idea, that it's the planet or the entire system which has the Investiture shenanigans going on, and the geometry of the moons is a result of that.

Brandon did confirm very recently (SP4 livestream) that Investiture, matter and energy are the same thing (I assume like mass-energy equivalence in our universe), so yeah, it would make sense that Investiture would cause gravitational fields. 

Quote

There are no planets with no Investiture. You would have to have no matter in order for there to be no Investiture, because matter, energy, and Investiture are the same thing.

- Brandon, Secret Project #4 Livestream, https://wob.coppermind.net/events/494/#e15593

Creating a cylindrically symmetric gravity well seems a bit hard though, the standard method in physics being to use an infinite line of mass. I suppose if you only need a finite effect containing the 12 moons, you might be able to approximate it with some significant gravitational sources located far above the poles like you suggested. However, if you did manage to create the cylindrical well, then wouldn't the planet also be affected by the axial geometry? I.e. you'd end up with a cylindrical planet rather than a spherical planet.

The moons apparently being the source of the Aether spores, and them being worshipped as gods, suggested to me that the moons were the source of the Investiture. I guess we don't really have enough information at all about how Aethers work to make too many deductions about the metaphysics. Apparently they don't even believe they were created by Adonalsium... and I guess I've always just assumed Investiture and Adonalsium were connected. Maybe you can have 'free Investiture' (a la The Charter vs Free Magic in the Old Kingdom books).

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2 hours ago, kelianmao said:

Apparently they don't even believe they were created by Adonalsium... and I guess I've always just assumed Investiture and Adonalsium were connected.

This is still one of the most casually mindblowing factoids about the Aethers to me. Like... Is this some new tier of hubris? I almost wanted to say Nihilism but that isn't quite what i'm looking for...

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With regards to the Aethers belief of their own creation. They are from Ado still. I can't find the quote for it, but I know its there.

 

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I think the third picture ("flat-topped: this configuration has 3 fold symmetry: 4 offset rings of 3 moons each") is closest to what Brandon described in his spoiler stream about Secret Project #1.

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I wonder if the moons are not really orbiting in the conventional sense, but are held up by some equivalent of iron/steel lines from Mistborn*, with the spores falling along the line - thus the rigid icosahedron shape, the planet + all moons basically form one rigid structure, the "support beams" are just invisible.

If the moons are Aethers they might have vastly less mass than we'd expect- they could be "shadowed on the Physical" like seons, shades, or many spren - visible Physically but with little mass and only partial solidity.

 

*hmm, what about the hion lines from SP3? Obviously those are visible to everyone, unlike iron/steel lines, but it might still be precedent.

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This is amazing! Great work!

Also, I kind of want it to be the first icosahedron, the physics is handwavy already, might as well choose the coolest looking option! 

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There are two ways this could work...

Suppose  the inhabitants see the spore oceans as part of the planet.  Therefore the oceans and planet are Realmatically connected.  Now let's assume that the moons see the aether oceans as part of themselves.  Now the oceans and moons are connected.  Over time, would this be enough connection to create a Spiritual and Cognitive "tether" between the moons and the oceans?

 

Alternately let us suppose that the Aethers do not mix with each other (unproven but core to this reasoning).  If each Aether has a different Investiture "spin" (theoretical Investiture property akun to quantum numbers) then it is likely that they will repel each other.  It is possible then that the interplay between the planet's gravity and their Investiture repulsion could be enough to get them into an icosahedral shape and hold them there.  Assuming they were already in orbit, this could result in the geostationary orbits we see.

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17 hours ago, Brgst13 said:

There are two ways this could work...

Suppose  the inhabitants see the spore oceans as part of the planet.  Therefore the oceans and planet are Realmatically connected.  Now let's assume that the moons see the aether oceans as part of themselves.  Now the oceans and moons are connected.  Over time, would this be enough connection to create a Spiritual and Cognitive "tether" between the moons and the oceans?

