Real-life physics in Bionicle

[Toa Of Virtues]

I was thinking that he worked as a telescope under the assumption that the planets he wanted to study were too far away to visit, but there could be an area of closely placed planets with life, it's just very unlikely. But yes, faster than light travel is somewhat of a swear word in the scientific community. It also gives historians nightmares.

[Letagi]

It's totally plausible in the sense that it complies with the known laws of physics. I was saying nothing about how close we are to actually achieving it. But if Greg said there's no FTL in the storyline, then that pretty much settles it anyways.

 

And yeah, we know that Mata Nui did actually visit the planets he observed, so no long distance sensory equipment.

 

Has anyone tried to tackle the issue of how the shattering and subsequent reforming of Spherus Magna is possible?

 

-Letagi

[bonesiii]

It's totally plausible in the sense that it complies with the known laws of physics.

I think stating this confidently is going too far. Warp removes some of the issues, but relies on unknowns, which may very well break other laws of physics.

 

And it doesn't really matter for Bionicle (G1 anyways); the super-long lifespans already imply a story that is avoiding the issue of FTL. So IMO Greg's turning it down does make sense, even if I'd call it optional. But for a real-life thing, whether it's completely plausible is unknown, and probably a no. (But that goes for a lot of answers here too, don't get me wrong. Like I mentioned with my intangibility answer; only parts of that are plausible, and other parts still seem impossible in the real world as far as we know.)

 

 

 

Shattering/reforming: There's been topics about it before, and I've commented on parts of it. I don't feel like trying to be thorough on it right now, but I'll try a little.

 

First, the original explosion of course relies on a fictional substance, but the idea of a core made of explosive material for unknown reasons isn't impossible. If you take that as a given, there's a lot of other things that would have to be just right for it to work. In my retelling (although I forget if I've actually mentioned it in-story) I establish that something about the rotation of the planet related to its poles weakens rock there in a conelike pattern (explaining the symmetry), although that seems unlikely in real life. If you take that as a second given, though, and if the explosion was gradual enough (similar to a point I raised in that Voya Nui topic open right now), it's possible that force could go out through those two weaknesses and the pieces could fly out gently enough but accelerate through sustained force over time, and reach escape velocity.

 

The rest gets shakier. Gravitational warping of the pieces would not likely be gentle enough for anybody to survive. However, I solve this with Mata Nui exerting a power over it for a while (basically kinetic dampening... which would probably not be possible in real life). Stable orbits from vertical blasts are questionable but possible if they both had a roughly equal weight deviation. The need for a long period of stabilizing before merging is possible has been one of the toughest to explain, but I think somebody suggested that the inhabited side of Bota Magna had to fuse metamorphically (or maybe even volcanically?) before it could re-enter without breaking into smaller pieces. (And the smaller pieces problem would be an issue for Bara Magna inhabitants with both moons.)

 

The weird shaped dust cloud is difficult, but possibly something like a radically tilted magnetic field of Bara as a result of the Shattering would explain the pinches in it.

 

The reforming is basically impossible without a really powerful power.

[Xan]

It's totally plausible in the sense that it complies with the known laws of physics. I was saying nothing about how close we are to actually achieving it. But if Greg said there's no FTL in the storyline, then that pretty much settles it anyways.

 

And yeah, we know that Mata Nui did actually visit the planets he observed, so no long distance sensory equipment.

 

Has anyone tried to tackle the issue of how the shattering and subsequent reforming of Spherus Magna is possible?

 

-Letagi

https://www.youtube.com/watch?v=h3kB0Z4HdSo

 

A bit like this?

 

Never liked the Agori anyway. 

 

But seriously, how would SM split into 3 smaller bodies?

[Toa Of Virtues]

Can anyone estimate the mass of spherus magna and the MU? I want to do a few calculations to see how plausible it would be to launch a rocket of that size on such a large planet.

[Letagi]

I don't think there could be anything unusual enough about the planet's rotation to cause controlled fracturing like that, but the energized protodermis itself could do it, if the veins were arranged in a specific pattern.

 

The other thing is that 100,000 years is not nearly enough time for any of the three fragments to become spherical. Besides, once they're spherical, they wouldn't fit together at all, because they certainly didn't start out spherical.

 

Another problem is maintaining the atmosphere. It should completely dissipate.

 

I was just thinking that the gravity would also change for the three bodies, but then I realized it might not. Gravity is proportional to the mass of a body and inversely proportional to the square of its radius. That means that if each fragment decreased in mass by one quarter and in radius by one half (or one ninth and one third, one sixteenth and one quarter, etc.), the surface gravity would remain the same. This would be far too precise to happen by accident, though.

 

-Letagi

[bonesiii]

I wouldn't rule out something natural for the poles, actually.

 

The rest (other than the gravity issue) was probably all solved by Mata Nui's powers, both during the Shattering and Reforming.

 

The gravity issue was something I'd theorized about that something (probably a side effect of having EP in the core) dampened gravity over Earth levels, and if the moons were larger than Earth (as canon art requires), this would make gravity the same on all three, and the total as SM. Unfortunately somebody decided to throw a brief version of this at Greg and he didn't seem to understand the issue and turned it down, saying the gravity IS higher. So... that leaves the canon ironically apparently in some kind of real-world-like scenario where basically how it must "actually" be is not ever how it's portrayed in-story; everything must seem much heavier. And SM as one (and BaraM pretty much) would have crushing gravity, making pretty much the whole story fail lol.

