Doppler Effect: Calculating the Velocity of a Star
How can we calculate the velocity of a star using the Doppler effect?
In the scenario where an element X has an emission line in the lab at a wavelength of 500 nm and we observe it in a stellar absorption spectrum at 505 nm, what is the velocity of the star with respect to us?
Calculating the Velocity of a Star Using the Doppler Effect
The Doppler effect is a phenomenon that causes a shift in the observed frequency or wavelength of waves when there is relative motion between the source of the waves and the observer. In the given scenario, the shift in wavelength from 500 nm to 505 nm indicates that the star is moving away from us.
To calculate the velocity of the star, we can use the formula:
velocity = (change in wavelength / original wavelength) * speed of light
Substitute the given values into the formula:
change in wavelength = 505 nm - 500 nm = 5 nm
original wavelength = 500 nm
speed of light, c = 3 x 10^8 m/s
Converting the change in wavelength to meters:
change in wavelength = 5 nm * (1 m / 10^9 nm) = 5 x 10^-9 m
Substituting the values into the formula:
velocity = (5 x 10^-9 m / 500 nm) * (3 x 10^8 m/s) = 3 x 10^6 m/s
Therefore, the velocity of the star with respect to us is approximately 3 x 10^6 m/s.
Detailed Explanation of Calculating the Velocity of a Star Using the Doppler Effect
The Doppler effect is a fundamental principle in physics that describes the shift in frequency or wavelength of waves due to motion between the source and the observer. In the context of astronomy, this effect is frequently used to determine the velocity of celestial objects, such as stars, based on the observed shift in wavelength.
In the given scenario, the emission line of element X in the lab is measured at a wavelength of 500 nm. However, when we observe this emission line in the stellar absorption spectrum, the wavelength is found to be 505 nm. This increase in wavelength signifies that the star is moving away from us, causing a redshift in the spectral lines.
To quantify the velocity of the star, we utilize the Doppler effect formula:
velocity = (change in wavelength / original wavelength) * speed of light
By substituting the known values, such as the change in wavelength (5 nm), original wavelength (500 nm), and the speed of light (3 x 10^8 m/s), we can calculate the velocity of the star with respect to us. The final result of approximately 3 x 10^6 m/s indicates the speed at which the star is moving away from our observational point.
This calculation demonstrates the practical application of the Doppler effect in determining the velocities of astronomical bodies and offers valuable insights into the dynamics of celestial objects in relation to Earth.