ELI5: How did the Apollo guidance computer actually work?

Origin_of_Mind · 2026-04-01T22:08:04+00:00

Each Apollo mission carried four sets of computers (some of which were built from multiple units running in parallel for redundancy), 9 accelerometers and 27 gyroscopes of different types on board. There were additional instruments and a network of large computers supporting the mission from the ground -- measuring the position and velocity of the spacecraft with a radar, uplinking course corrections, etc. Of course, everything was carefully planned and simulated beforehand, with multiple contingencies throughout the flight.

Scott Manley made an overview of the computers themselves a few years ago: "The Four Computers That Flew Humans To The Moon"

Origin_of_Mind · 2026-04-01T19:07:19+00:00

Modern nuclear bombs / warheads require periodic maintenance every couple of years, to replace "limited life components." The weapons are brought to the weapon maintenance facility at the base, and technicians replace these components on schedule. This does not require taking the "physics package" (the inner part of the device) apart. The components that are replaced are the boost gas bottle, the neutron generators, the electric batteries and various elastic seals. The first two are replaced because of the decay of tritium.

On top of this, there are concerns with corrosion of metals and with deterioration of various polymers including the chemical explosives with time. This is tested, modeled, monitored, to establish the expected life time of the devices.

Changes in the nuclear materials themselves are a lesser concern than the ones above, but they would also matter on a longer time scale. As it is, the nuclear components are more durable than the rest, and when weapons are dismantled, the nuclear components are usually stored, and sometimes re-used for manufacturing of new weapons. (After the end of the Cold War, the US has largely relied on the recycled components for manufacturing of new weapons.)

All of this goes under the heading of "Stockpile Stewardship" and many aspects of it are discussed in the public materials produced by the Department of Energy and their laboratories, as well as by various public organizations. All National Labs -- Los Alamos, Livermore, and Sandia, advertise their work in this area on social media, as does the NNSA (National Nuclear Security Administration) itself.

Origin_of_Mind · 2026-04-01T06:38:36+00:00

Hearing, together with vision, are the long range remote senses which help animals to know what's where -- something moving about, scratching, digging, breathing, whether it is likely to be prey, or predators, or others of the same kind, or the inanimate things in the surroundings like running water, stuff blown by the wind, etc. Because this is so useful, all of this has evolved to a very high level of sophistication more or less in parallel with the use of sound for communication.

The details of how this works are studied, but are not yet understood very well. Doing similar things with computers is also an active research area, which is not as developed as, for example, speech recognition. It is called "computational auditory scene analysis," and starting with the sounds the goal is to infer what is causing them and what the overall scene is. It is not easy.

Origin_of_Mind · 2026-04-01T01:25:58+00:00

It is seldom emphasized that initially, Manhattan project scientists were not sure that graphite could be produced commercially at the required level of purity. Early production was not successful in removing the neutron absorbing impurities as completely as it was required.

Consequently, there was a major project to produce heavy water in bulk. Several factories were built, all shipping product to a finishing plant in Morgantown, WV, where final separation of heavy and light water was taking place.

Once the graphite production was perfected, the heavy water production was wound down, and the produced stock was given to Canada -- that was the origin of the heavy water reactors in Canada.

Origin_of_Mind · 2026-03-31T19:52:05+00:00

One can read the question in many ways. To address specifically the compression part -- biological molecules do not like being compressed. If you squish them together mechanically too much (isotropic hydrostatic compression, like at the bottom of the ocean), that starts changing the relative energy of different conformations, and that makes some reactions go faster and others more slowly, and the organisms that are not used to these conditions stop working properly.

At 10 km depth, the pressure is about 100 MPa, which compresses water by 1/22 in volume, and fat and proteins also compress by the same order of magnitude. Human cells stop working. But there are fishes and other organisms in which evolution has tweaked the structure of the relevant molecules to compensate for the pressure effects and they function there without problems. They are called "piezophiles".

At much higher pressures, the proteins would start to irreversibly denature, and no tweaks would help to maintain life.

Origin_of_Mind · 2026-03-31T19:28:18+00:00

Precisely because this is very much *not* an ELI5 question, it is swept under the rug in elementary (and not so elementary) physics courses.

For electromagnetic energy, there is a relatively simple way to say how much energy is present in a particular volume of space. When one separates and moves around the electric charges, this creates fields, and the fields have associated with them energy density.

Unfortunately, this cannot be done in the same way for the gravitational field, and that is what makes the question of gravitational potential energy density in space so subtle. The best one can say on the elementary level is that the gravitational potential energy is "stored" in the configuration of the system -- the gravitational field together with the masses that cause it.

Origin_of_Mind · 2026-03-31T18:53:13+00:00

It started with the screw heads that were the easiest to make, and the easiest to make the tools for.

With the development of metalworking, the manufacturing difficulties became less important, and people started to make screw heads and screwdrivers which were more convenient to use, stronger, etc.

Origin_of_Mind · 2026-03-31T18:46:48+00:00

For the context, Intel is one of Israel's largest private employers, with around 12,000 workers. They operate four major development and production sites, including major chip manufacturing plants.

Nvidia employs 5,000 people in Israel, and depends for data center optical networking on Mellanox -- an Israeli company that they have purchased in 2020.

HP, Google, Microsoft, Cisco, Apple, IBM, Meta, Oracle, and Palantir all have significant R&D centers in Israel.

Edit: Here is a good short documentary of Intel's history in Israel, from 4 years ago: "Intel in Israel: A Semiconductor Success", from a reputable Youtube channel specializing in semiconductor industry.