The distinct oceans exist because the spores are always dropped on the same places. Hence the condition required to form them and allowing them to exist would be the same. They cannot cause themselves.

17 hours ago, Brgst13 said:

 

Alternately let us suppose that the Aethers do not mix with each other (unproven but core to this reasoning).  If each Aether has a different Investiture "spin" (theoretical Investiture property akun to quantum numbers) then it is likely that they will repel each other.  It is possible then that the interplay between the planet's gravity and their Investiture repulsion could be enough to get them into an icosahedral shape and hold them there.  Assuming they were already in orbit, this could result in the geostationary orbits we see.

What kept the system stable while the oceans were beginning to form?

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2 hours ago, Oltux72 said:

What kept the system stable while the oceans were beginning to form?

Good question.  I was unclear in my explanation.  The Investiture epulsion between the moons (since they either contain or form the Aethers) would lead to their being evenly spaced around the planet.

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2 minutes ago, Brgst13 said:

Good question.  I was unclear in my explanation.  The Investiture epulsion between the moons (since they either contain or form the Aethers) would lead to their being evenly spaced around the planet.

Well, no. I am sorry, but I am afraid I need to pick nits. It will keep them evenly spaced, but not around the planet. They would hover at the height where the repulsion from the other moons outweighs the attraction from the planet's gravity. And they would aim for maximum distance from each other, so they go to the vortices of a polyhedron. We agree on that don't we?

But what keeps the planet at the center of the arrangement? As soon as the planet is shifted a bit off center, the attraction to the moon now next to it increases and decreases to the others. One moon crashes onto the surface, the others escape into space. You found a metastable solution for the system. You can correct that with the spores on the planet's surface, but they weren't there initially.

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9 minutes ago, Oltux72 said:

But what keeps the planet at the center of the arrangement? As soon as the planet is shifted a bit off center, the attraction to the moon now next to it increases and decreases to the others. One moon crashes onto the surface, the others escape into space. You found a metastable solution for the system. You can correct that with the spores on the planet's surface, but they weren't there initially.

Well, no, not really.  You are forgetting that the moons are in orbit around the planet.  As the planet approaches one of them, Kepler's Equal Area Law dictates that its orbital velocity will increase, and the orbit will become less circular.  This may cause changes in the repulsion between the moons.  This repulsion will lead to a restoring of balance and the icosahedral structure.

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2 minutes ago, Brgst13 said:

Well, no, not really.  You are forgetting that the moons are in orbit around the planet.  As the planet approaches one of them, Kepler's Equal Area Law dictates that its orbital velocity will increase, and the orbit will become less circular.  This may cause changes in the repulsion between the moons.  This repulsion will lead to a restoring of balance and the icosahedral structure.

The problem with that is the regular solar eclipse we saw. That requires a geostationary orbit, or they are not in orbit and indeed hover.

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On 5/21/2022 at 9:07 AM, Brgst13 said:

Alternately let us suppose that the Aethers do not mix with each other (unproven but core to this reasoning).  If each Aether has a different Investiture "spin" (theoretical Investiture property akun to quantum numbers) then it is likely that they will repel each other.

You wouldn't even need different spins, since it's usually like charges that repel. However, if they really were held apart by repulsion, how would you get the spore-falls? Wouldn't the repulsion cause the stream of spores to be pushed away from the planet instead? Or maybe the spores - being inactive Aethers (activated only by water) - are 'neutral' and thus are not repelled and fall to planet... Very interesting idea!

I'm not sure about the shape they would form, assuming they are orbiting as well as repelling. The angular momentum of the orbits could break the spherical symmetry of the repulsion. Though, I guess they don't have to perfectly equally spaced; it's only said that 'one of the twelve is always visible', but that is still easily achievable with a squashed icosahedron.