 

There's no clear resolution of that now; we just sort of have to pretend something like my old theory is the case anyways, or live with the gravitational contradiction. Of course, in real life, nothing that we know of could absorb gravity anyways, so a real life SM would just not work anyways. However, much of that could just be solved by having all the relevant things actually be much smaller than the canon sizes. (And we don't have actual math for the megaplanet, just that it's larger than Earth.)

[Toa Of Virtues]

I'd still like to see just how much energy it would take to get Mata Nui off of Spherus Magna, even if the gravity isn't cannon, kinda. We know the size of Mata Nui, so we can estimate his mass pretty well. With Spherus Magna, maybe we can find the size of Aqua Magna using Mata Nui as a scale with this image and then use Aqua Magna as a scale with this image.

Edited January 19, 2015 by Toa Of Virtues

[RahiSpeak]

I did some math and I think I know the sizes of Aqua Magna and Spherus Magna. Still, I can't say that my math is right so you may want to check me.

 

Okay, the first step that I took in determining the size of Aqua Magna is I measured the length of an imaginary chord (geometry) that cut through the planet, utilizing the image you provided, that totaled about 13 cm in length. I then measured perpendicular to the midpoint of that chord (6.5 cm) to the edge of the planet that turned out to be around .7 cm. After the previous steps is where I became unsure of how exactly to proceed (hey, I just started pre-calculus). But, nonetheless, I did think of something, just not sure if that something was right. What I did is I found one of the angles (arctan(.7/6.5)) and used that information to construct what I assume to have been a 60-sided polygon (I played around with a 10-sided polygon and found that my calculated angle was equal to the exterior angles; was I right?). I didn't want the whole polygon, so I divided it by 4 (I only wanted to focus on 90 degrees of it) and figured that at the end of 90 degrees my original triangle would have changed its orientation. Since I did NOT want to calculate the lengths of each individual triangle along the way, I averaged the lengths of the triangles' legs and multiplied by 15 (can I do that?). So, the radius of the circle (or planet) came out to be 54 cm. That, of course, would be the size of Aqua Magna if the whole thing were to be displayed on my computer screen (it would certainly not fit ). I then proceeded to measure height of Mata Nui, who was 7.5 cm. He was angled at 45 degrees, so I multiplied this by the square root of 2, so he is about 10-ish cm in height. The final step to determining Aqua Magna's size was to divide 54 by 10-ish to get 5-ish, then multiply everything by Mata Nui's height (12,000-something km) and viola! The radius of Aqua Magna is 62,000 km. That is incredibly large, so I am second guessing my job, but keep in mind that Mata Nui is twice the size of earth. The size of Spherus Magna is easy after that; since it is 6.75 times bigger than Aqua Magna, multiply 62,000 by 6.75 and the planet has a radius of 420,000 km. To put that in perspective, Jupiter has a radius of only 70,000 km. Hmm... now that I type this up I'm beginning to question the credibility of my math skills; unless Greg never compared these sizes to real-life planets, but I doubt it. At very least, someone can take this, point out the error (if any), and give a more accurate answer. I know that I am not that good at explaining my process, so ask questions if necessary.

 

I dare not attempt calculating the mass of these planets, at least right now.

Edited January 20, 2015 by RahiSpeak

[bonesiii]

I did some math and I think I know the sizes of Aqua Magna and Spherus Magna. Still, I can't say that my math is right so you may want to check me.

Not gonna parse your math, but please keep in mind that the canon size may not be based on the images we've seen at all, since Greg denied anything weird going on with gravity. That suggests it can't be more than a few times the mass of Earth to keep it within levels where animations as portrayed are close to right. (That might not be clear from my previous answer, so FTR. )

[Toa Of Virtues]

Love the math! A bit busy to check it all now, but I think there is even a simpler way to find the size of Aqua Magna. You'll have to estimate what Mata Nui's height would be if he was standing on the horizon, since he appears bigger as he fell towards the "camera."

 

And I think that we all know that it can't possibly be cannon, as the gravity might even crush the planet into a black hole by this point (which I also want to find out), but it's just fun speculating all of this. I wonder how massive Solis Magna would have to be...

Edited January 20, 2015 by Toa Of Virtues

[Letagi]

Kudos to RahiSpeak for going through the calculations! If you folks don't mind, I think I'll give this a try using a different approach. I'm going to use some basic scaling using the images we have, and Newton's equation for acceleration due to gravity which deals with mass and radius simultaneously.

 

Gravity is proportional to the mass of a body and inversely proportional to the square of its radius. Specifically, the equation is as follows:

 

g = (GM)/r²

 

Where g is acceleration due to gravity in m/s², G is the gravitational constant (6.67*10^-11 Nm²/kg²), M is the mass of the body in question in kilograms, and r is its radius in metres.

