This cheat sheet covers how light from astronomical objects changes wavelength when the source and observer move relative to each other. Redshift and blueshift help astronomers measure whether stars, galaxies, and gas clouds are moving away or toward us. Students need these ideas to connect spectra with real measurements of motion, galaxy rotation, exoplanets, and the expanding universe.
The sheet is organized around the Doppler effect, interpreting spectra, and using redshift in astronomy.
The most important idea is that wavelength increases for objects moving away and decreases for objects moving toward us. For speeds much less than the speed of light, the fractional wavelength shift is approximately equal to radial velocity divided by the speed of light: z = Δλ / λ0 ≈ v / c. Positive z means redshift, negative z means blueshift, and larger absolute values mean faster motion along the line of sight.
At cosmological distances, redshift is also linked to the expansion of space, not just ordinary motion through space.
Key Facts
- Redshift occurs when observed wavelength is longer than rest wavelength, so λobserved > λrest and z > 0.
- Blueshift occurs when observed wavelength is shorter than rest wavelength, so λobserved < λrest and z < 0.
- Redshift is calculated with z = (λobserved - λrest) / λrest = Δλ / λrest.
- For nonrelativistic speeds, radial velocity is approximately v = zc, where c = 3.00 × 10^8 m/s or 3.00 × 10^5 km/s.
- A positive radial velocity means the object is moving away from the observer, while a negative radial velocity means it is moving toward the observer.
- The Doppler effect changes wavelength and frequency, with light shifted to longer wavelength and lower frequency when the source recedes.
- Spectral lines are identified by comparing observed wavelengths to known laboratory rest wavelengths of elements.
- For distant galaxies, Hubble's law relates recession speed and distance as v = H0d, showing that more distant galaxies generally have larger redshifts.
Vocabulary
- Doppler effect
- The change in observed wavelength or frequency caused by relative motion between a source and an observer.
- Redshift
- A shift of spectral lines toward longer wavelengths, usually indicating that the source is moving away or that space has expanded.
- Blueshift
- A shift of spectral lines toward shorter wavelengths, usually indicating that the source is moving toward the observer.
- Rest wavelength
- The wavelength of a spectral line measured in a laboratory when the source is not moving relative to the observer.
- Radial velocity
- The component of an object's velocity along the observer's line of sight.
- Cosmological redshift
- Redshift caused by the expansion of space between a distant galaxy and the observer.
Common Mistakes to Avoid
- Confusing redshift with a red color is wrong because redshift means spectral lines move to longer wavelengths, even if the object does not look visibly red.
- Using observed wavelength in the denominator of z is wrong because redshift is defined as z = (λobserved - λrest) / λrest.
- Treating all redshift as ordinary motion through space is wrong because distant galaxies also show cosmological redshift from the expansion of space.
- Ignoring the sign of velocity is wrong because positive velocity usually means moving away, while negative velocity means moving toward the observer.
- Applying v = zc at very high redshift is wrong because that approximation only works well when speeds are much smaller than the speed of light.
Practice Questions
- 1 A hydrogen spectral line has a rest wavelength of 656.3 nm and is observed at 660.0 nm. Calculate z and decide whether the source is redshifted or blueshifted.
- 2 A galaxy has z = 0.025. Using c = 3.00 × 10^5 km/s, estimate its recession velocity with v = zc.
- 3 A spectral line with rest wavelength 500.0 nm is observed at 497.5 nm. Find the radial velocity in km/s and state whether the object is moving toward or away from Earth.
- 4 Explain why astronomers use spectral lines instead of the apparent color of a galaxy to measure redshift or blueshift.