# Can my spaceship figure out its position using Cepheid Variables?

In my story, reasonably far in the future, an intrepid group of explorers are on the first manned mission to the Andromeda galaxy, travelling close to the speed of light. They slumbered in suspended animation for thousands of years, in their frame of reference (to a stationary observer, it would have been much longer), but were awakened by the ship's systems after an error somewhere in the bowels of the computer sent the ship off course. The main computers are down, and the crew don't know what year it is or where exactly they are. They can make some basic distance measurements by looking at the angular sizes of Andromeda and the Milky Way, but not to great precision.

Fortunately, the ship is equipped with a telescope, and the main engineer happens to be an ex-astronomer. The backup navigational system relies on manual observations of Cepheid variables, stars that have a fixed relationship between their pulsational periods and their absolute magnitudes. The ship has a database of the positions of nearby dwarf galaxies, and by observing Cepheids in four of these galaxies (using multiple Cepheids in each galaxy, to reduce measurement error), and determining their periods and apparent magnitudes, the crew can calculate the distance to each galaxy. Using trilateration, these measurements can then help them figure out where exactly they are, to greater precision.

Eventually, they'll discover that they are, fortunately, still in in the Local Group, about 500,000 parsecs from the Milky Way and 400,000 parsecs from Andromeda, placing them off course. However, they're still firmly within the galaxy group.

This is my current proposal for an ad-hoc improvised navigational system for when something goes wrong on the ship. I'm not looking for other options at the moment, but I'd like to know whether or not this is plausible, and what problems I haven't thought about.

To be explicit, here are some of the things I'm concerned about (although there may be other problems):

• The speed of the ship means that light from the stars would be highly red-shifted (if $v=0.99c$, then $z=13.11$, which is enormous). I would hope this could be corrected for, but it's still fairly extreme.
• I really don't know for sure how much metallicity variations in the Cepheid populations would affect the observations.
• We've detected extragalactic Cepheids from Earth; Edwin Hubble used them to measure the distance to Andromeda. This makes me think that detecting Cepheids from intergalactic space is possible, but it's highly dependent on the telescope being used.

Is my method realistic, or are there some major problems I haven't thought of, like the points I raised above?

Note: I'm not asking for general methods for how to find the location of my ship. That's been discussed quite a lot (at least for interstellar travel) in How can I know where to point my spaceship?, Stellar Navigation for Dummies - Finding your way home, and other related questions. This means I'm not interested in answers involving alternative methods such as triangulation or networks of pulsars - just Cepheids, as the question says. Please don't digress into these!

• If it's "a few thousands years in the future", and they've been traveling for "thousands of years", when did they leave? ("Thousands" as "two" doesn't feel right.) – RonJohn Aug 21 '18 at 18:26
• Are the intrepid explorers still somewhere in the Local Group? Can you maybe give an upper limit on the distance that they are from the Milky Way? If they are significantly outside of the Local Group, I think they are doomed. – kingledion Aug 21 '18 at 18:50
• @kingledion I've now specified roughly where they are - it's still within the Local Group, but they've deviated from the quickest route to Andromeda. I haven't decided yet which are the closest dwarf galaxies, but I imagine that won't matter for the purposes of this question. – HDE 226868 Aug 21 '18 at 19:01
• I'm confused. Aren't you the guy who generally answers these types of questions? – ShadoCat Aug 22 '18 at 0:56
• "Fortunately, the ship is equipped with a telescope, and the main engineer happens to be an ex-astronomer." Don't you mean: "Of course the ship is equipped with various telescopes for navigation and for studying the Andromeda Galaxy when they get there, and of course many crew members are trained for navigation just in case something goes wrong with the computers"? – M. A. Golding Aug 22 '18 at 19:20

# Challenges

From my perspective, the biggest challenge is whether or not you can actually observe any Cepheids. If you are hundreds of thousands of parsecs from the Milky Way, then you won't be able to see the (many of) the Cepheids that we know from our current databases. Also a concern is orientation. If we looked at the Milky Way end on, in the plane of the galaxy, even from relatively nearby, we would have trouble resolving stars other than the ones nearest us. It would be much better to look for us to be looking along the axis of a galaxy for variable stars. Of course, not all galaxies have a clean axis, in that case we'd want to be looking at it from the same relative direction as the Milky Way.