 

We'll assume that surface gravity on SM is equal to that of Earth, or 9.8 m/s². Having a huge radius would fine, because if we assume equal surface gravity to Earth, that means that SM also has equal average density to Earth; its total mass thus increases accordingly, so mass and radius remain balanced. It would thus not collapse into a black hole.

 

Now, ToV has provided a good picture that we can base our calculations off of. It's not quite perfect, because the picture of MN crashing onto Aqua Magna is drawn with a 3D sort of perspective, so the arc length of the planet that the image's angle subtends will be a little larger than is indicated in the circle that ToV drew. But it's a very good approximation.

 

MN's length in the original image is 9 cm. However, he's not lying straight, and he's at an angle relative to the observer. I would estimate that his actual length is this image would be 15 cm. But that's open to other opinions. I'll go with that number for now (since it's the first step in the calculations, a small error here could translate into a big error later on).

 

The original image, on my screen, is 0.195 m horizontally. The shrunken image, in the image that ToV made, is 0.021 m, or 11% the size of the original image. Mata Nui is 0.15 m in the original image, so he's (0.15 m)(0.11)=0.0165 m in the shrunken image. On my screen, the blue circle is 0.147 m in diameter, so it's 0.0735 m in radius. That radius divided by MN's scaled-down length gives us the number of times larger the radius of Aqua Magna is than the length (or height) of Mata Nui. This looks like:

 

(0.0735 m)/(0.0165 m)=4.45

 

Thus, Aqua Magna's radius is 4.45 times the height of MN. We know MN is 80,000,000 feet tall (8*10⁷ in scientific notation; or, at least, that's what I remember. BS01 doesn't seem to say.). That's equal to 9.6*10⁸ inches. Converting to centimetres (*2.54), we have 2.4384*10⁹ cm which is 2.4384*10⁷ m. (2.4384*10⁷ m)(4.45)=1.0851*10⁸ m. This is the radius of Aqua Magna. That's 17,032 times the radius of Earth. Seriously, Greg?

 

Let's now find the mass of Aqua Magna. We know it has the same surface gravity as SM, which we're assuming is the same as Earth's. Here are the calculations (this is going to be a very big number):

 

g=(GM)/r²

 

gr²=GM

 

(gr²)/(G)=M

 

M=[(9.8 m/s²)(1.0851*10⁸ m)²]/(6.67*10^-11 Nm²/kg²)

 

M=1.7200*10²⁷ kg

 

That's the mass of Aqua Magna. Three orders of magnitude greater than the mass of Earth (1000 times). That's actually not as big as I was expecting based on its ridiculous radius. But it's still huge.

 

Now, moving on to the second image, the one of BM and AM breaking off from SM (I actually like to think of this image as being from many millennia after the Shattering, because AM and BM have already become spherical and look like they could be in stable orbits. But anyways...). First, just for fun, let's calculate the size and mass of BM.

 

AM measures as 0.55 cm in radius on my screen. Bota Magna measures as 0.85 cm in radius. We don't have to convert to metres because we're working with a ratio, which is unitless. The ratio is (0.85)/(0.55)=1.5455. Thus, BM is 1.5455 times larger in radius than AM.

 

AM is 1.0851*10⁸ m in radius. Therefore, (1.0851*10⁸ m)(1.5455)=1.6770*10⁸ m is BM's radius. Let's calculate its mass. From before,

 

M=(gr²)/(G)

 

M=[(9.8 m/s²)(1.6770*10⁸ m)²]/(6.67*10^-11 Nm²/kg²)

 

M=4.1321*10²⁷ kg. Dividing by AM's mass, we get (4.1321*10²⁷ kg)/(1.7200*10²⁷ kg)=2.3884. Therefore, BM is 2.3884 times as massive as AM. This makes sense based on what we know of their sizes.

 

Now let's do the calculations for SM. We can use the data for either AM or BM for this. Both should yield the same answers. Let's use AM.

 

From before, AM measures as 0.55 cm in radius on my screen. SM measures as 3.6 cm in radius. (3.6 cm)/(0.55 cm)=6.5455. SM is thus 6.5455 times as large in radius as AM. AM is 1.0851*10⁸ m in radius. (1.0851*10⁸ m)(6.5455)=7.1025*10⁸ m. That's 111,482 times the radius of Earth. Again - seriously?

 

Let's calculate SM's mass. Using the same formula from before,

 

M=(gr²)/(G)

 

M=[(9.8 m/s²)(7.1025*10⁸ m)²]/(6.67*10^-11 Nm²/kg²)=7.4118*10²⁸ kg.

 

There we have it: the mass of Spherus Magna. Let's use the data on BM just to make sure.

 

BM's screen radius is 0.85 cm. SM's is 3.6 cm. The ratio is (3.6)/(0.85)=4.2353. SM is thus 4.2353 times as large as BM. BM is 1.6770*10⁸ m in radius. (1.6770*10⁸ m)(4.2353)=7.1026*10⁸ m. Notice that this is off very slightly from the first value we found for the radius of SM. This is likely due to rounding that I did to keep from having to type out ridiculously long numbers.

 

And, just for fun, let's calculate SM's mass using this radius.

 

M=(gr²)/(G)

 

M=[(9.8 m/s²)(7.1026*10⁸ m)²]/(6.67*10^-11 Nm²/kg²)

 

M=7.4120*10²⁸ kg. Again, this is nearly the same as what we got before with AM's data.

