Now if only the US (and others) would get their act together and build out a backup system to GNSS. China, for example, has built out an eLoran system:
The main principle of celestial navigation is pretty easy to visualize.
Pick a celestial body that's in your sky right now, like the Sun. At any given time, the Sun is directly over a single point on the globe (the GP, or Geographic Position). So if you measure the Sun as being directly over your head, you know where you are exactly on the globe, after consulting your clock and almanac.
But, if you measure the Sun at a non-overhead angle, then you and everyone else with that same measurement must be on a circle whose centre is the Sun's GP. (Visualize the circle as the edge of a flashlight beam being pointed directly downward at the GP.) The rest of celestial navigation is refinements to figure out where you are on that circle.
The USA who just threatened to invade a few NATO allies? People working with USA for the next few years seems pretty foolhardy. Surely everyone else in NATO needs to be getting together and building it defense system that exclude USA.
For (e.g.) eLoran, each chain is independent of every other chain. So the network chain(s) run in the EU are not dependent on the chains in US/CA, are not dependent on the chains in Russia, or the Middle East:
I'm pretty sure the threatened invasions are just distractions to change the conversation from the H1B debacle.
If for no other reason than Canada is a country a lot of Americans actually care about (many have relatives there), and without a formal declaration of war congress could step in at any time and declare the whole thing illegal, enabling the military to refuse orders relevant to the invasion.
But as an American who has been a little sick of Europe mooching off of our military overwatch (see various European nations running out of bombs during the Libya campaign), I'm all for an independent European military command with independent capacity. The Cold War is over, the Russian tank hordes that once threatened to roll across Western Europe haven't managed to roll halfway across Ukraine with even reluctant, intermittent, indirect western support. We don't need to be under some monolithic military command anymore, Europe does not (or at least should not) need US strategic overwatch to fend off Russia.
As for the "European militarization has historically led to world wars" argument, the UK, France, and Russia all have nukes. Germany could probably build a few in a long weekend if sufficiently motivated. We aren't going to see a WWI or WWII rematch unless the AI "revolution" actually turns out to be more than smoke and mirrors for dumb money and enables perfect missile defense or something.
So yeah, please get an ex-US NATO off the ground so we can focus on China.
> So yeah, please get an ex-US NATO off the ground so we can focus on China.
If the US does not care about its European allies, it no longer has the economic power to "focus on China". From an European perspective, China is far away and not particularly threatening. If there are no specific reasons to support the US, it's better to not take sides and trade with both sides.
BRICS is already a serious challenge to the Western hegemony. If the US thinks that "the West" has no longer a reason to exist, it will be seriously outnumbered by those who don't share its ambitions.
> BRICS is already a serious challenge to the Western hegemony.
A semi-joke-y observation:
> Pretty straightforward really. You combine Brazil's history of monetary stability, with Russia's respect for property rights, India's domestic tranquility, China's financial transparency, and South Africa's investment opportunities - and hey presto, you've got a new global money.
If the 'BRICS currency' is made up of only a small group, then it's not going to be useful, especially the restrictive countries that are in the name.
But if you expand it, sure it could become more useful, but then you've got competing interests and desires and a coördination problem on policy and such.
Further: I've yet to see an explanation of how this thing will actually work. Does each country given up their own currency, Euro-style? Is there a 'theoretical currency' that everyone pegs their own to? What are the consequences for de-pegging (if any)? Are bonds issued in BRICS or the country's own currency?
This European perspective is one of the reasons that many developing countries outside of Europe didn't condemn Russia's invasion of Ukraine. As India's External Affairs Minister had remarked, "Europe has to grow out of the mindset that Europe's problems are the world's problems, but the world's problems are not Europe's problems."
BRICS is a total joke. Some of the member countries have taken limited unilateral actions to challenge Western hegemony but BRICS as a group has never taken any meaningful coordinated action and never will. India won't go along with anything that benefits China. South Africa is a failed state. Brazil has no global ambitions. And the Russian Empire is bleeding to death in Ukraine; even if they eventually "win" their ability to challenge us has disintegrated.
BRICS is not supposed to be a coordinated power. It's a tool for creating the multipolar world order Putin has been dreaming of for decades. A world where the US is just one power among many and the dollar just one currency among many.
And the best way to achieve that is creating a wedge between the US and its allies.
My impression is the US has pretty consistently tried to dissuade the EU from developing any kind of capable military organisation and to instead do it as part of NATO.
