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There is a strong relationship between a galaxy's distance and the speed it moves away from our solar system. The further a galaxy, the faster it moves away.
Radial velocities are defined as whether an object is moving toward you or away from you along your line of sight.
Using exposure times that were sometimes up to 80 hours long, Slipher was the first to measure radial velocities of spiral nebulae.
The radial velocity of a star is measured by the Doppler Effect that its motion produces.
Slipher measured two dozen more spiral nebulae and recognized that they were all travelling at incredible speeds, too.
Some were blueshifted and moved toward the Milky Way, but most were redshifted and moving away.
The light waves coming off Andromeda are "blueshifted". This means its light waves are pressed together by the Doppler effect and end up appearing more blue because of its movement toward our solar system.
Approaching the sun at 300 km/s (which is about a million kilometers per hour)
This is far faster than any other object in the Milky way, which suggests that the nebula is not within our galaxy.
The Doppler Effect is the change in wavelength of sound or light that is due to the relative motion of the source toward or away from the observer.
If a star is moving away from you, you see the wavelengths stretched out and the wavelength is a positive number. Spectral lines appear on the red end of the spectrum --> redshift
If a star is moving toward you, you see the wavelengths as compressed and the wavelength is a negative number. Spectral lines appear on the blue end of the spectrum --> blueshift