Q&A

# Can velocity drift be used to calculate a radio wave source's distance from Earth?

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If you're studying radio signals from Earth, is it possible to calculate whether a radio source is 'near' as in near Earth or 'very far away' as in somewhere far out in space from velocity, or velocity drift?

If velocity isn't a feature in how to calculate rough distance/ to gather some distance information, then is there some other way?

Thank you.

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Yes, it can. We can determine the distance to the source if we have an idea of what's causing that shift in velocity.

Let's say that we have a source moving at a speed $v$ away from us. If it emits a photon of wavelength $\lambda_e$, we will observe that photon to have a wavelength of $$\lambda_o=\lambda_e\left(1+\frac{v}{c}\right)$$ due to the Doppler effect. This in turn means that we can calculate the object's speed if we can measure $\lambda_o$ and know $\lambda_e$: $$v=c\frac{\lambda_o-\lambda_e}{\lambda_e}$$ Let's take a look at how this is used by radio astronomers.

One of the most important spectral lines at radio wavelengths is the 21 cm line, so named because it has a rest wavelength of 21 cm. It arises from a change in the spin of an electron in an atom of neutral hydrogen, which we sometimes call the spin-flip transition. The probability of such a transition is extremely low, but if you put together enough neutral hydrogen - say, in the form of an interstellar cloud - you can produce a detectable signal.

Astronomers have used the 21 cm line to map the Milky Way. We have a rough idea of how clouds should move throughout the galaxy. If we point our telescope at a particular cloud in the sky, we can measure its radial velocity via the 21 cm line and insert that velocity into models of the Milky Way's rotation to determine the cloud's location. This in turn allows us to figure out its distance to Earth. (Unfortunately, for most clouds of neutral hydrogen in the sky, each possible radial velocity yields two possible locations in the galaxy, so we have to break that degeneracy.)

The second way we can use radio waves to determine the distance to a source is by observing distant galaxies. On scales larger than galaxy clusters, the universe is expanding at an accelerating rate. Hubble's law tells us that a galaxy a distance $d$ from us should recede at a speed $$v=H_0d$$ where $H_0$ is Hubble's constant. If we have $v$, we can easily calculate $d$ from Hubble's law.

So, how do we determine the radial velocity? Well, we can certainly use the 21 cm line. Alternatively, if the source is a radio galaxy - a galaxy whose central supermassive black hole is causing intense radio emission - we can try to fit the galaxy's spectral energy distribution (SED), which shows how emission varies across different frequencies. If we have a model SED for the particular type of galaxy, we can fit its parameters to the observations. This will tell us, among other things, the redshift, and by extension the radial velocity.

Fitting SEDs isn't always the best method of measuring the radial velocity of high-redshift objects, and for both theoretical and instrumental reasons, we actually often use optical or infrared telescopes to study the galaxy's spectral lines, and use those to determine the redshift, rather than the SED. You can find a lot of papers talking about determining redshifts of radio galaxies - but by observing with visible light!

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Certainly, given some assumptions. If you know the expected spectrum (or frequency, or at least it has identifiable peaks) of the signal, then you can get the relative speed (not velocity) from the Doppler effect. Assuming the object is in orbit (or freefall) around something in the Solar system, you know what speed is compatible with what orbit. Measure the speed during several days and you'll know if it is in orbit around Earth. Then there is also directionality of the receiving antennas, this will give you very good estimate of the direction of the transmission (depends on the frequency, but some arcseconds are certainly possible). This allows you to calculate the orbit exactly.

Of course, unless the transmitting party wants to deceive you deliberately...

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is it possible to calculate whether a radio source is 'near' as in near Earth or 'very far away' as in somewhere far out in space from velocity, or velocity drift?

No. Electromagnetic wave, and radio frequencies are in there, propagates at c. We know from relativity that c is an invariant in all reference frames, therefore whatever radio wave you measure, it will be always travelling at c.

The speed at which light waves propagate in vacuum is independent both of the motion of the wave source and of the inertial frame of reference of the observer. This invariance of the speed of light was postulated by Einstein in 1905, after being motivated by Maxwell's theory of electromagnetism and the lack of evidence for the luminiferous aether; it has since been consistently confirmed by many experiments. It is only possible to verify experimentally that the two-way speed of light (for example, from a source to a mirror and back again) is frame-independent, because it is impossible to measure the one-way speed of light (for example, from a source to a distant detector) without some convention as to how clocks at the source and at the detector should be synchronized. However, by adopting Einstein synchronization for the clocks, the one-way speed of light becomes equal to the two-way speed of light by definition.

If you know the frequency at which the radiation was emitted and you measure the frequency at which you are receiving it then you can determine the relative radial velocity between you and the emitter, by using the Doppler effect.

The Doppler effect for electromagnetic waves such as light is of great use in astronomy and results in either a so-called redshift or blueshift. It has been used to measure the speed at which stars and galaxies are approaching or receding from us; that is, their radial velocities. This may be used to detect if an apparently single star is, in reality, a close binary, to measure the rotational speed of stars and galaxies, or to detect exoplanets. This redshift and blueshift happens on a very small scale. If an object was moving toward earth, there would not be a noticeable difference in visible light, to the unaided eye.

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If velocity isn't a feature in how to calculate rough distance/ to gather some distance information, then is there some other way?

Triangulation (or more generally, multilateration). From earth, you can get an immediate and real time observation with a baseline of 12742km, using two connected sites on opposite sides of the globe. If you wait 12 hours, you can do it with one station and multiple observations, though the signal will need a bit more processing if it is from a moving source. Space-based detectors may give you better signal quality, longer baselines, longer uninterrupted observation periods, etc.

Given a longer period of time (eg. 6 months, half an orbit of the sun) and a much more slowly moving, stationary or very distant object, you can use the orbit of the earth to do measure the object's parallax to find its distance. You can measure things out to about 100 parsecs like this, about 326 lightyears. Whether you'd get that much accuracy on your specific source depends on too many other factors to list here, but the possibility exists. 