 

So, here are the numbers we found (and taking the average of the two slightly different numbers we got for the radius and mass of Spherus Magna):

 

Radius of Aqua Magna = 1.0851*10⁸ m

Mass of Aqua Magna = 1.7200*10²⁷ kg

Radius of Bota Magna = 1.6770*10⁸ m

Mass of Bota Magna = 4.1321*10²⁷ kg

Radius of Spherus Magna = 7.10255*10⁸ m

Mass of Spherus Magna = 7.4119*10²⁸ kg

 

Okay, that was a bit more math than I was planning on doing. But it was worth it.

 

-Letagi

 

Edit: Had a bit of a scare for a moment there - I just tried using the SM numbers to calculate escape velocity, and made an input error that caused me to get a number about ten times the speed of light! In that case, it would most certainly have collapsed into a black hole. But I just tried running the numbers again, and everything's good. Surface acceleration due to gravity of SM with these numbers is indeed 9.8 m/s², and escape velocity turns out to be 117,987 m/s. About ten times that of Earth, but that's not at all unreasonable. Now, if we can figure out the mass of Mata Nui, we can determine the amount of force needed to accelerate him to that velocity in order to escape SM's gravity (assuming my math is good, which I'm pretty sure it is). I think I'll leave that to someone else, or at least until tomorrow.

Edited January 20, 2015 by Letagi

[Toa Of Virtues]

Woah, I love it! Those are some pretty big planets! However, it doesn't make sense that they will have the same average density as Earth, seeing that Jupiter's average density is much lower than Earth, even though it's surface gravity is many times higher. I would think that Spherus Magna would have to be made of a very thin gas.

 

Seeing that the largest planet discovered is only 13 times the mass of Jupiter, I don't think we'll be stumbling across the Solis Magna system any time soon.

 

I really want to calculate the energy it would take to launch MN, but I'm studying for finals this week, and this is not in my curriculum. So until then, I call dibs! Debate the mass of MN until then.

[Letagi]

SM can't possibly be made of gas; it's obviously a rocky planet like the first four in our solar system, given that it has geography, just a whole lot bigger. Also, that wouldn't comply with the laws of physics. With any planet, the further down you go, the denser the planet becomes. The gas giants in our solar system have gaseous atmospheres, but their interiors are made of metallic hydrogen due to the pressure, and they have rocky cores. The surface of SM is obviously solid. Its density thus has to increase even more as we go deeper beneath its surface; thus, it's made of rock and metal.

 

This has to do with how planets form within solar systems. Planets are formed via a process called accretion, which is essentially the gradual accumulation of small pieces of material due to their mutual gravitational attraction. This material is left over from the initial formation of the system's sun. Spherus Magna is obviously in the habitable region of the Solis Magna system; in other words, it's the correct distance from the sun to have a temperature that allows liquid water to exist on its surface. At that same temperature, rock and metal are solid. This means that, via the process of accretion, all planets in and near a planet's habitable zone are predominantly rocky.

 

But really, the reason I assumed that Spherus Magna's average internal density is the same as Earth's is that is has to be to yield the same surface gravity. And assuming that SM's surface gravity is the same as Earth's is very reasonable. We know that the Great Beings lived on SM for millenia, and they're about the same size as Toa/Glatorian, and completely organic. Biologically speaking, they're probably very similar to us, and would thus require the same sort of conditions that Earth provides.

 

-Letagi

Edited January 20, 2015 by Letagi

[Toa Of Virtues]

I don't doubt that Spherus Magna must be solid, or that its surface gravity is equal to Earth, but they might be mutually exclusive. I bring up my point with Jupiter again, it has a much lower average density than Earth, but the surface gravity is much greater.

 

I simply don't see a planet many times the size of Jupiter, with an even higher average density, having the same surface gravity as Earth. You seem to be implying that surface gravity is only dependant on average density, which makes no sense to me.

Edited January 20, 2015 by Toa Of Virtues

[Letagi]

You're forgetting that a planet's surface gravity is inversely proportional to the square of its radius. As its size increases, its surface gravity goes down, not up - exponentially, in fact. As the numbers show, it's totally possible. The math works.

 

And saying that average density is what determines surface gravity is essentially correct. Density is mass in relation to size (mass divided by volume). Surface gravity is also mass in relation to size (mass divided by the square of the radius, and all multiplied by a constant).

 

The reason why Jupiter's surface gravity is larger than Earth's (only by about 2.5 times, mind you) is that its mass is too large in relation to its radius. This is an interesting property of gas giants. It's the same effect as stacking lots of pillows on top of one another. At first, the ones near the bottom don't compress much. But as you add more and more, they become increasingly compressed. Eventually, you might need to add twice or three times or ten times as many pillows as you would have had to initially (adding exponentially more mass) in order to achieve the same increase in height. For instance, Saturn is 83% as large as Jupiter, but only about one-third its mass. The result of this is that Saturn's surface gravity is almost identical to that of Earth (10.44 m/s² vs. 9.8 m/s²).

 

-Letagi

Edited January 20, 2015 by Letagi

[Toa Of Virtues]

Edit; didn't read. My bad.