On 5/22/2022 at 5:33 AM, Oltux72 said:
On 5/22/2022 at 5:29 AM, Brgst13 said:

Well, no, not really.  You are forgetting that the moons are in orbit around the planet.  As the planet approaches one of them, Kepler's Equal Area Law dictates that its orbital velocity will increase, and the orbit will become less circular.  This may cause changes in the repulsion between the moons.  This repulsion will lead to a restoring of balance and the icosahedral structure.

The problem with that is the regular solar eclipse we saw. That requires a geostationary orbit, or they are not in orbit and indeed hover.

I'm not sure what you're arguing here, Oltux. Isn't having geostationary orbits exactly what Brgst is proposing, that somehow the angular momentum of orbits stabilize the equilibrium between gravity and repulsion?

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4 hours ago, kelianmao said:

You wouldn't even need different spins, since it's usually like charges that repel. However, if they really were held apart by repulsion, how would you get the spore-falls? Wouldn't the repulsion cause the stream of spores to be pushed away from the planet instead? Or maybe the spores - being inactive Aethers (activated only by water) - are 'neutral' and thus are not repelled and fall to planet... Very interesting idea!

The idea is that the repulsion to other spores would drive them to the vortices of a polyhedron.

4 hours ago, kelianmao said:

I'm not sure about the shape they would form, assuming they are orbiting as well as repelling. The angular momentum of the orbits could break the spherical symmetry of the repulsion. Though, I guess they don't have to perfectly equally spaced; it's only said that 'one of the twelve is always visible', but that is still easily achievable with a squashed icosahedron.

I'm not sure what you're arguing here, Oltux. Isn't having geostationary orbits exactly what Brgst is proposing, that somehow the angular momentum of orbits stabilize the equilibrium between gravity and repulsion?

No, Brgst13 proposed geosynchronous orbits at most. We have the pesky fact they need to spaced at the same distances and always above the same point of the planet and, albeit implicitly, that they have to stay up in the sky where they are for at least centuries.

Let me give you a 2D example. Assume that A and B repel each other and that X attracts A and B. So we can have:

A ----- X ------ B

with everything totally at rest. Now something perturbs the system to:

A --- X -------- B

At this point A and X are doomed to collide, while B will escape into space
If A and B orbit around X, this will not happen. That is perfectly true. The problem with orbiting X is that they cannot stay over the same point on the surface of X unless they are over the equator.

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1 minute ago, Oltux72 said:

If A and B orbit around X, this will not happen. That is perfectly true. The problem with orbiting X is that they cannot stay over the same point on the surface of X unless they are over the equator.

Well thats what the repulsion would be for, right, keeping them away from the the equator? Whatever equilibrium is reached keeps them in a rigid structure that rotates geosynchronously, maintaining their positions in the sky.

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3 minutes ago, kelianmao said:

Well thats what the repulsion would be for, right, keeping them away from the the equator? Whatever equilibrium is reached keeps them in a rigid structure that rotates geosynchronously, maintaining their positions in the sky.

The thing is that the icosahedral polygon depends on them not needing orbit speed to stay up. That is you you not only need it to keep them off the equator but away from each other up in the sky. If they repel each other the system's stable state will be something with them having elliptical orbits, so that when one of them is cose to the planet, the other ones will be spaced out as far as possible. They will certainly not stand still in the sky for an observer on the planet.

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Also, for stability, you must consider perturbations with more than just opposing moons; theres an entire 3d structure. For example in 2d, if:

     C
     |
A -- X -- B
     |
     D

gets perturbed to 

     C
     |
 A - X --- B
     |
     D

Yes, A is now closer to planet X. However, A is now also closer to moons C and D, meaning it gets repelled away (from the planet X), while B is now further from C and D so it gets less repelled from X. So long as this repulsion is stronger than the increase in gravity, then this is a restoring force, and the system is stable. The angular momentum of the orbits should also work to keep the orbital radius higher. If the equilibrium is stable, any perturbations are quickly dampened out, and the orbits stay circular, never becoming eccentric enough to affect the appearance of the moons in the sky.

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