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Suppose we (a spacecraft, probe, or similar) know our location only to within a few billion km (a few Tm) in any direction in 3D space, and we want to determine our location to a higher degree of precision than this.

That was basically a question on Worldbuilding SE that I answered, where I suggested measuring the angles to known pulsars in order to triangulate one's position in 3D space. The part I didn't know about was exactly how you'd make those angle measurements, so I sort of assumed a naiive approach of basically just looking around using either an optical telescope or a high-gain radio antenna (possibly a phased array that can be reconfigured on the fly, not dissimilar from how modern RF direction finding in 2D is done).

A comment to that answer by Philipp simply states that "You can measure your angle to a pulsar by measuring its red-shift."

How does measuring the redshift help determine the angle to the pulsar, and how would one realistically go about doing it in such a situation?

As far as I understand, redshift can tell us about the relative movement of objects in space that give off EM radiation. But here, we aren't really interested in relative movement, but rather in an angle relative to some known or fixed plane (such as the spacecraft platform). I just don't see how the former realistically helps us establish the latter.

(I'm not a physicist, and don't even play one on TV, so please go easy on me. Some math is fine, though, and I expect might be helpful.)

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  • $\begingroup$ Not sure if this should be tagged pulsars or not, but I'll leave it up to those more familiar with the respective tags' scope to pick out better tags, if any, for this question. Also, if this is better posed for example on Space Exploration or Astronomy, please feel free to migrate. $\endgroup$
    – user
    Commented Mar 18, 2016 at 20:20

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The pulsars are moving relative to you. If you go to a different spot in the galaxy then the relative velocity will change (assuming you are at rest in some galactocentric frame). i.e. There will be a different angle between the pulsar velocity vector and the line between you and the pulsar and hence there will be a change in the pulsar Doppler shift, manifested as a speeding up or slowing down of the pulsar period.

I am quite sceptical about this as a long-term navigation method. (I) We need to know the accurate positions and velocities of the pulsars and also have a precise knowledge of how the pulsar spindown will proceed in the future. (II) Pulsars emit beamed light into quite a narrow cone. If you move to another part of the galaxy you won't see the same pulsars. (III) The pulsar phenomenon does not last long on Galactic scales, perhaps only a million years. (IV) Pulsars are changing their positions rapidly - moving at typical speeds of 100-500 km/s and thus using them for an extended time needs detailed knowledge of the potential they are moving in.

There are much easier methods involving the positions of distant quasars (to define a reference frame) and then triangulating using the positions of long-lived, relatively nearby but slowly moving entities like the Magellanic clouds and Andromeda.

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Pulsars are relatively faint objects, so we can only observe the pulsars that are in our Galaxy (or in its surrounding globular clusters). As such, they do not have a redshift.

I can speculate that Philipp may have conflated two separate things. The International Celestial Reference Frame uses the location of about 200 quasars to define a very accurate inertial reference frame. These quasars all have substantial redshifts, although the redshift is not necessary in determining the reference frame, only the position of the quasar on the sky. The other is a pulsar map. One can identify a pulsar by its period and then use the distances to a set of known pulsars to triangulate one's position. In fact, if the distances of the pulsars to some reference point are already known, then you would not need to measure the distance to the pulsars again. You could just measure their position on the sky.

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  • $\begingroup$ But the distances to pulsars aren't known (accurately). $\endgroup$
    – ProfRob
    Commented Apr 6, 2020 at 17:02

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