Question: I’m pretty sure I understand what redshift and blueshift are. What I don’t get is how the Doppler Effect applies, since the speed of light is constant regardless of the source’s or observer’s state of motion. Could you do an animation explaining how that works with a binary star system? — KS, Colorado
Answer: Of course. What you see in the animation above is two “yellow” stars in orbit around each other. The change in color as they revolve corresponds to what we detect as a changing frequency (f) or wavelength (λ) of the light observed. Both f and λ measure color. For any type of wave, f and λ are reciprocals: f = 1/λ.
My animation shows color changes from yellow to blue and red. For reference: the average frequency of blue light is f ≈ 640 THz, for red light f ≈ 455 THz, and for the original unchanged yellow light f ≈ 520 THz. FYI: 1 THz =1012 waves/second. My animation is an exaggerated simulation. As you will see, such large changes in frequency do not happen in reality.
Understanding the physics of the Doppler Effect for light requires a solid grasp of Einstein’s theory of Special Relativity. That’s way beyond the scope of Sky Lights. We will present and use the equation, but without derivation. If you want to know more, and see how the equation is derived, here’s a good link.
Before we delve into the Doppler Effect for light waves, it would be beneficial to read my August 8 post where we investigated the Doppler Effect for sound waves. That’s an easy lesson relying only on classical Newtonian physics. It uses a different Doppler Effect equation, but there’s some good parallel concepts.
You are correct that light waves always travel at 3 × 108 m/s regardless of any motion of the source and/or observer. Unlike sound waves, you can’t “chase after” light waves and effectively compress their wavelength. In the case of light (or any electromagnetic wave), changes in the observed frequency (and wavelength) are a result of the time dilation (and length contraction) predicted by Special Relativity. The Doppler Effect for light is calculated using the following equation, which assumes that any relative motion of source and observer is along the line joining them:
fo = f × [(c – v)/(c + v)]0.5 where
fo = the frequency observed,
f = the frequency emitted,
v = the relative speed of the light source and observer (+ when approaching, – when receding), and
c = 3×108 m/s (the speed of light)
I’ll save you some algebra — if you want to know the relative speed (v) it can be calculated using:
redshift: v = c × (f/fo – 1)
blueshift: v = c × (1 – f/fo)
So for the extreme color changes in this animation, using just the redshift equation, the two stars would have to be orbiting with a tangential speed of:
v = c × (f/fo – 1) = 3×108 m/s (520 THz/455 THz – 1) = 4.3 × 107 m/s
That’s about 14% the speed of light, so it’s not a very realistic simulation. Most binary stars orbit with speeds on the order of 104 – 105 m/s, and the change in color is subtle — it can only be measured with a spectrometer.
It’s worth noting that the speeds of binary black holes, just before they merge, can approach the speed of light. That’s what LIGO discovered earlier this year. But those are extreme scenarios, and not at all typical for binary stars.
There’s another type of redshift that we observe when looking at distant galaxies, and it’s caused by the expansion of space over the lifetime of the Universe. But that’s a topic for another post.
Next Week in Sky Lights ⇒ August 23-24 Triple Conjunction