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Electromagnetic radiation encompasses a broad range of wavelengths and frequencies, from radio waves to gamma rays. These waves are vital in astronomy because they enable us to observe distant celestial objects like stars, planets, and galaxies. When dealing with light from distant stars, such as in our original exercise, we're often focusing on the visible spectrum, a small section of the entire electromagnetic spectrum.
By observing electromagnetic radiation, scientists can gather essential information about stars, including their composition, temperature, motion, and even potential planets orbiting them. This broad spectrum of waves travels through space at the speed of light, helping us understand the universe.
In the case of the Doppler Effect for Light, which is part of electromagnetic radiation, the apparent frequency of light changes due to the relative motion between the light source (like a star) and the observer (such as on Earth). This phenomenon plays a key role in astronomy as it helps in studying how stars and galaxies move.

Special relativity, introduced by Albert Einstein, revolutionized our understanding of space, time, and motion. Its core principles include the constancy of the speed of light in a vacuum and the idea that the laws of physics are the same in all inertial frames.
One of the essential consequences of special relativity is time dilation and length contraction, which become significant when dealing with objects moving at speeds close to the speed of light. For our exercise, special relativity provides the framework for understanding how the observed frequency of electromagnetic radiation changes due to the relative motion between the observer and the source through the relativistic Doppler effect.
In our problem, the star's movement away from Earth at a speed close to a significant fraction of the speed of light requires us to apply a relativistic correction to calculate the frequency observed. This ensures that our measurements align with the principles of relativity, accounting for the high velocities involved.

Frequency shift refers to the change in the observed frequency of a wave when the source of the wave moves relative to the observer. This shift can result in a higher or lower frequency depending on whether the source is moving towards or away from the observer. In the context of light waves, this concept is closely associated with the Doppler Effect.
A frequency shift can manifest as a redshift or a blueshift. If an object in space, like the star in our problem, moves away from us, the light it emits shifts to lower frequencies and longer wavelengths, a phenomenon known as redshift. Conversely, if the object approaches, we observe a blueshift, where the frequency increases.
Calculating the frequency shift requires an understanding of the source's velocity relative to the observer. In our mathematical solution, substituting given values into the Doppler effect formula for light helps us find the new frequency that an Earth-based observer would measure.