The ice analogy isn’t so bad, but I hate analogies in Physics anyway. If you can’t understand the concept without comparing it to a fucking soft-drink or balloon or whirlpool or something, maybe theoretical physics isn’t for you. It doesn’t have to be equations, you can explain these things qualitatively, without resorting to analogies that merely hint at the nature of things, whilst leaving their implications totally unclear.
The whirlpool is, as @Qingu explains, absolutely nonsensical as an analogy.
Though I’d let the ice-soda one slide, if you were talking to a kid, but I mean come on… it’s dark matter, you can’t simplify it like that in order to convey the implications of it. You’re better off just explaining the implications of it, because that’s all we really know about it anyway….
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Galaxies do not behave as would be expected from the amount of mass we can observe in them.
They behave as if there is a great deal more mass than we can observe.
The otherwise undetectable dark matter is theorized to account for this mass.
Nothing else is “known” or even theorized about it. We can only guess at its nature, as it is undetectable. It is just a theoretical device, used to account for this ‘extra mass’ that is required to explain why galaxies behave the way they do.
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Anyway, despite what I just said:
It’s not like ice in soda, it’s more like salt dissolved in a glass of water. You can’t see it, but it is there, and it adds mass to the glass of water.
Right now, the only thing that suggests there is salt dissolved in the water is the fact that it weighs too much for its size, to be just plain water. Much too much, in fact.
So we think ‘maybe there is something we can’t see, dissolved in there’.
And we call it ‘salt’ ‘dark matter’.