However, average density of your SM is not the same as Earth. Earth is 5520 kg/m^3 while your SM is only 50 kg/m^3.

Perhaps I am simply overlooking something. It's 2:30 here, so i may just be too tired to get it right now. Ill look at this tomorrow.

Edited January 20, 2015 by Toa Of Virtues

[Letagi]

Okay, so after looking up some numbers and running some numbers myself, I take back what I said about density determining surface gravity. Saturn's average density is 687 kg/m³, but it has almost the same surface gravity of Earth. SM's average density is even smaller, as you said. Apologies for the confusion; I got a little ahead of myself.

 

The stuff I said about Jupiter is correct though; it's not my logic, it came from my university astronomy class. Let me rephrase.

 

Density is mass over volume. Jupiter has a very high mass, and a very large radius. However, its mass in proportion to its radius is huge. Like, enormous. Its mass is 317.8 times that of Earth. Its radius is only 11 times that of Earth. When we plug those numbers into the gravity formula, taking out the gravitational constant (i.e. focusing purely on its surface gravity relative to Earth), we get (317.8)/(11)²=2.62 as the ratio of Jupiter's surface gravity to Earth's surface gravity. Google tells me that Jupiter's actual surface gravity is 24.79 m/s². Earth's is 9.8 m/s². (24.79)/(9.8)=2.53, which is nearly the same ratio as before. Just off by a little due to some rounding.

 

-Letagi

[bonesiii]

I wonder how massive Solis Magna would have to be...

Solis Magna could be completely normal, and probably is, given its color and that normal physics were confirmed for Bionicle stars.

[Toa Of Virtues]

Ok, so what does this mean for SM? With that density, would it be a gas giant? Jupiter's avg density is 1320 kg/m^3, and your SM is less than that.

 

Because of how large it is, it would probably have to spin very slowly as to not tear itself apart. Regular day/nighr cycles would be near impossible.

[Letagi]

Geez, I don't know how I didn't see that last night. I must have been really tired.

 

You're right, such a small average density would have to make it a gas giant.

 

The calculations for finding the maximum possible rotation speed given the mass and radius that I found are easy enough. I might do those later today. But it still leaves us with the problem of SM being a gas giant.

 

-Letagi

[Toa Of Virtues]

Hey, you got all your calculations correct, and that was pretty impressive. It would have taken me ages to figure all that out.

 

What is the lowest average density a rocky planet can have? Perhaps we can find a non-lethal compromise, even if the gravity is much higher. And what if it did have the same average density of Earth, just how lethal would that be?

[Letagi]

Incidentally, we're covering this in my geophysics course this week, so if I can't figure out those calculations, I'll know them within the near future.

 

And I'm taking a geology of the solar system course, so the question of what the lowest possible density a rocky planet can have should be one that my prof for that class can answer. I'll get back to you later today!

 

-Letagi

[Votuko]

Nice job with the calculations, Letagi - setting surface gravity to 9.8m/s^2 seems like the way to go.

(I would consider trying to calculate the gravity shown in TLR from watching a falling object, but I imagine the animators would have either assumed Earth gravity as default, or took a shortcut and just gave falling objects a constant downwards velocity. Either way, I don't expect there is anything canon to be learned...)

 

If you haven't realised already, I think the reason you were having difficulty with the densities is that you forgot that the mass of a planet is proportional to radius cubed, while surface gravity is inversely proportional to radius squared. So a larger planet of the same density does have stronger surface gravity, as one would expect.

For the record, what you said about surface gravity depending on density would only work if mass were proportional to the radius squared, so that it cancelled the 1/r^2 in the gravitational force equation and left a directly proportional relationship.

 

 

I think the most useful statistic to look at is density, because that can be used to imply planet composition and see whether it really is feasible. So (using mass/volume with your measurements) here goes:

 

Aqua Magna: 305 kg/m^3

Bara Magna: 199 kg/m^3

Spherus Magna: 50 kg/m^3

 

Not looking good, seeing as Earth, a rocky planet, is roughly 5000 kg/m^3. SM seems to be closer to the density of air! (1 kg/m^3)

Perhaps this could be saved if the planet and moons were made hollow, with the surface having the density of rock. But looking at SM, the solid part could only be a thin shell 1% of the volume of the planet (to make the densities work), making an impossibly unstable planet. That level of hollowness would also be visible during the Shattering (the moons would be dish shaped, for example), so is not canonically possible.

 

Another option is powerful antigravity fields beneath the surface of the planets, seeing as Gravity is a controllable element in BIONICLE. That way, the planets could be the density of rock all the way through, but 99% of the gravity caused by that much larger mass could be cancelled out by something. The properties of Energised Protodermis are largely unknown, so maybe that could do it (incidentally, EP with Gravity powers would be a good plot device for explaining away the physics problems of the Shattering itself).

 

The last question to ask is that seeing as BaraM, AM and BotaM have different sizes, WHY is their gravity so similar? The densities above imply that the "hollowness" or "antigravity" or whatever has been fine-tuned for each to give comfortable gravity for the inhabitants. The only theory I could suggest is that telepathic EP in the planet and moons was conspiring to keep gravity survivable for the inhabitants, for some reason (is it a symbiotic relationship somehow?).

