How many celestial objects are required for navigation?

Question

Weirdly, I couldn't find a similar question already asked. If it has, please forgive me!

The 'easy' answer is three celestial bodies are needed to navigate a spaceship in space. Position + Brightness triangulates location. I'm looking for precision to... let's say figuring out A) what solar system I'm in, and B) where I am relative to my "home" solar system. Pretend the home star is dim enough that it's easy to lose in the "wash"

Except... what happens when two of them are lined over each other? When one is hidden behind another object? When two are overlapping and a third is hidden?

Pretend for a second we're dealing with a system that wants to be able to orient with no 'backtracking' so to speak - no "well, we were at X position A years ago going in Beta velocity" to eliminate possibilities - more on the "We just came out of a wormhole, where the heck are we?"

Do we need to have 5 celestial objects to always orient towards? 6? Where's the sweet spot of the fewest objects to know, while maximizing the ability to always orient within the same galaxy?

I'd imagine using other galaxies for navigation is optimal... if they can be found. I was thinking "brightest objects in the galaxy" would make for good navigation landmarks, but I just don't know. Hence this question!

Answer 1

I think you're asking the wrong question. If you have a few hundred points, it won't do you any good if they're all on the other side of the galaxy's core. You won't be able to see them. This is the "random jump" problem. If you randomly jump to any point in the galaxy, how much do you have to know about the galaxy to figure out where you are?

Note that any analysis would be limited to the quality of your sensors. If you sensors were infinitely awesome, you could probably just spot the supergiant black hole in the middle of our galaxy, then figure out your orientation from the blue giants that orbit it.

For a reasonable level of sensors, you'd start by figuring out, in general terms, which way is up. Identify which directions have fewer local stars, and those are probably in the direction of your spiral galaxy's axis.

After that, you'll want to scan for hypergiants. There are about twenty that we know of but, as mentioned, we can't see through a lot of the dust clouds. If you have them all mapped, however, you should be able to spot one of them, identify it by spectra, then figure out how far you are from it by its apparent magnitude. That'll tell you generally where you are, but you'd need to spot three of them to compensate for the possibility that you've misidentified one. Adjust for time dilation, and that should get you within a few light-years.

I don't know how this translates to "how many." If you change it to "how many orders of magnitude," I could give you a solid answer of 2.

Answer 2

Potentially "one", with a sufficiently creative interpretation of "celestial object". If you're in the Milky Way, find Andromeda, and use the distortions of its apparent shape to work out what angle and distance you're viewing it from.

Probably more usefully: quasars and distant galaxies will be too far away to be of much direct use for finding your location, but two such "background" objects (or one extended object) will give you your attitude, and they will be almost immediately identifiable. Once you have an accurate notion of your spacecraft's orientation, you only need direction and distance to one known "nearby" object to determine your location, provided you can be sure of correctly identifying it. You should be able to find and identify Sagittarius A* in radio pretty easily, and thus at least roughly locate yourself within the Milky Way.

The accuracy will be dependent on how well you can measure the distance, and that will in turn depend on how far you are from the thing you're measuring your distance from. However, once you've determined your rough location, you can open up a database of pulsars and other identifiable objects and pick something nearby that will give you more precise results.

Also, while you only need one "local" object at minimum, multiple objects will give you more accurate results, especially since it'll be a lot easier to get precise direction measurements than precise range measurements. You don't need them all at the start, though: each time you add one, you'll be starting with a better estimate of your location and have a better idea of where the object you're looking for should be.

Finally, once you've located four known millisecond pulsars, you have much more accurate approaches at your disposal based on measurements of their pulses, in a process very similar to GPS. If you have good data on the pulsars, this could get you your location within less than a kilometer.

Answer 3

Your talking about Triangulation, aka figuring where you are based on points of interest, not Navigation.

Ideally, you would require a minimum of 3. It doesn't actually matter if they overlap or not (assuming you can always see the POI), because you would know their positions relative to each other and know where they had to be to form a straight line (It would also be pretty stupid to pick 3 POIs that happen to form a straight line).

Technically it would be possible with just 1 point of interest, because if you knew its size, orientation and position, you could calculate your own distance and orientation and then pinpoint your location. E.g. If you saw the pillars of creation, you would determine your own orientation based of its orientation, and then determine your distance based of its size/light.

Answer 4

3 is a minimum. For accuracy and reliability, there should be many.

We have to make an assumption about the sensitivity and accuracy of travelers' instruments. That will significantly affect the possible options. Let's say that our travelers can do observations as good as our modern astronomy can. Only, for dependability, observed signal must be one-two orders of magnitude higher than what we are able to detect.

First, any methods relying on measured distance to a celestial object will be highly inaccurate. If we can identify just one visible object, we can orient ourselves with respect to this object, but can not know our coordinates. Even with two objects, our possible location will have a range of possibilities, and only three would give us the ability to pinpoint our position accurately.

Which objects to pick for orientation is a good question. The first candidate in our galaxy would be the supermassive black hole Sagittarius A* (already mentioned in Robert Rapplean's answer), which is a very bright and distinct source of radio waves and should be detectable even if obscured by dust and gas clouds.

Space travelers should have a catalogue of celestial objects and then, upon observation, identify at least some of them in the sky. Possible candidates for those are:

1. Bright galaxies, like Magellanic clouds and Andromeda. They are less likely to be obscured than intragalatical objects;
2. Supergiants and hypergiants. At least some of them should be visible from any point in the galaxy;
3. Bright radio sources like Cassiopeia A and Cygnus A. They are less likely to be obscured than optical sources.

However, if we are trying to get high (less than 1 light year precision) accuracy at a great distance from home, "time travel" effects would make this task more complex. As already mentioned in the comments, our observed universe comes with a "time lag". Thus, observed position and spectrum of all of our beacons is different from their actual position. So if we are relying on a hypergiant that is 10,000 light years away, it's actual position can be some 10 light years from what we see. Depending on how far from home we travel, relative position of the beacons would change, and even with advanced computations, 3 object might not be enough for precise location determination.

Answer 5

I think you still only need three, but the three varies, so you need orientation information on many galaxies, for the reasons you stated.

Presuming your ship is capable of at least the level of the current James Web telescope, you can store many thousands of relatively bright galaxies and identify them. Then wherever you are, you need to identify three galaxies in 3 roughly "different" directions; say within 20 degrees of the X,Y,Z axes of whatever your personal orientation happens to be), or even search for an orientation in which it is possible to identify three such galaxies. Knowing the galaxies and their angles should pinpoint your position in 3-D space.

This should also work at any point in space, in other galaxies or between galaxies. You only need three identifiable galaxies to navigate with, and it would be a rather poor spaceship that cannot store a map of many thousands of such galaxies; I imagine we need less than a few hundred K per galaxy, so less than a terabyte of storage. We can literally store that on a thumb drive today.

Think of it as cities in the USA; If I am in Oklahoma City and don't know that, but I can see San Francisco at one angle, New York City at another, and Miami at a third, there is only place they can intersect at those three precise angles.