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I'm only just beginning to scratch the surface of the possibilities in interstellar travel. I know that pulsars can be independently identified by means of measuring their pulses, and that once enough have been identified they can be used to identify one's position in space.

My question is: How long (on average) would a pulsar need to be observed in order to identify it from its pulses alone? More to the point, how long would a craft need to watch the pulsars it finds to identify them and get a "fix" on its location based on that? (That is, is the distribution uniform, or is it skewed one way or the other and, if so, how does that affect the average time required to identify enough pulsars?)

For the purposes of this question, we're assuming highly accurate observational and measuring tools and equipment, rather than a bearded old man with a telescope in his backyard making all his calculations by hand.

I suppose another way to ask the same thing would be: What's the average cycle duration of pulsars, and how much skew is there to the distribution?

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Kromey
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    This is incredibly dependent on how much and how good your tech is. If you have a million cameras on the outside of your ship that can record light levels with 64-bit precision you'll find yourself in seconds. If you have a geezer with a telescope and a spinning disk with a hole to measure pulse rates it's going to take years. – Loren Pechtel Apr 25 '14 at 16:40
  • @LorenPechtel That's a very good point. Let's assume for the purposes of this question the absolute best observational tools and techniques science and technology have provided us. (The genesis of the question is my research for a hard-sci-fi novel involving interstellar travel, and I want to as much as possible avoid meaningless technobabble while still providing realistic explanations for how it all works.) Of course, an answer encompassing both ends of the spectrum would certainly get my up-vote, and The Green Checkmark! – Kromey Apr 25 '14 at 16:45
  • I still don't think you can get a good answer because you can always add more cameras until you run out of hull. It's a problem that's subject to parallelism--how many sensors do you want to carry around. – Loren Pechtel Apr 25 '14 at 21:25
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    And still another unknown: How unknown is your location? If your stardrive can't hop you more than 10ly then once you find a pulsar you have substantially narrowed your search for additional pulsars--and each additional pulsar narrows the search more. On the other hand, if your drive is good for 10,000ly the first pulsar tells you nothing about where others might be. It will also be much harder to identify pulsars if you can go that far--pulsars are NOT consistent through time and thus you'll get more cases of a signal that you can't tell which pulsar it is until you have more data. – Loren Pechtel Apr 25 '14 at 21:30
  • @LorenPechtel They're not? I thought the advantage of pulsars was that they are consistent. I mean, isn't that why they're useful as highly-accurate clocks? If they're not, though, that certainly does complicate matters. Do they change at a predictable rate at least? Still, the point of the question isn't so much how to scan the sky to find pulsars in the first place, but how long does a given pulsar have to be observed in order to identify it from a list of known pulsars? – Kromey Apr 25 '14 at 22:03
  • In general they slow at a predictable rate. However, they also suffer the occasional quake that causes them to speed up. Continuing to observe the pulsar will not gain any more information. You get two data points--bearing and tick rate. If you have enough pulsars in your database there are going to be overlaps in the tick rate, you'll need to find enough pulsars to resolve any ambiguities. Remember, the Pioneer plaques have a lot more than just 4 pulsars shown. – Loren Pechtel Apr 26 '14 at 01:16
  • A great research-inspiring question! – Deer Hunter Apr 26 '14 at 11:32
  • Also keep in mind that due to the doppler-effect the apparent spin-rate of a pulsar will change when your relative velocity to the pulsar changes. It might be possible, though, to compensate for this by measuring its red/blue shift. – Philipp Apr 26 '14 at 13:03
  • @Philipp I hadn't considered Doppler shift -- but would it affect the flash rate? According to current understanding (which I don't understand) light always travels at the same speed no matter where it's being observed from, so while it might look "redder" or "bluer" there should always be the same time between pulses regardless of relative speed -- shouldn't it? – Kromey Apr 29 '14 at 01:43
  • @Kromey The doppler effect does of course affect both high-frequency oscillation (light wavelength) and low-frequency oscillation (pulse rate). But here is not the place to explain this. – Philipp Apr 29 '14 at 07:45
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    Since this question received one close vote as off-topic, I would like to argue that astronavigation is on scope here as it is directly relevant to spacecraft operation. We've previously discussed star trackers, Polaris equivalent stars on Mars, and so on here on [space.se]. – TildalWave Apr 29 '14 at 16:43

1 Answers1

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Here's a correct answer: A craft couldn't.