So from this perspective, we want to find a large quantity of far away Cepheid variables to ensure that we can observe them. We'll specifically look for Cepheids outside of the Local Group; these stars should be visible to our intrepid explorers since both the distance and viewing angle of these stars will be relatively unaffected by even 500,000 pc of distance.

# Available data

There are plenty! I went through some star catalogues and found...

• There are 34 good quality Cepheids in NGC 1365 at 18 Mpc.

• NGC 2090 at 12.3 Mpc away has 34 more Cepheids.

• 27 Cepheids in IC 4182 have been spotted at 5.0 Mpc. Note, here a distance was given as a distance modulus (m - M) of 28.47, which I solved using m - M = 5log d - 5; where d is distance in parsecs, and the log is base 10. I only bring this up in case I messed up the calculation.

• NGC 300 at ~1.9 Mpa has 16 identified Cepheids.

# How good is your telescope?

Basically, there are a lot of good, viable Cephids in just about every galaxy that you look in. For all four of the papers linked, the source was Hubble. So as long as you have a 2.4 m telescope (or futuristic equivalent) and 70 minutes of exposure time; and as long as your computer can do the redshift calculations, you should be good.

# Conclusion

I was researching a part of Cepheid extinction, but I left it out since it doesn't seem relevant. You don't need to find specific Cepheids, you just need to find some of them. The galaxies outside the local group won't change perceptably in distance from each other in a few thousand years, and the galaxies that we are currently able to find Cepheids in are very far away, even compared to the distance that you would be from the Milky Way.

As long as you have a present day ability to detect Cepheids (highly telescope dependent!) then you should be able to put together your location in a couple of days.

• Awesome, thank you! I have one final question: Is there reason to believe that the same period-luminosity relation applies to these extragalactic Cepheid populations, or would corrections of some sort (for metallicity, age, etc.) be needed? Oh, also - and I suppose I should really just look this up myself - how well are the distances to those galaxies known? – HDE 226868 Aug 23 '18 at 20:37
• @HDE226868 Woof, I ignored the metallicity part of your question on purpose :) I think that part is beyond me. But I do have this paper that I didn't understand: arxiv.org/pdf/0909.0181.pdf – kingledion Aug 23 '18 at 20:39

The field of view of your telescope will be severely affected in addition to the red shift at 0.99 C. One thing that you will have to overcome is the severe distortion of all images that come into the telescope will be concentrated almost into a single point the images will then be pretty much indistinguishable from each other. You would have to slow to non relativistic speeds in order to make useful observations in the first place.

• Hey, thanks for the answer! Can you maybe go into a bit of detail about exactly how and why the images would be distorted? Thanks. – HDE 226868 Aug 23 '18 at 21:41
• @HDE226868 Mathaddict is right, the effect is called Penrose-Terrell rotation. See for example here for an explanation. At 0.99c the rapidity would be around 2.65, which would cause a pretty noticeable effect. – pregunton Aug 23 '18 at 21:52
• A video representation of the full relativistic effects of Terrell Rotation: youtu.be/JQnHTKZBTI4?t=2m36s Even at .5c, the distortion is severe. – Ghedipunk Aug 23 '18 at 22:01
• Thanks for the support, this is exactly what I was referring to. – Mathaddict Aug 23 '18 at 22:10

Your method could work, although I am not certain how accurate it will be.

IMHO astronomical techniques to measure angles are much more precise than astronomical techniques to measure apparent magnitude, calculate absolute magnitude, and calculate the distance from the difference. So the question is whether using Cepheid variables will ever become more precise than astrometric techniques measuring the angles to various astromonical objects.

