We observe an absorption line of Oxygen at 504 nm in Star A and at 508 nm in Star B. We know in the lab
this line has a wavelength of 500 nm. How are Star A and Star B moving relative to each other?
To determine how Star A and Star B are moving relative to each other based on the observed absorption lines of Oxygen, we can use the concept of the Doppler effect.
The Doppler effect states that the observed wavelength of a wave (in this case, light) is shifted as a result of the relative motion between the source of the wave and the observer. If an object is moving toward the observer, the observed wavelength appears shorter (blue-shifted), and if an object is moving away from the observer, the observed wavelength appears longer (red-shifted).
In this case, since Star A's absorption line of Oxygen appears at a longer wavelength (504 nm) compared to the lab value (500 nm), it indicates that the line is red-shifted. This implies that Star A is moving away from the observer.
Similarly, Star B's absorption line of Oxygen appears at a longer wavelength (508 nm) compared to the lab value (500 nm), suggesting that the line is also red-shifted. Therefore, Star B is also moving away from the observer.
In conclusion, both Star A and Star B are moving away from the observer, but the shift is greater in Star B as its absorption line is at a longer wavelength (508 nm) compared to Star A's absorption line (504 nm).
To determine how Star A and Star B are moving relative to each other based on the observed absorption lines of Oxygen, we can use the concept of redshift and blueshift.
When an object is moving away from us, its observed wavelengths are longer (shifted towards the red end of the spectrum), which is known as redshift. Conversely, when an object is moving towards us, its observed wavelengths are shorter (shifted towards the blue end of the spectrum), which is known as blueshift.
In this case, Star A's absorption line of Oxygen is observed at 504 nm, which is longer than the lab value of 500 nm. This indicates a redshift, implying that Star A is moving away from us.
On the other hand, Star B's absorption line of Oxygen is observed at 508 nm, which is shorter than the lab value of 500 nm. This indicates a blueshift, implying that Star B is moving towards us.
Therefore, based on the observed shifts in the absorption lines of Oxygen, we can conclude that Star A is moving away from us and Star B is moving towards us.
To determine how Star A and Star B are moving relative to each other, we need to make use of the Doppler Effect. The Doppler Effect refers to the change in wavelength of light or sound waves due to the relative motion between the source and observer.
In this case, we have observed an absorption line of Oxygen at 504 nm in Star A and at 508 nm in Star B. We know that in the lab, the line has a wavelength of 500 nm.
The Doppler Effect equation for light is given by:
Δλ/λ = v/c
Where:
Δλ is the change in wavelength observed
λ is the original wavelength observed in the lab
v is the relative velocity between the source and observer
c is the speed of light
Using this equation, we can calculate the relative velocity (v) between Star A and Star B.
For Star A:
Δλ_A = λ_A - λ_lab = 504 nm - 500 nm = 4 nm
For Star B:
Δλ_B = λ_B - λ_lab = 508 nm - 500 nm = 8 nm
Substituting these values and the known speed of light (c = 3 × 10^8 m/s) into the Doppler Effect equation, we can solve for the relative velocity (v).
For Star A:
4 nm / 500 nm = v / (3 × 10^8 m/s)
v_A = (4 nm / 500 nm) × (3 × 10^8 m/s) ≈ 2.4 × 10^6 m/s
For Star B:
8 nm / 500 nm = v / (3 × 10^8 m/s)
v_B = (8 nm / 500 nm) × (3 × 10^8 m/s) ≈ 4.8 × 10^6 m/s
So, Star A is moving away from Star B with a velocity of approximately 2.4 × 10^6 m/s, and Star B is moving away from Star A with a velocity of approximately 4.8 × 10^6 m/s.