We haven't mapped the whole of space yet so...

a craft with no other means of identifying its position

... can't know if it's near known or unknown pulsars. If you really have no idea of where you are or what your attitude is then looking around you isn't actually that useful. For example, you wake up in a forest, and from the flora and fauna you surmise that you must be in the Amazon rain forest. But you could easily be on another planet, in another galaxy, far far away.

Now if you have knowledge of your approximate position, say somewhere in the milky way, then you can start using pulsars and other things you see in space to calculate your position. You would need three known pulsars to triangulate your position (with 2 pulsars you can only know you're in 1 of 2 possible locations). If you know enough about the pulsars you could do some interesting red shift calculations to find out how far away from them you are. When it comes to the actual identification process, the duration of observation required is dependant on how many pulsars it might be, based firstly on your expected position and then on initial observations.

For example if you see a pulsar and you think you're near 1 of 10 pulsars then you can assume the pulsar you're seeing is one of the 10. Then you observe the pulsing of the pulsar and see at what rate it pulses. The longer you observer the pulsar the more accurate you calculation of it's spin can be, and hence the easier it is to rule out the other 9 pulsars.

EDIT:

The reason for a simple answer not being given to this question (by me at least), is that it is highly dependant on which pulsars you are looking at. For example take the following collection of pulsars and pulse frequencies:

A  0.98
B  0.12
C  0.51
D  0.78
E  0.15
F  12.01

It's clear that if you are trying to identify pulsar F it is going to be an easy task. If you see more than one pulse per second you can be confident that the other pulsars are ruled out. Now consider the following collection:

A  13.52
B  12.08
C  10.54
D  15.23
E  11.98
F  12.01

To identify pulsar F in this collection you Need to be able to observe the pulsar for around 13 seconds to rule out pulsar B as a potential candidate. This assumes that you can only count the number of pulses in a given number of seconds. This is unlikely, but there will be a limit to how accurately you can time pulses, dependent on the design of your hardware.

To surmise, the duration required to identify pulsar F in collection 2 is 13 times that of collection 1; this is why it's dependent on the number and characteristics of pulsars in range.

EDIT 2:

The following is based on values for 1,861 pulsars.

median: 1.88 Hz
highest: 716.35556 Hz  (PSR J1748-2446ad)
lowest: 0.084897259 Hz  (PSR J1841-0456)

Distribution plots

This looks to me like a large number in the 1 - 4Hz range say around 700. So if the values are evenly distributed in this range there is approximately 0.004hz between each pulsar's equatorial frequency. The longest frequency involved in this large subset is 1Hz, which suggests that if you can measure to the nearest 0.004Hz then you can identify the majority of pulsars in 1 second or less. If your measuring accuracy is lower this will increase the time require.

Reference: The data is a composite from 52 published works. A list can be found at the bottom of the page HERE, under external sources.