I doubt that an expedition to the Andromeda galaxy that takes thousands of years with the crew in suspended animation will be the very first interstellar expedition using a newly invented faster than light drive.

For one thing, a method of suspended animation for humans will have to be invented, and it will have to be tested by successfully reviving people in suspended animation for periods of decades, centuries, or even millennia before being tried for a millennia long space expedition.

People will have to be revived with no ill effects after longer and longer and longer periods, so if the expedition to Andromeda is expected to require X thousand years in suspended animation, people should have already been revived after X thousand years in suspended animation. And it may have taken several times X thousand years for people to gradually build up to being in suspended animation for X thousand years.

Instead of the expedition to Andromeda being the very first faster than light expedition from Earth, it is much more likely that Earth humans will have explored parts of our galaxy with the faster than light drive for tens, hundreds, or thousands of years and have reached various stars that are tens, hundreds, thousands, and maybe even tens of thousands of light years from Earth by the time that they decide to send an expedition to the Andromeda Galaxy.

They might even have explored the entire Milky Way galaxy or even sent expeditions to various satellite galaxies of the Milky Way, like the Magellanic Clouds, for example, before deciding to send an expedition to the Andromeda Galaxy.

So Earth humans should be spread out across many light years and parsecs of space by the time an expedition to the Andromeda Galaxy is planned and sent.

One thing that Earth based astronomers are very good at and constantly improve at is measuring small angles accurately.

A degree of arc is 1/360 of a circle or 0.002777 of a circle, an arc minute is 1/60 of that or 0.0000462 of a circle, an arc second is 1/60 of that or 0.0000007 of a circle, a milliarcsecond is 0.001 arcsecond, a microarcsecond is 0.000001 arcsecond, and so on.

The angular size of the Moon as seen from Earth is 29.3 to 34.1 arcminutes, and the angular size of the Sun as seen from Earth is 31.6 to 32.7 arcminutes, depending on the orbital distances of the Moon from Earth and Earth from the Sun. The average resolving power of the unaided human eye is about one arcminute.

Because the Sun and other stars orbit around the center of the Galaxy with periods of about 250,000,000 years at the Sun's distance from the center, the directions between the sun and other stars change slowly, a change that change is called the proper motion of the stars. Proper motion was suspected but not proven until 1718, and then astronomers began searching for and measuring proper motion more and more accurately.

The distance from Earth to the Sun varies during Earth's elliptical orbit around the Sun, but is defined as an Astronomical Unit, or AU, of 149,597,870.7 kilometers. At any one moment, Earth is in one specific direction as seen from the Sun, and exactly half a year later Earth is in the exact opposite direction as seen from the Sun and about two Astronomical units from its previous position.

A unit called a parsec, first defined about 1913, is the distance at which one AU would appear to be cover a single arcsecond. A parsec is about 206,264.806 astromical units, or about 3.261 light years. If an astronomical object was exactly one parsec from the Sun, it would appear to move by two arcseconds when measured from Earth at two times half a year apart, and would be said to have a parallax of one arcsecond.

In the late 1830s astronomers tried measuring the parallaxes of various stars with large proper motions, that were probably close to Earth, and succeeded in measuring the parallaxes of 61 Cygni at about 3.948 parsecs, Alpha Centauri at about 1.34 parsecs, and Vega at about 7.68 parsecs.

Since then techniques for measuring smaller and smaller angles, and thus measuring smaller and smaller parallaxes and greater and greater distances, have been developed. The Hipparchos satellite measured the parallaxes of over 100,000 stars to an accuracy of 0.002 arcsecond between 1989 and 1993, while the Gaia satellite launched in 2013 is supposed to get parallaxes with an accuracy of 20 microarcseconds or 0.00002 arcseconds.

One method of increasing the accuracy of parallax measurements of distant stars is to increase the length of the baseline by taking measurements from distance regions of the solar system.