 

 

tl;dr

We must invent the Greg-field, a fundamental field which fixes the unfixable errors in BIONICLE physics...

[Toa Of Virtues]

I'll tell the scientists at Fermilab to start looking for the Greg Boson next time I go there (which is actually pretty soon!)

 

Of course, we can invent a new super lightweight and strong material just for this, but creating it would be a miracle of science. Imagine, a solid that would float on air, that would be pretty cool. Granted, the air would sink below this solid and go into the core, but I don't think it ever specified that their air is mostly composed of nitrogen and oxygen, like ours, so perhaps they breathe an even lighter atmosphere.

[Letagi]

Nice job with the calculations, Letagi - setting surface gravity to 9.8m/s^2 seems like the way to go.

(I would consider trying to calculate the gravity shown in TLR from watching a falling object, but I imagine the animators would have either assumed Earth gravity as default, or took a shortcut and just gave falling objects a constant downwards velocity. Either way, I don't expect there is anything canon to be learned...)

 

If you haven't realised already, I think the reason you were having difficulty with the densities is that you forgot that the mass of a planet is proportional to radius cubed, while surface gravity is inversely proportional to radius squared. So a larger planet of the same density does have stronger surface gravity, as one would expect.

For the record, what you said about surface gravity depending on density would only work if mass were proportional to the radius squared, so that it cancelled the 1/r^2 in the gravitational force equation and left a directly proportional relationship.

 

 

I think the most useful statistic to look at is density, because that can be used to imply planet composition and see whether it really is feasible. So (using mass/volume with your measurements) here goes:

 

Aqua Magna: 305 kg/m^3

Bara Magna: 199 kg/m^3

Spherus Magna: 50 kg/m^3

 

Not looking good, seeing as Earth, a rocky planet, is roughly 5000 kg/m^3. SM seems to be closer to the density of air! (1 kg/m^3)

Perhaps this could be saved if the planet and moons were made hollow, with the surface having the density of rock. But looking at SM, the solid part could only be a thin shell 1% of the volume of the planet (to make the densities work), making an impossibly unstable planet. That level of hollowness would also be visible during the Shattering (the moons would be dish shaped, for example), so is not canonically possible.

 

Another option is powerful antigravity fields beneath the surface of the planets, seeing as Gravity is a controllable element in BIONICLE. That way, the planets could be the density of rock all the way through, but 99% of the gravity caused by that much larger mass could be cancelled out by something. The properties of Energised Protodermis are largely unknown, so maybe that could do it (incidentally, EP with Gravity powers would be a good plot device for explaining away the physics problems of the Shattering itself).

 

The last question to ask is that seeing as BaraM, AM and BotaM have different sizes, WHY is their gravity so similar? The densities above imply that the "hollowness" or "antigravity" or whatever has been fine-tuned for each to give comfortable gravity for the inhabitants. The only theory I could suggest is that telepathic EP in the planet and moons was conspiring to keep gravity survivable for the inhabitants, for some reason (is it a symbiotic relationship somehow?).

 

 

tl;dr

We must invent the Greg-field, a fundamental field which fixes the unfixable errors in BIONICLE physics...

Yeah, I figured the density vs. gravity problem had to do with the different exponents. Thanks for confirming, though.

 

Antigravity could work. Here's another idea I came up with. It's far-fetched and purely speculative, but it might just work.

 

We know that EP has some bizarre properties. One of those properties is the ability to change its own properties. Maybe it can change its fundamental interactions as well; specifically, maybe its mass can be switched from positive to negative.

 

We know that it's always been positive in-story, given that it seems to react to gravity the same way as everything else. But if we set the mass of the EP inside SM to negative, then we can multiply the mass that I calculated by any number we want, yielding a higher density and allowing for a rocky planet, as long as we balance that with that same number minus one times the mass that I calculated in negative mass EP. Same net mass, same radius, same surface gravity, but with the density of rock.

 

As for the problem of keeping the gravity on the fragments exactly equal to that of SM, you're right that the chances of that happening by itself are almost zero. Maybe the Great Beings knew the Shattering was inevitable, but engineered it so that the fragments would be habitable. I wouldn't put it past their abilities.

 

-Letagi

[Toa Of Virtues]

Negative mass is a clever idea, but I think using a lightweight material is much more plausible. After some research, we might have already made a material that can do this; aerogel. Aerogel has a density of 4.98 kg/m^3 (lower than what we need!), and can support many times its own weight.

 

So, Spherus Magna is probably made out of an aerogel, very similar to those we have now.

Edited January 21, 2015 by Toa Of Virtues

[Letagi]

Using aerogel would definitely work, but SM would have to be an artificially-created planet. We need to keep in mind how planets form. During accretion, heavy materials sink to the centre of the forming planetesimal. Even if there was a naturally-occurring aerogel that was produced in stars or supernovae and that was left over from the formation of Solis Magna and accreted to form SM, the aerogel would be on the surface of the planet, but we know the surface is rocky. I think that having a planet made with a quantity of material that can oscillate between having positive and negative mass makes more sense. The planet could have formed normally, accrtting the positive-mass EP that had to be present in the early Solis Magna system, and at some point in its history, the EP's mass turned negative, giving rise to surface conditions that allowed for the development of life.

