Question

1. what is the radial velocity (vrad) of a star if its measured spectral doppler shift (δλ) = 10 nm towards the blue end of the spectrum? assume you are observing a dark line in the green at 500 nm (λlab). use the doppler effect equation below. show your work! vrad = δλ/λlab c where \c\ is the speed of light (186,000 mi/sec or 300,000 km/sec... you pick!) radial velocity of star = __________ in the star moving towards or away from us? ________ how do you know? __________

Explanation:

Step1: Identify given values

$\Delta\lambda = 10$ nm, $\lambda_{lab}=500$ nm, $c = 300000$ km/sec

Step2: Apply Doppler - Effect formula

$V_{rad}=\frac{\Delta\lambda}{\lambda_{lab}}c$
Substitute the values: $V_{rad}=\frac{10}{500}\times300000$

Step3: Calculate the radial velocity

$V_{rad}=\frac{10\times300000}{500}= 6000$ km/sec

Answer:

The radial velocity of the star is 6000 km/sec.

To determine if the star is moving towards or away from us, we note that since $\Delta\lambda$ is positive and the shift is towards the blue end (shorter wavelengths), the star is moving towards us. This is because a blue - shift in the spectral lines indicates a motion of the source (the star) towards the observer.