And once a faster than light space drive is invented, the accuracy of parallax measurements of distant stars can be increased 206,264.806 times by making observations from two observatories in interstellar space 2 parsecs apart on opposite sides of the solar system with a baseline 206,264.806 times as long as Earth or satellite based observations.

Orbiting near Earth, the Gaia satellite is expected to measure parallaxes with an accuracy of 10 percent out to the distance of the galactic center, which is about 8,090 plus or minus 310 parsecs, or 26,400 plus or minus 1,000 light years. Putting exact copies of the Gaia satellite 2 parsecs apart would increase the distance that parallaxes are accurate to 10 percent by 206,264.806 times, out to distances of about hundreds of millions of parsecs and light years.

Putting copies of the Gaia satellite at 2,000 parsecs apart would increase the accuracy a thousand times better than that. So by the time that an expedition is sent to the Andromeda Galaxy the distances to all the major stars, nebulae, and other important objects in our galaxy and nearby galaxies like the Andromeda Galaxy should have been measured very precisely.

So if the crew of a ship headed from our galaxy to the Andromeda Galaxy need to measure their position in space, they can try precisely measuring the angles to different astronomical bodies.

for example, the angles to the super massive black holes at the centers of the Milky Way Galaxy, the Andromeda Galaxy, and the more distant galaxy M87 in the Virgo Star Cluster can be very precisely measured.

If the spaceship is not on a straight line between the centers of the Milky Way and Andromeda Galaxies, their super massive black holes will not be exactly 180 degrees apart as seen from the space ship.

By measuring the the angles to the two super massive black holes, they might determine that the spaceship is 5 degrees off of a straight line between them as measured from the Milky Way's black hole and 1 degree off that straight line as measured from Andromeda's Galaxy's black hole. So the spaceship should be on the surface of a five degree angle cone around the line with the cone's point at the Milky Way's black hole and also on the surface of a one degree angle cone around the line with it's point at Andromeda's galaxy's black one. And the spaceship thus must be somewhere in a circle where the two cones intersect.

And if they make the same sort of calculations with the super massive black holes at the centers of the Milky Way and M87 galaxies, they can fix their position on another circle where two cones intersect, and there should be only one or two points where the two circles intersect.

There are several hundred globular star clusters in the various galaxies in the local group, and the angles to globular star clusters can be measured almost as precisely to those of super massive black holes. So finding the angles to two or more globular star clusters in the Andromeda Galaxy and two or more globular star clusters in the Milky Way Galaxy, for example, should enable them to fix their position fairly accurately.

And if they measure the angle to some astronomical body, perhaps the one selected to be their destination in the Andromeda Galaxy, very precisely, and then move the ship one parsec in a direction *0 degrees away from the direction to that object, and then remeasure the angle to that object, the difference in the angles will be the parallax and thus the distance of that object.

According to my knowledge of the current state of astronomy, the measurement of angles to find position in space is much more advanced and precise than the calculation of distance by the difference between the measured apparent magnitude and estimated absolute magnitude of an astronomical body. Of course once the distances and absolute magnitudes of Cepheid variables is known much more precisely due to more advance parallaxes, using them as distance indicators will become much more precise, but I do not know if it will every catch up and surpass the accuracy of parallax measurements.

And see these questions:

• While I appreciate the effort you put into this, my question isn't "What's the best way to determine my ship's position?" - it's asking specifically about the technique I'm looking at. So . . . most of this answer isn't really relevant. Maybe I'll ask a follow-up about triangulation - in which case this would be a great answer to that - but it's not helpful here. – HDE 226868 Aug 22 '18 at 0:42

I think this method is feasible, but however still quite coarse.

If we can measure the distance of a star with 1 light year precision (and I am pretty sure that is already a pretty accurate measurement), all the related and inferred measurement will have an indetermination of the same magnitude.

And 1 light year is 9500 billion km, or 63k AU... still precise when you compare it to the size of a galaxy, fairly inaccurate if you have to move within something the size of our solar system.