 

Also, I asked my geology prof to make sure, but his answer was as I had suspected earlier. The lowest possible average density of a rocky planet would be about that of water ice, so a little under 1 g/cm³ or 1000 kg/m³.

 

-Letagi

[Toa Of Virtues]

We have to keep in mind, though, that protodermis can transform any material that touches it. Perhaps it changed the surrounding rock into an aerogel-like substance. Why would it do this? Maybe it was the destiny of the planet to support life.

 

So, it may have been a gravity-crushing giant in the past, but the EP could have been changing the planet from the inside out.

Edited January 21, 2015 by Toa Of Virtues

[Letagi]

Ooh, I like that idea. I've actually wondered for a while why the protodermis deposits in the planet didn't destroy or transform the planet itself. With your idea, it already did transform it.

 

-Letagi

[bonesiii]

My original gravity absorption (over Earth level) relied on transformation too. For the record, it being in the core could have made it not react with most of the planet, assuming a roughly stable wall around that central chamber so the rock above wouldn't collapse into that pocket and get destroyed or transformed. Even if it wasn't originally in the core, its normally reacting like an acid to rock would make it end up eating its way down to the core eventually.

[Toa Of Virtues]

Haha the more I learn about aerogel, the cooler it sounds! Apparently, it is also used as a super insulator, since most of it is air.

 

It almost seems like mystery material straight from Bionicle world. I'm glad this planet can actually work in real life, this is my new headcannon.

[Votuko]

Let's have a look at aerogel, then:

 

As I calculated above, the average density required for SM to work is 50 kg/m^3.

Rock has density of 5000 kg/m^3, so a SM made of rock would be 100 times too massive. Therefore even if your aerogel approached zero density, 99% of the volume of SM would have to be aerogel to give the desired average density for the planet.

 

Now thinking about spheres, that means that more than 99% of the radius of SM would have to be aerogel to give that volume. It wouldn't be a small aerogel chamber at the core of SM - just about everything apart from the crust would have to be aerogel!

 

Now, it seems unlikely that EP could have reached 99% of the planet's volume to turn it into aerogel if that is the explanation you choose; and if it could, what made it leave the 1%? Deliberate intent? "Destiny"? (*coughs*)

Furthermore, if only the crust of SM is rock then the moons would have been mostly exposed aerogel as they broke off SM, which wasn't mentioned anywhere in the story . (The aerogel must look like stone from a distance?)

The fatal error, in my opinion, is that this aerogel must naturally sink below rock despite being far less dense than rock in order for the moons to form spheres with rocky surfaces, a physics error of similar severity to gravity on SM itself...

 

So in conclusion, I don't think that just making SM out of some (physics-obeying) magic material is going to fix this - gravity is two orders of magnitude lower than we would expect for a rocky planet, so whatever material we choose, the planet must be almost entirely made of it. It looks like antigravity (or Greg Bosons) may be necessary as part of any feasible solution...

Luckily it is canon that elemental Gravity control is possible, even though it breaks the laws of physics! (Probably something I shouldn't mention in the real life physics thread. (Elemental powers pretty much require an additional fundamental field to draw energy from, transcending real life physics, but I digress...))

 

 

Side note: In real life, according to General Relativity, the energy content of negative pressure produces antigravity. (Although the effect is too weak to use as a solution for SM.)

Edited January 21, 2015 by Xelphene

[Toa Of Virtues]

You have a point, but aerogel is probably the only way you could even think of doing it in real life. In story, though, we can just adjust the gravitational constant to make it fit, or as you said, introduce a new force.

 

You can maybe make the aerogel explanation work by thinking that EP can change it back and forth. EP was responsible for the explosion, so it could have made a shell for the moons before the explosion, and constantly be pushing the heavier rocks to the surface (so they don't sink below the gel).

[RahiSpeak]

It is called energized protodermis, yes? So, why not replace obscene amounts of a very light substance (aerogel) with an actively supporting one? Humans have already made materials that can expand and even move when exposed to heat or another source of energy. Imagine that underneath the surface of Spherus Magna there might have been a sea of energized protodermis with the crust being held up by large pillars of a material that expands when exposed to energy; most of the planet's interior is empty space. The main source of energy could be from the planet's core, but one day Mr. E.P. gets a bit excitable, and BOOM! The Shattering.

 

Oops, dinner time, I'll add more later if I feel I need to.

[Votuko]

It is called energized protodermis, yes? So, why not replace obscene amounts of a very light substance (aerogel) with an actively supporting one? Humans have already made materials that can expand and even move when exposed to heat or another source of energy. Imagine that underneath the surface of Spherus Magna there might have been a sea of energized protodermis with the crust being held up by large pillars of a material that expands when exposed to energy; most of the planet's interior is empty space. The main source of energy could be from the planet's core, but one day Mr. E.P. gets a bit excitable, and BOOM! The Shattering.

Oops, dinner time, I'll add more later if I feel I need to.

I think you may have misunderstood - the aerogel is also "actively supporting", otherwise SM would implode.