Although I have to assume that with Trump as president for a second time a lot of people in europe are going to have to worry that the US can't be relied on in the way it could in the past so I think you might get your wish.
> and without a formal declaration of war congress could step in at any time and declare the whole thing illegal, enabling the military to refuse orders relevant to the invasion.
I’m pretty sure that war requires congressional approval BEFORE an invasion full stop. Congress in recent history has been fairly cavalier about letting the executive launch military action and looking the other way, but it’s not actually supposed to work this way.
> The Cold War is over, the Russian tank hordes that once threatened to roll across Western Europe haven't managed to roll halfway across Ukraine with even reluctant, intermittent, indirect western support
This is a gross mischaracterization of the situation that significantly underplays what actually happened I think. Without what Biden did right before the war saying “it’s going to happen” and mustering broad domestic and international support as well as using sanctions to freeze Russian assets and use them to pay Ukraine for reparations, Ukraine wouldn’t exist today.
We’re talking about $70B of military HW and $23B in terms of economic and humanitarian aid and another ~87B for the Ukrainian government to keep the lights on. That’s from the US alone. The international community has also contributed another $100B.
> We aren't going to see a WWI or WWII rematch unless the AI "revolution" actually turns out to be more than smoke and mirrors for dumb money and enables perfect missile defense or something.
It’s a slower burn. Putin isn’t going to try to take everything at once. It’s the Hitler annexation strategy over a longer time period. A little Georgia here, a little Crimea there, now it’s the entirety of Ukraine. Partly because his country is weaker but also because war is more expensive to prosecute than 100 years ago due to technology and the resistance is much better prepared for such an attempt.
Where do you think Eastern and Western European civilians will flee if any of those countries is drawn into conflict with Russia? Conflict forces desperate immigration which then creates anti-immigration counter responses in domestic populations here in the US.
China is important but what are we going to do there? Do you think we’re going to successfully defend an invasion of Taiwan when it happens? Cause that’s going to be their first military action. And if people are complaining about supporting Ukraine, how do you think they’ll fair regarding Chinese nationalists?
Finally, I’m pretty sure the troops and equipment we need there are also fairly different. If China is delivering huge numbers of land troops to Taiwan in the first place I’d say the battle is very lost. It’s going to be a sea/land siege so if the US gets directly involved it’ll be a meeting of the navies.
The question was “Greenland and Panama” and the answer was “I wouldn’t rule anything out”. It requires a pretty hard squint to convert that into a threat “to invade a few NATO allies”. This sort of intentional misunderstanding of an exaggeration does so much more harm than good.
A western defense system that excludes the USA is naive at best.
If these countries were our allies the answer would be “I have no idea why you would even be thinking that question”, not “we won’t rule anything out”.
Not ruling anything out is not a threat. Panama is not a NATO country. One is not a few. ‘Military options’ is not synonymous with invasion. “Invading” is a funny term for an area currently occupied by several US major military bases. The list continues.
I hate to sound snarky, and I mean this genuinely, but forcing people to defend someone is not a way to generate allies. A decade of “what he actually said was” is enough to turn even the most strident progressives towards the middle at least.
> Now if only the US (and others) would get their act together and build out a backup system to GNSS. China, for example, has built out an eLoran system:
What prevents other countries from using these other systems?
> They are moving towards quantum navigation (esp subs)
How does that help the merchant marine that is part of the logistical supply chain? Are container ships going to get this quantum nav boxes too? The US pays airlines a retainer to be a reserve fleet [1]: will they get these boxes as well in case of emergency?
What happens to all the civilian infrastructure that need navigation and timing signals?
Considering only the "military" ramifications of GNSS disruption is myopic.
>As The American Practical Navigator (aka “Bowditch”) states, “No navigator should ever become completely dependent on electronic methods. The navigator who regularly navigates by blindly pushing buttons and reading the coordinates from ‘black boxes’ will not be prepared to use basic principles to improvise solutions in an emergency.”
I wonder if this mindset is also applied, for example, to the rest of the military. Does the Army regularly practice land navigation? I know they get at least one landnav class, but it is a perishable skill. If you don't practice, you'll soon forget about it.
I guess this could also be useful to civilians. Being able to do stuff without relying too much on electronics.
Some Army units, particularly ground combat units, regularly practice land navigation with map and compass. I don't think they typically spend much time on celestial navigation beyond the basics of finding heading based on constellations. They're not usually carrying sextants.
