A star is observed to have strong hydrogen absorption lines. The Hα line in that star observed at 654.7 nm. How fast is it moving? Give your answer in km/s. Round your answer to the nearest integer (ie, with no decimal places), and retain your positive or negative sign. Is that star in the previous question moving toward us or away from us?
The correct answer and explanation is:
To determine how fast the star is moving, we use the Doppler effect for light. The observed shift in the wavelength of a known spectral line tells us about the motion of the star relative to Earth.
Step 1: Understand the information given
- Rest wavelength of Hα (Hydrogen-alpha) line = 656.3 nm
- Observed wavelength = 654.7 nm
- Speed of light, c = 299,792 km/s
Step 2: Calculate the wavelength shift
Δλ=λobserved−λrest=654.7 nm−656.3 nm=−1.6 nm\Delta \lambda = \lambda_{\text{observed}} – \lambda_{\text{rest}} = 654.7 \, \text{nm} – 656.3 \, \text{nm} = -1.6 \, \text{nm}
The negative value indicates a blueshift, meaning the star is moving toward us.
Step 3: Use Doppler shift formula for velocity
Δλλrest=vc\frac{\Delta \lambda}{\lambda_{\text{rest}}} = \frac{v}{c}
Rearranging to solve for velocity vv: v=Δλλrest⋅c=−1.6656.3⋅299,792 km/sv = \frac{\Delta \lambda}{\lambda_{\text{rest}}} \cdot c = \frac{-1.6}{656.3} \cdot 299,792 \, \text{km/s} v≈−0.002438⋅299,792≈−731 km/sv \approx -0.002438 \cdot 299,792 \approx -731 \, \text{km/s}
Final Answer:
- Velocity: −731 km/s
- Direction: Since the value is negative, the star is moving toward us.
Explanation (300 words)
In astronomy, the motion of stars can be measured using their spectral lines. One of the most prominent lines is the Hydrogen-alpha (Hα) line, which has a rest (laboratory) wavelength of 656.3 nanometers (nm). When we observe a shift in this wavelength, it means the star is either moving toward or away from us—a phenomenon described by the Doppler effect.
If a star is moving toward Earth, its light waves are compressed, leading to a blueshift (shorter wavelengths). Conversely, if it’s moving away, the light is stretched out, causing a redshift (longer wavelengths). In this problem, the observed Hα line appears at 654.7 nm—shorter than the rest wavelength—indicating a blueshift.
Using the formula for Doppler shift: v=Δλλrest⋅cv = \frac{\Delta \lambda}{\lambda_{\text{rest}}} \cdot c
we calculate the speed at which the star is approaching. The result, −731 km/s, confirms a rapid motion toward Earth. The negative sign is crucial; it tells us about the direction of motion, not just speed.
Understanding such motion helps astronomers learn about stellar dynamics, galaxy behavior, and even the expansion of the universe. This particular star, moving toward us at hundreds of kilometers per second, might be part of a larger stellar stream or interacting system.