As I mentioned above, the problem with making the planet hollow is that you would need everything apart from a thin crust to be empty space to make the mass work. And if it were like that, during the Shattering the moons would have looked like circular pieces of an egg shell, rather than the lumps of rock shown in canon images, and you would be able to see right through the planet through the holes they left...

The aerogel scenario is better if only because the aerogel could look like there was rock there, even if it was actually a lighter material.

[RahiSpeak]

 

It is called energized protodermis, yes? So, why not replace obscene amounts of a very light substance (aerogel) with an actively supporting one? Humans have already made materials that can expand and even move when exposed to heat or another source of energy. Imagine that underneath the surface of Spherus Magna there might have been a sea of energized protodermis with the crust being held up by large pillars of a material that expands when exposed to energy; most of the planet's interior is empty space. The main source of energy could be from the planet's core, but one day Mr. E.P. gets a bit excitable, and BOOM! The Shattering.

Oops, dinner time, I'll add more later if I feel I need to.

I think you may have misunderstood - the aerogel is also "actively supporting", otherwise SM would implode.

As I mentioned above, the problem with making the planet hollow is that you would need everything apart from a thin crust to be empty space to make the mass work. And if it were like that, during the Shattering the moons would have looked like circular pieces of an egg shell, rather than the lumps of rock shown in canon images, and you would be able to see right through the planet through the holes they left...

The aerogel scenario is better if only because the aerogel could look like there was rock there, even if it was actually a lighter material.

I didn't misunderstand, but I did mispeak. I meant a non-static material; a substance capable of expanding.

 

While I did forget about the "egg-shell" planets, the possibility still remains. For one, no matter the theory, gravity was greater before the Shattering than after because of the decrease in mass. Keep that in mind. So since the the cause of the Shattering happened deep within Spherus Magna anyway, it is reasonable to assume that there would be a large ejection of magma from the planet's presummably molten core. This ejection (and the one on the other side) could have formed a large portion of Bota Magna and Aqua Magna while the "egg-shell" pieces could have wrapped around it like one wraps a bowling ball with wrapping paper.

[Toa Of Virtues]

Gravity may have been the same if EP has a way to control the density of the planet. That would probably be the simplest explanation. To make the shattering seem more natural, EP probably made the aerogel look like a naturally occurring mineral.

 

Now that I think of it... Those rocks they used as kohlii balls looked way too light to be made of regular stone...

[bonesiii]

For one, no matter the theory, gravity was greater before the Shattering than after because of the decrease in mass. Keep that in mind. So since the the cause of the Shattering happened deep within Spherus Magna anyway, it is reasonable to assume that there would be a large ejection of magma from the planet's presummably molten core.

1) Keep in mind that with my original theory, only the emitted gravity would be greater before the Shattering. Since any over Earth's level (or thereabouts) would be absorbed, the gravity felt would be the same on SM, and the three fragments. This is the most consistent with all portrayals, and would seem to be the simplest theory. (But again, if you want a real-world-physics-only version, it probably doesn't work... just reacting to that "no matter the theory" bit. )

 

2) I don't think the core is molten. It's generally thought there may be some molten layers near the surface, but the core basically has to be solid, for the most part, to hold up Bara Magna's olive-shaped surface for 100,000 years. Admittedly, a lot of molten rock might fit the moon reshaping part, so your theory works there, but that also already works with enough fracturing of both moons' rock. Large fragments in that would not be safe for inhabitants, due to the intensity of the resulting quakes, but small enough ones could flow roughly like a liquid, similar to molten rock, without the temperature issues of a solid and thin crust fracturing to bend around the molten section.

 

Also, if it was already molten as it sounds like you're assuming, an explosion would more likely blast the molten rock out the sides and it would probably rain down on the top of the crust section, killing a lot more; if it was solid, the fracturing could happen as it accelerates up from the difference from gravity pull on the sides and upward push in the middle from the jet of venting, exploding EP (or whatever gradual explosive would replace it in a real-world version), so the fragments could go more down than up, until they settle around the mostly intact solid middle.

 

Both are unlikely to be safe enough for survival without the option the actual story has of Mata Nui using a power to control things to be safer, but I think fracturing probably has the best chance. (And I don't think any of these are reversible without his power.)

[RahiSpeak]

Alright, well, the purpose of of my theory was to remedy the above mentioned sinking of the rock sitting on top of the much lighter aerogel.

 

Colatteral damage and survivability may be an issue, but really no more than any other current theory. After all, in real-life, an explosion of epic proportions would not produce two spheres. Instead, since the explosion would have to be strong enough to seperate the rock of Bota Magna and Aqua Magna from the rock of Spherus Magna, the likely outcome would be a bunch of shattered pieces as the would-be planets are blown apart by the force. Take a stone tile, suspend it between two saw-horses, then smack the center with a hammer (with proper eye protection of course!). Does the hole look something like the hammer's head? Probably. Does the piece on the ground bear any such resemblance? Eh, no. In fact, it is really quite "shattered", if I may say, into a bunch of smaller pieces, but not in the survivable, planet-like way. It really seems far less survivable to me than rock enveloping magma (or whatever you were suggesting).

 

Okay, I wait with bated breath for your reply. (Did I spell "bated" right?)