Electromagnetic radiation from a star is observed with an...

Electromagnetic radiation from a star is observed with an earth-based telescope. The star is moving away from the earth at a speed of 0.520c. If the radiation has a frequency of 8.64 $\times$ 10$^{14}$ Hz in the rest frame of the star, what is the frequency measured by an observer on earth?

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Key Concepts

Reference Frames

Observations of physical quantities such as frequency depend on the frame of reference in which they are measured. In this context, the star's rest frame provides the emitted frequency of radiation, while the Earth's frame, due to the relative motion between the star and the observer, measures a different frequency, illustrating the importance of considering relativistic effects.

Relativistic Doppler Effect

The relativistic Doppler effect describes how the frequency of electromagnetic radiation changes when the source and observer are in relative motion at speeds comparable to the speed of light. Unlike the classical Doppler effect, it accounts for time dilation and other relativistic corrections, resulting in a formula that uses the square root of (1 - v/c) over (1 + v/c) for sources moving away.

Electromagnetic Radiation

Electromagnetic radiation consists of waves of electric and magnetic fields that propagate through space, carrying energy as quantized photons. Its properties, including frequency and wavelength, determine its position in the electromagnetic spectrum, which relates to how energetic or observable the radiation is.

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