Ships are far more isolated than land crews, and direction-finding is much harder at sea than on land. If you're part of an organization that cares where you are and wants you back, you are pretty easy to find your general location venture off on a land journey and get stuck. A single human might be hard to find under a rock or snow, but an army unit that wants to fund is easy to spot.
It's really funny to watch a bunch of people contradict the US Navy when it comes to navigation at sea. No, a cell phone isn't going to work in the middle of the Pacific and no, the US Navy doesn't use Google maps. Go get on an actual boat sometime and sail out of sight of land, you lose cell signal way before you're even over the horizon.
Have there been any computer vision systems that can approximate celestial navigation using common sensors like a camera, An electronic compass, and a tilt sensor? Something like a computer vision based auto sextant. This is an idea I have thought about for a while but I have zero background in this area.
Yes, starcams are standard equipment on satellites including Cubesats because they provide more precise attitude information than any other available sensor. There are numerous free-software packages for star tracking; a quick search finds https://github.com/spel-uchile/Star_Tracker. I don't know if there's, like, an Android app that will do the required sensor fusion to tell you where on Earth you are.
The closest unit I can think of right now was the SR-71's celestial navigation unit. I don't know how it worked internally, but it supposedly navigated the spy planes to targets across the globe before GPS existed.
A number of ICBMs used / uses a similar approach. In space, stars are always visible well, and terrestrial navigation aids may have been jammed or destroyed when ICBMs are put to use.
From one SR-71 memoir I remember the factoid that sometimes the electromechanical star tracker was sensitive enough to catch stars in the daylight while the plane was still on the ground. Makes one wonder what is possible now with modern digital photographic sensors and processing power. And miniaturisation of course, the 60s celestial navigation unit was the size of a fridge.
Not exactly what you're looking for, but spacecraft can use optical star trackers which compare what they see to a catalogue of known stars to determine orientation.
I'm not aware of any specifically, but one of the instruments that can be used as a data point to further reduce error when navigating in a zero-GPS/zero-radio-signal environment is an INS. The very highest precision ones are quite classified and used on submarines.
Curious how navigation at night was not possible without expensive equipment, sounds like they were relying only on starts in the morning and evening? Are the measuring something like angle of those morning/evening stars or their set/rise times with respect to the sun?
It is not true- the authors sound very inexperienced with celestial navigation. There are many ways including the lunar distance method to get a position at night with regular equipment. The math is more complex than a simple noon solar sighting, but it can be done with just a regular cheap plastic sextant and a watch.
It’s also no big deal to go 12 hours with no position. If you know your speed and heading you can accurately estimate your position much longer than that.
Overall, they also made it sound almost impossibly difficult for a large team of professionals, when solo and otherwise short handed recreational sailors have been reliably sailing around the world with celestial navigation for more than a century- through all possible conditions.
Note that they were staying roughly 2 miles within the actual track, while having the bulk of the work being done by a combo of officers and newbs that they had just trained. That's high accuracy standards for celestial nav, not even counting that this is most of other people's first time doing this in anger.
> Curious how navigation at night was not possible without expensive equipment, sounds like they were relying only on starts in the morning and evening?
As a sibling comment notes, it is possible. There are tables for lunar distance:
So does that mean USN ships are issued with a precision mechanical chronometer for longitude, like John Harrison's original marine chronometer that won the Royal Navy's Longitude Prize?
An electric timekeeping device which is not networked would presumably be good enough for this purpose wouldn’t it? The concern is ewar not so much the ship not having electricity.
Believe it or not, some people still use slide rules and books on trig tables for this very purpose. They use them too. No sense in having them if you aren't competent at using them.
> analog navigation techniques became relevant again
I'm not sure exactly what methods were used in this navigation exercise, but if they write down numbers with finite precision at any point in the process, then the method has at least some digital component to it. Note that digital means the use of digits, not necessarily any involvement of computers or electronics.
For example, if they take a reading on a sextant, write down a number, and manually transfer it to a coordinate on paper, then that is a semi-digital process. If they take a number and then look up some kind of trigonometric table, that is definitely digital and not analog. But if the navigation process entirely consists of analog mechanical linkages and at no point any number is read out, then I would deem it 100% analog.
> using the radian rule, steering 1 degree off base course for 12 hours at a speed of 16 knots results in nearly 3.5 nm left or right of track (565 yards per hour)
This brings up a laughable feature of the US customary measurement "system", a hodge-podge of units with no coherent logic to it: 1 nautical mile ≈ 2025.371... yards, an awkward number that isn't even whole. This is because 1 nautical mile = 1852 metres exact and 1 yard = 0.9144 metre exact. Converting between these units would be a pain. (Whereas at least 1 mile = 1760 yards exact.)
