A certain galaxy has a Doppler shift given by ƒ₀ - ƒ = 0.1015 ƒ₀. Estimate how fast it is moving away from us.

Verified step by step guidance

1. Understand the Doppler effect: The Doppler shift formula for light is given by \( \frac{\Delta f}{f_0} = \frac{v}{c} \), where \( \Delta f = f_0 - f \) is the change in frequency, \( f_0 \) is the original frequency, \( v \) is the velocity of the galaxy relative to the observer, and \( c \) is the speed of light.
2. Identify the given values: From the problem, \( f_0 - f = 0.1015 f_0 \). This means \( \Delta f = 0.1015 f_0 \).
3. Substitute \( \Delta f \) into the Doppler shift formula: \( \frac{\Delta f}{f_0} = \frac{v}{c} \). Using \( \Delta f = 0.1015 f_0 \), the equation becomes \( \frac{0.1015 f_0}{f_0} = \frac{v}{c} \).
4. Simplify the equation: The \( f_0 \) terms cancel out, leaving \( 0.1015 = \frac{v}{c} \).
5. Solve for \( v \): Multiply both sides by \( c \) to isolate \( v \), giving \( v = 0.1015 c \). This is the velocity of the galaxy moving away from us.

Key Concepts

Doppler Effect

The Doppler Effect refers to the change in frequency or wavelength of a wave in relation to an observer moving relative to the source of the wave. In astronomy, it is commonly observed in the light from stars and galaxies, where a shift towards longer wavelengths (redshift) indicates that an object is moving away from the observer.

Redshift

Redshift is a phenomenon where light from an object is shifted to longer wavelengths, typically observed in the light from galaxies moving away from Earth. It is quantified as the ratio of the change in frequency to the original frequency, and it provides critical information about the velocity of the object relative to the observer.

Velocity Calculation

Velocity calculation in the context of the Doppler shift involves using the observed shift in frequency to determine how fast an object is moving away. The formula relates the observed frequency shift to the speed of light and the original frequency, allowing astronomers to estimate the recession velocity of distant galaxies.