Why do different stars give out different amounts of...

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redshift?

Those that are moving away from us the fastest have the greatest red-shift.

Look up "Doppler shift".

For a quickie explanation (looking up "Doppler Shift", as suggested, will yield greater detail):

Ever notice that as something is moving toward you, the sound it makes is higher-pitched than normal, and as it goes away, the pitch drops? And the faster it's moving, the more pronounced the change? That's because the sound waves being emitted are compressed together as it approaches, meaning the sound has a shorter wavelength (the distance from the peak of one wave to the peak of the next), and as it goes away, the sound waves are stretched out, giving them a longer wavelength.

Something similar happens with light - as the source comes toward you, the photons it emits have their wavelength shortened, appearing more blue. (You don't notice it at ordinary Earthly speeds; you'd need sensitive instruments to prove that it's happening.) As it moves away, the wavelength is longer, making the light look redder.

And one of the truly astonishing discoveries of astronomy was when it was found that almost everything in the universe is rushing away from us, giving a red shift to the frequency of the light. The farther away it is, the faster it appears to be moving. Astrophysicists are able to determine an approximate value for the mass of the universe - and it's great enough that this should not be happening. Oddly, when they try to find the mass that generates the gravitational attraction that can be seen, the mass doesn't seem to be there. The current leader in explanatory theories involves an exotic substance called "dark matter", whose only interaction with the rest of the universe is gravitational - it emits no photons, therefore cannot be seen. The continued acceleration is then attributed to "dark energy", a sort of reversal of normal energy.

Also, as an addition to DeaconBlues' post, the reason for the compression of the waves is because the speed of the wave through its medium is the same, no matter the speed of the emitter.

If you're travelling at some speed (say 10 m/s relative to some stationary object) and throw a ball in the same direction you're travelling (at say 5 m/s relative to you), the absolute speed of the ball (ie. the speed of the ball relative to the stationary object) is the sum of your speed and the speed of the ball relative to you -> 10 m/s + 5 m/s = 15 m/s.

This doesn't happen with waves however, as the speed of waves is dependent on the nature of the medium and not in any way the speed of the emitter.

The speed of sound through dry air at 1 bar (pressure) is approximately 343 m/s.

In other words, if you're travelling at 16.67 m/s (60 km/h) in your car, the sound waves from the engine are moving at 343 m/s - 16.67 m/s = 326.33 m/s away from you in the forward direction. And 343 m/s + 16.67 m/s = 359.67 m/s away from you in the opposite direction. So you see, every time your engine generates a sound wave, the previous wave has moved away a shorter distance in the front than in the back. That's how the waves are being compressed. The difference is often audible from a bystander's point of view.

And the same thing happens with distant galaxies, except on a much larger scale. Red shifting (toward infra red really) is happening behind the galaxy (the waves are becoming longer) - so we know the galaxies are moving away from us. If they were to move toward us, we would observe a shifting in the blue (and ultra violet) direction.