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From what I understand space itself is expanding, and the Big Bang attempts to describe this expansion at the very early stages of the universe.

This is usually described in a visual way as 2 dots on the surface of a balloon as the balloon is being inflated.

We exist in space, so as space expands we are expanding too aren't we? If this is correct how do we know space is expanding at all?

I'll attempt to explain further... 2 dots on a balloon with a ruler drawn between them measuring 1 cm. As the balloon expands, so do the dots, and the ruler, and it always says that the distance is 1 cm. From an observers point of view (somewhere away from the balloon) the dots, ruler, and ruler are all getting larger - but from the point of view on the balloons surface nothing has changed.

Another way to describe this would be a man in a room, the room and everything in it (including the man) are getting bigger at the same rate. From the man's perspective nothing is changing but from outside the room - you can see everything is getting bigger.

I guess what I am trying to say is that we are in the universe, and expanding at the same rate as it (aren't we?) so how do we know it's getting bigger?

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the answer in this is fairly clear : physics.stackexchange.com/q/2110 –  anna v Mar 12 '13 at 15:27
    
Also physics.stackexchange.com/q/24324 –  John Rennie Mar 12 '13 at 15:58
    
So other forces negate the expansion. Does that mean some parts of space are more stretched out, or "thinner" than others? –  Pete Oakey Mar 12 '13 at 16:02
    
If you go to the balloon analogue, imagine an imperfection on the membrane, a grain of wheat, for example, caught in it. It will not expand though the balloon around it will be changing. What is balloon has the same expansion, what is solid resists this and there will be detailed equations to describe what is happening in the neighborhood of the grain. In the neighborhood of a galaxy slightly different equations will hold so in that sense there are differences in the "stretch". –  anna v Mar 12 '13 at 16:07
    
That's the kind of explanation I was looking for - nice and simple! Thanks now I understand. –  Pete Oakey Mar 12 '13 at 18:06
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marked as duplicate by John Rennie, Qmechanic Mar 12 '13 at 16:22

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The story was quite sad in early 20th century.

In 1908, Henrietta Swan Leavitt was working at Harvard College to measure the brighness of stars recorded in the observatory (women are not allowed to use telescopes). She measures the brigtness of the stars called Cepheid. She realized that cepheid's have a distinct brightness, and knowing a single Cepheid's distance would unlock the distance of other Cepheids.

The brightness of the starts is inverse square of the distance (light spreads out). From their, Hubble took over. I think you know the gist.

She was nominated for Nobel in 1924, but it was too late cause she died of cancer.

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