How did the spectrum help determine if a galaxy was moving closer or further away?(5 points)

The spectrum of light from a galaxy provides crucial information about its motion relative to Earth. Here’s how it helps determine if a galaxy is moving closer or further away:

1. **Redshift and Blueshift**: When observing the spectrum of a galaxy, astronomers look for shifts in the wavelengths of light emitted by elements in the galaxy. If the wavelengths are stretched (shifted towards the red end of the spectrum), this indicates that the galaxy is moving away from us (redshift). Conversely, if the wavelengths are compressed (shifted towards the blue end), this shows that the galaxy is moving closer (blueshift).

2. **Doppler Effect**: This phenomenon, commonly observed in sound waves, applies to light as well. The Doppler effect causes the observed frequency (and thus color) of light to change depending on the relative motion of the source and the observer. The change in wavelength can be quantified and directly relates to the speed at which the galaxy is moving away from or towards Earth.

3. **Spectral Lines**: Each element emits light at specific wavelengths, producing unique spectral lines. By comparing the observed spectral lines of a galaxy's light to those measured in the laboratory, astronomers can determine any shifts in these lines. The degree of this shift indicates the speed of the galaxy's motion.

4. **Hubble's Law**: The measurement of redshift (for galaxies moving away) has led to the formulation of Hubble's Law, which relates the distance of galaxies to their recessional velocity. This relationship indicates that more distant galaxies typically show greater redshifts, supporting the expansion of the universe.

5. **Quantification of Motion**: By measuring the extent of redshift or blueshift, astronomers can calculate the velocity of a galaxy in relation to Earth using the formula \( v = cz \), where \( v \) is the velocity of the galaxy, \( c \) is the speed of light, and \( z \) is the redshift parameter.

These methods enable astronomers to determine whether a galaxy is moving closer or further away with precision, helping to reveal the dynamics of the universe.