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Pellet One
Suppose that in one second, a gun fires three pellets. The pellets leave the gun a fraction of an inch apart, and that's their spacing as they hit the target.

But if the gun is moving away from the target, this changes. The second pellet is fired from a greater distance than the first, and the third is fired from still farther. So the group of pellets could be several inches apart when it hits the target.

Galaxy stationary with respect to earth

Galaxy moving away from earth
The same thing happens to light from a galaxy that's moving away from the earth. The crests of the lightwave are like the pellets. If the galaxy emits three crests in a particular amount of time, each subsequent crest has to travel farther than the one before it. So the light's wavelength - the distance between its crests - is longer when it reaches the earth than it was when it left the galaxy.
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