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While working at Mount Wilson Observatory, Hubble made some very interesting discoveries. Hubble chose a cepheid variable star in the Andromeda galaxy hoping to calculate its distance. First he determined the varied brightness of the star and then the actual and apparent brightness. From that, he was able to determine that the star was 900,000 light years away. Since the Milky way had been previously measured at 100,000 light years, this meant that the Andromeda Galaxy was further away than first thought.
It was later discovered that Hubble's measurement was slightly off. The cepheid star he used in the Andromeda galaxy was a brighter type than what we have in the Milky Way. This discovery meant that the Andromeda Galaxy was further away than even Hubble thought, approximately 2 million light years away. With an assistant, Hubble was able to use the concepts of the Doppler Effect to measure the doppler shift and the distance of as many galaxies as he could. Using the Doppler Effect and spectral lines he could see that things were moving away, meaning that the universe is expanding.
As long as their is motion, the speed can be calculated with a frequency shift (the Doppler Effect). The frequency of light seems to be higher or bluer when an object is coming toward us and lower or redder when it is moving away. Hubble picked a star and used its spectrum to determine the star's apparent and actual brightness. From the apparent and actual brightness, the distance can be calculated. From the distance and how quickly it changes positions, you can calculate the speed. Edwin Hubble was able to show a linear relationship between distance and the frequency shift.
The Doppler Effect is used to explain a change in sound frequency between a moving object and a stationary object. This effect causes the received frequency to differ in frequency from what was originally sent out if an object is increasing or decreasing in distance. The result is a noticeable difference in pitch.
When the source and receiver have a constant distance the frequency and pitch stay the same. If the distance is increasing, the frequency and pitch that the receiver hears is lower. Inversely, if the distance is decreasing the frequency and pitch will be higher.
Spectral lines can be used to determine the direction an object is traveling. When an object is traveling toward you, the wavelength is shorter and the waves are compressed. The shorter wavelength result in a blue shift. When an object is moving away, the wavelength is stretched and the waves are spread out. The longer wavelength results in a redshift.
One way to use the Doppler Effect to determine speed is by using a radar gun. Radar guns emit a radio wave with a set frequency, that reflects against the object moving toward it, back to the radar gun. The speed is calculated by the difference between that wavelength of the transmitted beam and how it is reflected back.