Unification- Chapter 2 - Spoilers

[dellstart]

Well, I could say I'm sorry for offending sensibilities...but I'm not.

For the record, I approve of this. One of the things I dislike about mainstream 'pheromone' style plots is how it is always very careful to avoid the kinds of hilarious consequences that would happen in real life.

If you squirmed uncomfortably in your chair when you read the first page of the chapter, then I consider that me doing my job.

Sorry Fel, I'm a 10 year veteran Furry. There is very likely absolutely nothing you could write that would shock me.

Well, I have to admit I did squirm a bit , but I understand with that , that this is something that that is a by product of their unique relationship.

[Taltos]

very nice chapter, liked it a lot. one thing [and i _do_ realise that this may be overly nitpicky, but the physicist in me just fumbled his will save]:
it may be that my gravitational theory course was too long ago, but gravity inside a hollow sphere (of equal density) is always zero due to potential theory, you wouldn't need the original moon to compensate.
and yes, it's SciFi, i know, but there's no story flow reason (like with, say, FTL travel) for this i can see, so i thought i'd point it out.

[Fel]

You're assuming the mass of the sphere's shell is negligible or small. This is large scale. Remember, the outer shell of Kosigi is 2 miles thick, and it's rock backed by heavy metal and armor plating. The inside surface of the sphere has sufficient mass to generate gravity. Weak gravity, but gravity nonetheless.

The proof is simple math: F = GMm/R². Force equals [the gravitational constant * mass of object 1 * mass of object 2], all divided by the distance between their centers squared. The outer shell is two miles thick, so IT is the mass of mass 1, and the object being attracted is mass 2. The distance is measured from the object to 1 mile into the outer shell. Now this is also a measure of calculus, for the mass on the far side also attracts the object, as does the mass at all angles to the object. If you add all of these myriad pulls together, what you find is that the lateral angular gravity equations cancel each other out to stop lateral pull, but their pulls along the same axis are cumulative (a phenomenon akin to centripetal force, the X component zeros out but the Y component remains, and all Y components are added together via a calculus limit to determine overall Y velocity). When it comes to the mass of the shell on the far side of an object from the center, that force is lesser than the force on the near side because it has a lesser distance, a smaller R. It does mitigate the pull of gravity on the near side, but cannot overcome it.

Therefore, the gravity in a sphere with an outside of 2 miles thick exerts gravity towards its outside when dealing with gravity exerted against objects within.

The "tennis ball" in the middle acts as a counterweight to create a balanced pull at the equal distance between the center mass and the shell. It needs to be there because gravity is as much a function of distance as it is mass. If the center wasn't there, the sphere would have a gravitational center near the center (it's not a perfect sphere), but that center would be the center that denoted where gravity would stop pulling towards the SIDES, not the INSIDE. The vast distance within Kosigi mathematically nullfies gravity at the center, which was the way it was designed, but the gravitational equation states at its face that the mass of the outer shell would pull objects towards the edges, not towards the center.

The center mass is there to push that mathematical zero point out to a spherical point halfway between the two, to create a zone of "zero gravity" in a volume within the space between the shell and the core.

Remember, it's not volume that creates gravity, it's mass. And there's just too much mass there for the outer shell not to generate a gravity well that attracts objects towards it.

Now mind, it's been years since I took physics, but that's how I remember it working to the best of my knowledge, and I'm not gonna change it now anyway.

[IdiotPaste]

So how in the hell did the build it without anyone noticing?

[Fel]

The original Kosigi was actually the outside shell. The surface is the surface of the original moon. They built it by literally excavating out the interior of the moon. The core at the center is the original core of the moon. The moon had many bases on it at the time, so the commercial traffic was concealed behind traffic between the planet and the moon bases, and the hole they used to do the work was covered over by a large starport. Remember, all non-Karinnes were restricted to the island of Academy, and the Karinnes never spoke of anything beyond the island to the students. So the students had no idea what they were doing up there.