ThePlanMan
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  • Would you mind providing a few references? – Deer Hunter Apr 28 '14 at 11:39
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    He's assuming some sort of stardrive, I don't think it's reasonable to declare it impossible based on a current lack of mapping. – Loren Pechtel Apr 28 '14 at 18:41
  • @DeerHunter I don't have any references. This is all just logic. – ThePlanMan Apr 28 '14 at 19:23
  • @LorenPechtel I'm assuming no such thing. I'm basing my answer on the specifics of the question. It would be a similar scenario if you were to awake from some sort of cryogenic storage. We as a species are not sure if the universe is infinite (current thinking is now leaning towards it being infinite), so no matter how well you map space, an infinite universe will always have an infinite percentage unmapped. :) – ThePlanMan Apr 28 '14 at 19:26
  • @FraserOfSmeg I could wake up somewhere completely new and unknown to me, and with but a compass and a map (and time) figure out my exact location on Earth -- or determine that I'm somewhere not on any of my maps. Either way, in the case of pulsars it takes some amount of time of observing each one to figure out if it's a mapped one or not, and I'm interested in figuring out how long that time is. – Kromey Apr 29 '14 at 01:46
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    @FraserOfSmeg Correction: When knowing the angle between two points in three-dimensional space but not your own orientation, you would know that you are on the edge of a circle, not on one of two points. – Philipp Apr 29 '14 at 08:08
  • @Kromey in your question you assume nothing is known about your position. In your comment you assume you are on Earth. Since the universe is vast you will probably (defiantly if the universe is infinite) come across groups of pulsars that are identical to those on your maps, but situated far from your known space. The time taken to identify a pulsar is dependent on the pulsars characteristics and what else is know, or how big the collection of possible pulsars is. – ThePlanMan Apr 29 '14 at 09:22
  • @Philipp I was assuming a non zero velocity of the ship when the measurements are taken. But you are correct if stationary you can only know your position on the edge of a circle. Also since pulsars typically radiate from two antipodal points you can conceivably gain more information that just their location, you should be able to find their relative attitude allowing you to define your position as one of two points. – ThePlanMan Apr 29 '14 at 09:27
  • @FraserOfSmeg My comment goes out of the to not make any such conclusion -- "or determine that I'm somewhere not on any of my maps". In any case, it takes time to measure pulsars to determine if they're known or not, mapped or not, and the question is asking how long that is. Maybe the bit about stardrives and spacecraft is muddying the waters, but I was trying to give context to the reasoning. Also, in 3-dimensional space, you need at least 4 points to find your position, not 3 (which would give you one of two points). – Kromey Apr 29 '14 at 14:19
  • @Kromey I'm pretty sure you only need 3 points to define your position in 3D space. This assumes the 3 points have no coordinate in common of course. If your question is how long does it take to recognise a pulsar then the answer is still dependant on the pulsar. If there's only one known pulsar near you then it's easy to recognise it. If there's thousands then it'll take significantly longer. – ThePlanMan Apr 29 '14 at 14:27
  • @FraserOfSmeg In 3-dimensional space, 3 points (any 3 points) define a plane; if you know your angle relative to all 3 points, then you know you're at one of two points on either side of that plane -- but not which side of the plane you're on. Just like 2 points in 2-dimensional space gives you one of two points, you need one more point to pin down exactly which of the two points you're on. – Kromey Apr 29 '14 at 14:37
  • @Kromey as I've said in a previous comment. This changes when you are in motion. Since all motion in space is relative, and since we're talking about very fast modes of transport I'd assume you're not stationary. – ThePlanMan Apr 29 '14 at 14:55
  • @FraserOfSmeg Multilateration arguments aside, the question is still unanswered: "How long (on average) would a pulsar need to be observed in order to identify it from its pulses alone?" The follow-up phrasing is because if the distribution is skewed one way or the other, the average time to identify X pulsars (where X>1) would not be the same as the average time to identify a single pulsar: if a pulsar can be identified in an average of 1s, but it takes (say) 14 pulsars to identify a position with the necessary precision, it might take an average of 2s to identify 14 pulsars. – Kromey Apr 29 '14 at 15:09
  • @Kromey please see edit. Does this answer your question? – ThePlanMan Apr 29 '14 at 15:43
  • @FraserOfSmeg It's certainly getting closer, but I'm more interested in real-world data (knowing, of course, that we're limited to drawing conclusions only on what we've thus far observed and deduced from that) than in illustrative imaginary data sets. I have edited my question in an attempt to de-muddy the waters and refocus us on what I wanted to know in the first place, which is how long is the average pulsar's cycle, and how skewed is the distribution? – Kromey Apr 29 '14 at 15:51
  • @Kromey how's that? – ThePlanMan Apr 29 '14 at 16:06
  • @FraserOfSmeg That looks like exactly the data I'm looking for! If you can add a reference for it, I can accept your answer. – Kromey Apr 29 '14 at 16:16
  • @Kromey reference added! – ThePlanMan Apr 29 '14 at 16:19
  • @FraserOfSmeg Exactly what I was looking for, thanks! – Kromey Apr 29 '14 at 16:30