By measuring more Cepheids they can increase accuracy, maybe to something around 1000 or 100 AU (a factor 10 or 100, respectively). Still, it would be more than a good approximation for inter-galactic, not for inter-planetary navigation.

• Take more measurements. Like GPS, the accuracy goes up the more satellites you're connected to. – user3106 Aug 21 '18 at 14:57
• Ideally, they'd look at, say, half a dozen or so Cepheids per dwarf galaxy (which I see I neglected to mention in the question), which should reduce the measurement error. – HDE 226868 Aug 21 '18 at 14:59

Yes it is. There are a current list of known pulsars with very unique qualities, including one that is so accurate on the pulse period, it is considered the most accurate time telling device known to man. The periods will vary from a few seconds to two or three minutes so it's quite possible to look for three pulsars to triangulate your position from anywhere in the universe where they can be detected by your sensors.

Edit: Having read up a little more, my answer is no, not as the lone mapping device. The problem is the pulse period is probably too long for a course correction within a day. The best documented example pulses anywhere between a few days to a few months at a time, depending on which ones you are looking at. There are also problems with precision with distance, and can be off by as much as 7,500 light years. Basically, too slow and in-precises to facilitate a quick navigation, but if you're willing to hang out in one spot for a few years... To be sure you're looking at the right types of pulsing. There are a few types that are prone to irregular pulsing and possibly some that may be prone to starting and stopping... not sure on that bit... which will cause delays. You can cut the years time delay down by having their pulse signatures and periods saved, but again, this may still result in a few months to find before you can set course.

Now, if they are sort of way points, and you use other methods for better course setting, you can resolve this by finding a few quick pulses and using those to triangulate your position. As I mentioned in pulsars, we used 14 to identify our location relative to them on Voyager, so more than half a dozen is not a bad idea. Say use the Cepheids to find a general direction to point the telescope to find a more accurate landmark.

• I'm not talking about pulsars, though - I'm talking about Cepheids. Plus . . . there's no analogous luminosity law for pulsars, at least none that I'm aware of. – HDE 226868 Aug 21 '18 at 14:54
• Why not pulsars, BTW? – John Dvorak Aug 21 '18 at 14:55
• @HDE226868: Yeah, we got that. Why do you require a period-luminosity law. I've looked at both phenomena on Wikipedia and Pulsars are more consistently used to identify where we are in the universe. Voyager and Pioneer both used a map of 14 Pulsars, identified by pulse time, to show where Sol was in relation to them. – hszmv Aug 21 '18 at 15:04
• This seems more commentary rather than an answer as it ignores the premise in the question. Don't get me wrong, not a bad idea, just doesn't really help with this question. – James Aug 21 '18 at 16:16

I could be wrong but I think not knowing when they've woken up, especially on the time scales of intergalactic travel will be a huge issue.

They definitely could make good course decisions on this basis if they knew when it was with a reasonable degree of certainty but with no good time or position fix I'm not sure if they can work this. Galaxies have high relative velocities, often with very high proper motions getting a good fix without knowing how much time has past will be awkward. You'll be able to get a pretty solid range estimate to each individual dwarf but their relative positions will be off to varying degrees depending how off you are with your time estimate. You end up knowing where you are relative to a bunch of points that aren't where you think they should be relative to each other and your destination.

Realistically if they're aiming at Andromeda it makes more sense to start the mission with a set of distinct landmarks, like Cepheids, supernova remnants (nebulae, neutron stars, pulsars), radio sources, quasars, supergaints, and what have you that can be combined to produce both a time fix (by interpolating the current beat pattern of many multiple fixed period beacons) and a navigational fix based on the position of multiple landmarks that are closer together and moving far slower relative to each other.

• On the sort of short timescales we're talking about (~10,000 years at the most), I think they'll be okay - within the Local Group, there shouldn't be significant motion. But you're right that having a varied network of beacons could be nice. – HDE 226868 Aug 21 '18 at 19:03