Hard Light Productions Forums
Off-Topic Discussion => General Discussion => Topic started by: LuaPineapple on September 23, 2008, 06:54:07 pm
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(http://i159.photobucket.com/albums/t139/LuaPineapple/SCAN0076.jpg)
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:lol: @ 'Has monkeys on it'
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So... where's the physics? :(
Also, gravity is not a force, it's acceleration. It just appears as a force on a co-ordinate system fixed to local gravitational center... :drevil:
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Bleh. F suddenly doesn't equal m * a?
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Bleh. F suddenly doesn't equal m * a?
It does, but that doesn't tell us which is the cause and which is effect for various reasons. In case of gravity, weight can be considered the consequence of acceleration just as well as acceleration the consequence of weight (gravitational force). At least, if you interpret things via general relativity, which basically states that gravitation is all about mass interacting with local space-time. Which means that it's the space-time that causes objects to acceleratingly fall towards each others, and not directly a force that forces them together.
Gravity only becomes force when someone looks at things from a co-ordinate system fixed to a local gravitational mass and interprets the cause of acceleration as a force. It's a valid interpretation in newtonian frame of mind, but in terms of relativity, gravity really isn't a force but acceleration that appears as a force (weight) when the acceleration is prohibited by things like floor, or surface of Earth.
After all, Earth weighs about 735 Newtons in my accelerating co-ordinate system... but I can't say that because Earth weighs 735 Newtons it has mass of 75 kg. ;7
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All of that is rendered invalid by the fluctuations in the aether (as seen on the left of the page). :D
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Didn't you save the Colossus with 30,000+ monkeys on it?
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Yah, but we re-did the mission and let the monkeys die.
I find 30000+ dead monkeys more funny then 30000+ live ones.
And they make less of a mess too.
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:lol: @ 'Has monkeys on it'
:( @ 'Has 30,000+ dead monkies on it'
:drevil: ;)
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Also, gravity is not a force, it's acceleration. It just appears as a force on a co-ordinate system fixed to local gravitational center...
A-ha! No-one expects the Physics inquisition!
It is not actually acceleration either, if you are careful with the terms. It is curvature of the local space time, that manifests itself as acceleration / force towards the center of mass.
If my General Relativity memories are accurate, you can actually make acceleration disappear with a suitable choice of coordinate system...
Mika
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Enterprise.
Has Shatner on it. -50N
:lol: :lol: :lol: :lol: :lol:
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I still like the 30,000+ dead monkey comment. If he didn't already have a custom title, this'd probably earn him one. Hell, it might still earn him one. :lol:
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Also, gravity is not a force, it's acceleration. It just appears as a force on a co-ordinate system fixed to local gravitational center...
A-ha! No-one expects the Physics inquisition!
It is not actually acceleration either, if you are careful with the terms. It is curvature of the local space time, that manifests itself as acceleration / force towards the center of mass.
If my General Relativity memories are accurate, you can actually make acceleration disappear with a suitable choice of coordinate system...
Mika
Yes, in free fall on homogenous gravity field (or space-time) neither acceleration or force can be measured.
However, in co-ordinates fixed to the center of mass, the local space-time will cause an acceleration of objects towards the center. Since the acceleration is due to space and time and since acceleration is completely dependant on definitions of time and space, being d2x/dt2 (second derivate of change of location in relation to change of time), it follows that the most simple way to interpret this is as simple space-time induced acceleration (in a fixed reference frame).
Whether it can be considered a force in General Relativity isn't really even a relevant question, since interpreting gravity as a force actually complicates things in that model.
Newton's gravity law sees the gravity as a force because it handles things in a fixed rigid reference frame, but the law
G = gamma * m * M / R2, where gamma is gravitational constant of unit Nm2/kg2 and the G is weight (or gravitational force)
could be just as easily written as
g = gamma2 * M / R2 where gamma2 is gravitational constant of unit m3/kgs2 and the g is actually the direct acceleration caused by gravitation, in relation to the center of gravity. M is of course the combined mass of the system.
For example, in case of Earth and stuff on it's surface, we can agree that the CoG is close enough to center of Earth to make no difference, and we can use the Earth's mass as M since the mass of single objects is proportionately ridiculously small, and the equation works as follows:
g = 9.80665 m s-2 (experimentally easy to confirm)
gamma = g * R2 / M
R = 6,378,100 m -> R2 = 4.06801596 * 1013 m
M = 5.9742*1024 kg
gamma = 9.80665 m s-2 * 4.06801596 * 1013 m / 5.9742*1024
gamma = 6.67764867 × 10-11 m3 kg-1 s-2
And this works just as well as Newton's formulation of gravity... to an extent. A good example is defining the gravitational forces affecting an object within a hollow, homogenous shell - assuming that the acceleration is simply pointing towards the center of gravity is an oversimplification that doesn't really work in all cases, and you'll need to jump through various hoops to get the correct results...and things can get hairy when resultant accelerations are considered in the more complex setups, and it's sometimes more prudent to view gravity as a force them as acceleration, if only to avoid headplosions...
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I have a feeling it is not entirely correct to say "acceleration induced by gravity". I cannot quite place my finger in the reason yet, but maybe I'll figure it out tomorrow. It has something to do with objects actually following their geodesic line that is defined by the initial state of the system and the local spacetime. And with the fact that in GR, gravity is put into the category of virtual forces that depend on the choice of coordinate system.
And maybe something with the object inertial mass being the same as the gravitational mass for some (yet unknown) reason.
But bah. I'll let the sleeping do the thinking of this stuff.
Mika
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From what I've learned, gravity is simply a consequence of the very geometry of space itself.
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Yeah, I think I'm starting to get the hang of the thing that bothered me about using acceleration.
When you look from a fixed coordinate system and turn up the mass of the object, you are causing more curved spacetime. At this point, the good old Cartesian coordinate system is butchered and coordinates x, y and z become x', y' and z' and they are not anymore the same parameters along each respective axis. The main reason for this is the time dilatation.
Now if one uses d2r / dt2 as in Newtonian fashion, one will not get it right.
Of course, it is completely possible it is me that is mistaken. That has been known to happen before.
Mika
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You should see what MY work looks like :drevil:
my teacher actually passed me once when i drew a picture of the Galatea getting beemed by the Lucy... I think it had something to do with Newtonian physics...
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And I just play Tetris on my laptop.
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offtopic:
i seriously had to answer the question
it line segment DEM congruent to segment JAD?
got me thinking...
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it line segment DEM congruent to segment JAD?
???