Analogously, let's say you're piloting an airplane at an altitude of 15000 feet and have a horizontal distance of 7 nautical miles to your landing site. What would be the descent angle if you flew down in a straight line? The answer is not immediately obvious because you can't do trigonometry on different units. Whereas if I said you're 4572 m high and 12964 m horizontal distance away, then the angle is arctan(4572/12964) ≈ 19.4°. And even if distances are reported in kilometres, even a child knows that 1 km = 1000 m.
Knots and nmi are not US customary units. 1nmi is 1 arcminute along the Earth's surface -- 1/60 of 1 degree. Knots are simply nmi/hr. Navigation is really just the application of spherical geometry. Not sure why they're referring to yards, I've never heard of those used in a navigational context.
If you want odd American units you should check out surveying. Units vary by geographical region.
Uh yeah they are. They are _customarily used_ in the US, so they count. They're literally used on all ships and planes. Any unit that is broadly used in the USA is USC. Further, they are indeed listed under the USC page: https://en.wikipedia.org/wiki/United_States_customary_units .
Sorry, I meant that they aren't exclusively US units like US has its own unique pound, etc. Nmi are widely used because elevation of a celestial body can be directly translated to it's Geographical Point's distance from your location with some mental math. Handy.
> tune to your favorite station on an analog FM radio ... dial
I mean, when an ad says "Listen to 123.4 FM!", they are literally conveying that information to you digitally; they are telling you the number to tune to.
A fully analog radio has markings to give you a rough guide of where the frequencies are, e.g. 99.0 MHz, 99.1 MHz, 99.2 MHz, etc. When you take the number in your mind and map it onto the markings, you are performing a digital-to-analog conversion (DAC). And because the dial is analog, you can make it fall between any marking you want; there are no steps that you're forced to take.
Meanwhile, a digital tuner would let you tune to 99.1 MHz and 99.3 MHz with nothing in between.
A smartphone has all the sensors: tilt, clock, camera. Even compass, though hardly needed. This should be enough to build an app to determine position at sea.
> Any navigation equipment that used electricity was prohibited, including all GPS sources, the Essex’s electronic Voyage Management System (VMS), and the computer-based celestial navigation software STELLA.
Cellphone clocks are quartz crystals. Ordinary quartz crystals have an accuracy of ±10 ppm. That's ±0.001%. That's plenty accurate unless you've been at sea for a long time. 10 ppm of a month is 26 seconds, during which time the equator rotates 12 km (6 arc minutes, 1.9 milliradians). That's not "a few degrees".
Of course if you have a GPS signal you can keep time to within nanoseconds, but I suppose we're assuming GPS is jammed.
Cellphone cameras typically have pixel pitch on the order of 250 microradians, but star trackers routinely deliver attitude information accurate to less than a tenth of a pixel, so 25 microradians, which is 5 arc seconds, not "a few degrees". Calibrating a star tracker for a mass-market camera with its nonlinear distortions is a pain in the ass but can be done. 25 microradians is 160 meters.
SatState from F-Droid shows that my cellphone's accelerometer (tilt sensor) seems to vary by ±0.01m/s² in each of its ≈200ms samples, which is about a milliradian of error, 40× worse than the camera error, about two weeks of clock drift. This isn't "a few degrees" either. Accelerometers can integrate over arbitrarily long periods of time to reduce noise; to reduce noise by 40×, assuming a Gaussian distribution, you need about 1600 samples (320 seconds, 5 minutes and 20 seconds) to average out to the same level as the camera error.
(It's easiest if the phone is sitting still during the averaging time, but both the gyros and the star tracker attitude information permit you to usefully average the accelerometer signal over time even when the phone is changing attitude.)
You probably do need to calibrate the angle between the accelerometer and the camera, but it probably won't change significantly over time for a given phone.
The clock seems like it could be the weak point here, but even the clock is only drifting a few hundred meters a day, and that only produces an east-west error.
* https://www.npr.org/2016/02/22/467210492/u-s-navy-brings-bac...
Now if only the US (and others) would get their act together and build out a backup system to GNSS. China, for example, has built out an eLoran system:
* https://rntfnd.org/2024/10/03/china-completes-national-elora...
An old USAF video explaining how the theory works (it assumes a geocentric worldview: the Earth is the centre of the universe (but it's not flat :)):
* https://www.youtube.com/watch?v=UV1V9-nnaAs
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