It took the original Karinnes nearly 200 years to hollow out the moon. It took another 45 years to build the the base within, but they were interrupted by the war, and it was only about 30% complete. It would have taken about another 100 years to complete the base.

As you might notice, the Karinnes always thought in the long term. Their patience and meticulous attention to detail concerning the Generations program is just one example of how "long term" they thought....97 generations worth of forward thinking.

[Mizriath]

Thanks Fel,

For chapter 2 & 3.

This is always a physics question for me... how do people create artificial gravity... they cannot increase mass so they increase compression?

[Fel]

Yes, "compression" is a good description of how it works.

One definition of gravity, and the one premised in the story, is gravity as a distortion of space, the famous "bowling ball on a stretched blanket" model. But, since this is three dimensional, mass "compresses" space, and that compression is gravity. Artificial gravity is a localized manipulation of space to generate artificial gravity. All Imperium/Karinne ships have an artificial gravity system built into the keel that simulates gravity for the ship. This field of gravity also extends beyond the ship, for those who remember Subjugation recall, when Zora used intersecting artificial gravity fields to disrupt a Trillane cruiser.

The equation of gravity given above actually fits this model. It's the mathematical equivalent of the amount of spatial compression caused by mass.

[Taltos]

i didn't want you to change it (moon in a moon is cooler anyhow, artistic license in SF is kinda strong anyways), i just had to point it out (as a physicist i can't pass such things up sometimes).

sorry, fel, but you're wrong. i am _not_assuming small mass. the only assumption is constant density (and even that is not strictly necessary). not only lateral pull is cancelled. if i had the time i'd look it up or calculate it, but quickly i just found a link by NASA which also explains it: http://www.grc.nasa.gov/WWW/K-12/Number ... rvtysp.htm

The gravitational force inside a hollow sphere shell of uniform areal mass density is everywhere equal to zero,[...]

This kinda is related to why it's called gravitational _potential_ theory, only relevant masses are those "inside" of your current location (as related to the center of mass), so the little moon inside would actually create a weak gravitational force.

this is also an easily understandable formulation (from a forum):

From any point inside the sphere, imagine a cone extending to a portion of the surface. Now extend that cone back to the opposite side of the sphere. If your point is not exactly at the center, your two cones will not intersect equal areas (and, so, not equal masses) because area is proportional to the square of the distance. HOWEVER, since gravitational force is inversely proportional to the square of the distance, the gravitational force from each of those portions of the surface will be the same. Since they are in opposite directions, the two equal but opposite forces cancel. The total gravitational force is 0.

[Ledsmith]

...The proof is simple math: F = GMm/R². Force equals [the gravitational constant * mass of object 1 * mass of object 2], all divided by the distance between their centers squared. The outer shell is two miles thick, so IT is the mass of mass 1, and the object being attracted is mass 2. The distance is measured from the object to 1 mile into the outer shell. Now this is also a measure of calculus, for the mass on the far side also attracts the object, as does the mass at all angles to the object. If you add all of these myriad pulls together, what you find is that the lateral angular gravity equations cancel each other out to stop lateral pull, but their pulls along the same axis are cumulative (a phenomenon akin to centripetal force, the X component zeros out but the Y component remains, and all Y components are added together via a calculus limit to determine overall Y velocity). When it comes to the mass of the shell on the far side of an object from the center, that force is lesser than the force on the near side because it has a lesser distance, a smaller R. It does mitigate the pull of gravity on the near side, but cannot overcome it.

Therefore, the gravity in a sphere with an outside of 2 miles thick exerts gravity towards its outside when dealing with gravity exerted against objects within.

The "tennis ball" in the middle acts as a counterweight to create a balanced pull at the equal distance between the center mass and the shell. It needs to be there because gravity is as much a function of distance as it is mass. If the center wasn't there, the sphere would have a gravitational center near the center (it's not a perfect sphere), but that center would be the center that denoted where gravity would stop pulling towards the SIDES, not the INSIDE. The vast distance within Kosigi mathematically nullfies gravity at the center, which was the way it was designed, but the gravitational equation states at its face that the mass of the outer shell would pull objects towards the edges, not towards the center.

