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Originally Posted by Phage
Surely you can see the connection between mass and gravitation? The mass of objects is crucial in how they orbit.
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vinaur is correct. If one object is much less massive then the other, the precise value of its mass is irrelevant (the big mass still matters). This is actually a very important point that inspired a lot of philosophical discussion in the past. It was also one of the things that led Einstein to develop general relativity.
I think that Shakran was over-generalizing from the result about galaxy rotation. There, you don't have one central mass with a bunch of negligible masses orbiting around. It's more like a continuous distribution. In this case, the acceleration required for an object to maintain an orbit depends on all of the mass inside its radius (away from the galactic center). The distribution of matter is therefore important in that case. Even so, this an of averaged property of the galaxy. If you were to drop a star off at some point, its motion would be basically the same as a marble's.
Anyway, Wiki's description of dark matter is accurate. It is most basically defined by phage's first post. There seems to be a lot of stuff out there that we can't see that interacts gravitationally with what we can see. Shakran mentioned one of these types of observations (odd galaxy rotation curves), but there are many others. You even see evidence for dark matter in cosmological observations. There is some microwave radiation left over from the very early universe that implies the existence of a lot of matter which doesn't seem to strongly couple to electromagnetic radiation. This is inferred by figuring out the details of the sound waves present in the matter that gave off this radiation billions of years ago (!).
Anyway, nobody knows what dark matter is. There's plenty of speculation, but nothing concrete at all. It is popular to think that dark matter is largely composed of some new type of fundamental particle, although there is little evidence of this.
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Some more fun dark stuff is Dark Energy that is the proposed antigravity that makes our universe expand faster and faster. It is caused from quantum fluxuations of free space.
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"Dark energy" is actually just a free parameter in the equations that everyone thought would be zero. Since the universe seems to be accelerating, the parameter is not zero. The interpretation of this as quantum fluctuations is a guess right now. In fact it's worse than that. Unless something has changed very recently, the expectation for the amount of dark energy based off this idea leads to perhaps the largest numerical discrepancy in the history of science. It's 120 orders of magnitude too large (or exactly zero with slightly different assumptions). Some people naturally consider this a major problem, and have been working very hard to figure out if it can be fixed.
Some others are content with the original reason that a dark energy parameter was introduced. Einstein's equations (of gravity) are technically ambiguous up to a constant, which was originally called the cosmological constant. In any case, it is very natural to include, and may simply be accepted as a fundamental constant needed to properly describe gravity. There are those who say that it would be a shame if the constant could not be understood in some more fundamental way, which leads back to the previous interpretation. That interpretation also led to the name "cosmological constant" turning into "dark energy."
There are other models as well, and the experimental results aren't good enough yet to say anything definite. For example, it is still possible that the conservative cosmological constant interpretation can be ruled out (if it is changing in time).