Relativistic Doppler Shift Calculator
What speed would turn red light green? The Doppler effect shifts light to shorter wavelengths (blueshift) when approaching and longer wavelengths (redshift) when receding. This calculator uses the relativistic Doppler formula to find the velocity needed to shift light from one wavelength to another. Perfect for understanding the physics behind astronomical redshift measurements.
How We Calculate This
The relativistic Doppler formula: λ_obs/λ_emit = √((1+β)/(1-β)) for approach. Solving for β: β = (R² - 1)/(R² + 1), where R = λ_obs/λ_emit. The sign indicates approaching (β > 0) or receding (β < 0).
Frequently Asked Questions
What is the relativistic Doppler effect?
The relativistic Doppler effect accounts for time dilation in the Doppler shift formula. Unlike the classical Doppler effect, it applies at high velocities where special relativity is important.
What is blueshift?
Blueshift occurs when a light source is approaching, compressing the wavelength toward the blue end of the spectrum. The observed wavelength is shorter than the emitted wavelength.
What is redshift?
Redshift occurs when a light source is receding, stretching the wavelength toward the red end of the spectrum. This is how we measure the expansion of the universe.
Why do we need the relativistic formula?
At significant fractions of light speed, time dilation affects the observed frequency. The relativistic formula λ_obs/λ_emit = √((1+β)/(1-β)) accounts for this, unlike the classical v/c approximation.
What is cosmic redshift?
Distant galaxies show redshifted light because space itself is expanding. This cosmological redshift is similar to the Doppler effect but caused by the expansion of space rather than motion through space.
Related Calculators
You might also find these calculators helpful: Time Dilation Calculator, and Space Travel Time.