The center mass is there to push that mathematical zero point out to a spherical point halfway between the two, to create a zone of "zero gravity" in a volume within the space between the shell and the core.

Remember, it's not volume that creates gravity, it's mass. And there's just too much mass there for the outer shell not to generate a gravity well that attracts objects towards it.

Now mind, it's been years since I took physics, but that's how I remember it working to the best of my knowledge, and I'm not gonna change it now anyway.

I have a B.A. in physics and a B.A in Astronomy and I'm very impressed with Fel's explanation. It is basically correct, the only natural gravity that would exist inside the sphere is on the very surface of the inside and on the surface of the core (if you jumped from the suface of the inside you would most likely float all the way to the other side). This is all assuming that the Karrines manipulated the core is such a way that is somehow canceled out the aspherical imperfections in density and thickness of the shell. If you want to see a real life 2D demonstation put a dozen or so cheerios into a bowl of milk and whatch what happens.

[Ledsmith]

ok so I started my post before the "other physicist" (taltos) made his post. He is more correct but, I'm assuming the Karrines are useing the core to cancel out the density and thickness anomolies of the shell rendering the gravity of the core nul. I still hold to my Cheerio demonstration when it comes to the gravity right at the surface of inside of the shell. Why else would the Cheerios seem to "sitck" to the side of a bowl.

[Taltos]

well, your cheerios stick because of surface tension and buoyancy. see http://en.wikipedia.org/wiki/Cheerio_effect
and it's not basically correct (without really heavy gravitational modification by the karinnes) because the outer shell is just not relevant if you are in the inner cavity, it's as if it is not there from a gravity standpoint. i thought at least the imo very intuitive quote at the end of my previous post would have explained that well enough.
there _is_ gravity in the entire cavity, which entirely comes from the core and the core alone, and decreases with 1/r^2 with the distance from the core.

i wonder how you motivate gravity being "only on the very surfaces of inside shell and core", because then you would get jumps/discontinuities in the gravitational force??

anyways, i think i'll back out of this because too much physics destroys a good SF tale. my well-minded attempt at a bit of physics education failed apparently.
[just for reference, if we have to start to lob titles around, i hold a master in physics, and am on the road to a phd in fluid mech, although i'd rather not have turned this into a pissing contest ]

[ANTIcarrot]

Why else would the Cheerios seem to "sitck" to the side of a bowl.

This is why pier review is so important.

[Fel]

But...there are no piers to review here.

I live near no oceans or major lakes.

And yes, I agree that TOO MUCH physics ruins a SF story. I posed my explanation for why I felt the physics would work the way they do, and it seems I am proven wrong. I'm man enough to admit it.

And yeah, the center core of Karis is supposed to be there to balance out the outer shell, to correct the fact that it's not a perfect sphere.

But, I'm still not gonna change it, because it sounds good enough to be believable at its face, and I'd spend like 2 weeks trying to rebuild the entire way the base works when I could be writing. So accept that the Subjugation universe runs on a physical law that trumps all others.

Fel's Law of THAT IS THE WAY IT IS.

[Ledsmith]

ok, I've been out of the field since college. I'm currently working as a statistical analyst for a manufacturing company so I'm sure I forgot a whole bunch of stuff. Gravity was never my thing anyway. I always enjoyed E and M, paticularlly radio astronomy (shouldn't it work exactly like a Faraday cage only with gravity instead of EM radiation).

I'm still sticking to my Cheerio analogy. Some people use a ball on a streched sheet. I use Cheerios in a bowl, its how my brain comprehends gravity. The Cheerios seem to accelerate towards the edge and other groups of O's. I find it difficult to believe that is all just surface tension. Lets not be biased, Cheerios have gravity too, and they help lower cholesterol in conjuction with a health lifestyle.