In astronomy, we often look at the light from stars to learn about their size, speed, and distance. One key tool is the emission and absorption spectra—the colourful “rainbow” of light that shows dark or bright lines at specific wavelengths. When we compare these lines to the same lines measured on Earth, we notice they are shifted to longer wavelengths. This shift tells us that the star is moving away from us, and it also helps us estimate the star’s radius.
A spectral line appears when atoms in a star’s atmosphere either absorb or emit light at very specific energies. Think of it like a musical note that only a particular instrument can play. On a spectrum, each line is a “fingerprint” of an element.
When a star moves away from us, the light waves stretch—just like the sound of a siren gets lower as an ambulance drives away. This is called the Doppler effect. The amount the line shifts is measured by:
\$\frac{\Delta \lambda}{\lambda_0} = \frac{v}{c}\$
where \$\Delta \lambda\$ is the change in wavelength, \$\lambda_0\$ is the original wavelength, \$v\$ is the star’s speed away from us, and \$c\$ is the speed of light.
Once we know the star’s speed, we can use the Hubble Law (for distant galaxies) or other distance indicators to estimate how far away the star is. Knowing the distance and the star’s brightness lets us calculate its radius using the Stefan–Boltzmann law:
\$L = 4\pi R^2 \sigma T^4\$
Here, \$L\$ is luminosity, \$R\$ is radius, \$T\$ is surface temperature, and \$\sigma\$ is the Stefan–Boltzmann constant.
| Star Type | Typical Radius (\$R_\odot\$) | Example Star |
|---|---|---|
| Red Dwarf | 0.1–0.5 | Proxima Centauri |
| Sun‑like (G‑type) | 1.0 | Sun |
| Blue Supergiant | 30–100 | Rigel |
Exam Tip: When you see a spectral line shifted to the red, remember to calculate the velocity first using the Doppler formula. Then, use distance estimates to find luminosity, and finally apply the Stefan–Boltzmann law to get the radius. Keep your units consistent—meters for distance, meters per second for velocity, and Kelvin for temperature.
Imagine you’re driving a car with a speedometer that shows how fast you’re moving away from a landmark. The spectral lines are like the lights on that speedometer: when they shift, you know you’re speeding away. The bigger the shift, the faster you’re moving, and the further you are from the landmark. By knowing how far you are and how bright the landmark appears, you can estimate the landmark’s size—just like we estimate a star’s radius.
Quick Check: If a star’s hydrogen line at 656.3 nm is observed at 658.0 nm, what is its radial velocity? (Use \$c = 3.0\times10^8\$ m/s.) 🎓