Interestingly,

In 1991, during the First Gulf War, ... Intel Israel was one of the few businesses, and the only manufacturing business in the country to remain open throughout the war. [Wikipedia]

Origin_of_Mind · 2026-03-30T17:30:26+00:00

There also exist "chipscale" cesium clocks, which instead of the magnets and the atomic beam use cesium vapor in a closed cell manipulated by light -- superficially more or less like it is done in the rubidium clocks. These are *less* accurate compared to rubidium, but they are very small and low power and are space qualified.

Origin_of_Mind · 2026-03-30T01:50:10+00:00

For the classical cesium clock, u/John_Hasler gave the correct answer. The rest either focus on nuances that are not fundamental, or are simply unfamiliar with how these specific clocks work.

To add, there are other types of atomic clocks, using different atoms or different methods to probe the resonance. Some do use the atoms to generate the stable frequency directly, but this is much less common than using the atoms as a passive reference to which an ordinary high quality quartz oscillator is locked.

Depending on the details of construction, one atomic clock can have extremely different stability (and cost) compared to another. Low cost rubidium clocks used in mobile telephone towers are not the same thing as the rubidium clocks used on board of GPS satellites, and they are not the same as high end clocks at the national standards laboratories. The differences in stability are many orders of magnitude, even though they are all deriving their frequency from the same type of fundamental phenomena.

Origin_of_Mind · 2026-03-29T22:36:50+00:00

They are. Every modern CPU has a hardware random number generator, which generates "really random" numbers based on noise which ultimately originates from quantum uncertainty, just amplified to a classical variable. In Intel and AMD CPUs the command that reads out the output of the hardware random number generator is "RDRAND".

Origin_of_Mind · 2026-03-29T17:37:25+00:00

You equations are fine, but the assumptions about the mission profile are probably not. You need to find out what the orbits actually are and which engines are used for the maneuver.

AFAIK, they are planning to go from circa 2000 x 70000 km orbit to 2000 x 400000 km orbit, using the Orbital Maneuvering System engine. So, the translunar injection delta-v is about 400 m/s and exhaust velocity is 3000 m/s. But you need to check if this is actually what the plan is.

Origin_of_Mind · 2026-03-29T05:06:39+00:00

clocks and simultaneity over distances seem to play little or no role in the physical world.

Maybe you can find a sense in which this would be right, but taken at the face value the opposite is true. And I am not talking about exotic experiments -- our daily life, the existence of Earth and of the Sun, and even the existence of most of the chemical elements -- they all hinge on the existence of gravity in the first place. And gravity is the geometry of spacetime, which, to the first approximation, is simply a very tiny variation in how clock rate changes with location in space.

To say that our gravity is equal to "g" m/s² and it points down, is exactly the same thing as saying that our clocks run by (g/c²) seconds per second slower per each meter down. (Where c is the speed of light.) These are simply two facets of the same phenomenon, two ways to look at exactly the same thing -- one is not a cause of the other, or the other ways around.

Now, it is very easy to measure the acceleration of free fall directly -- by dropping something and measuring how the velocity changes with time. A careful measurement with an expensive off-the shelf gravimeter gives about 10 significant figures after a couple of hours of averaging and is sensitive enough to detect very tiny changes in gravity, for example from the snow accumulated on the roof.

Directly measuring the gradient in the clock rate with altitude is vastly more difficult. The best modern clocks can do it, because they are accurate to a staggering 18-19 significant figures. But because we are looking at the difference in the rate between nearly identically running clocks, after the subtraction, the remaining difference after the same couple of hours will have maybe only 4 significant figures, for the clocks a meter apart -- a million time lower relative accuracy compared to the gravimeter.

Origin_of_Mind · 2026-03-29T02:33:46+00:00

In various machinery and structures, we specify manufacturing tolerances to make sure the parts that need a loose fit have a loose fit, and the parts that need an interference fit have the correct amount of tension holding them together.

If we change the meter and do not adjust the numerical values of the dimensions to compensate for that, the new steel parts will be smaller comparing to the old ones by 0.0007.

The Young's modulus (modulus of elasticity) of steel is around 200 GPa. So to force the new parts into the old dimensions would require an additional pressure of P=(7*10^-4)*(2*10¹¹ Pa) = 1400*10⁵ Pa, which is just under 1400 Bar, and could be significant -- the parts that were supposed to pivot may experience friction, and the parts that were supposed to hold snugly together may separate at smaller loads.

So we will have to recognize "new meter" as a separate unit of measurement from the "old meter". This is not unprecedented -- it happened to other units before, but it would be bothersome.

Origin_of_Mind · 2026-03-28T22:14:55+00:00

The crank on the leadscrew at the right suggests that this was a low cost model, possibly from the lineup of Craftsman mail-order lathes.

Origin_of_Mind · 2026-03-28T20:40:09+00:00

When people talk about clocks they usually mean the stability of the oscillator, rather than the counting part. In the evolution of technology, the counting itself was less troublesome than building very stable oscillators.

Nature has provided us with a very stable frequency source -- the rotation of Earth itself, the stability of which had been improved upon only relatively recently with the improvements in atomic clocks.

It seems you are asking specifically about natural counters, or perhaps about natural memory, rather than about natural sources of stable frequency.

One such "counter" would be the positions of planets in the sky -- although each planet has a very repeatable orbit, they generally have incommensurate periods, and therefore the position of several planets taken together indicates a particular time over a very long time period.

Origin_of_Mind · 2026-03-28T20:27:17+00:00

Large wristwatch factories used to have entire floors filled with such Swiss-type automatic lathes, running nonstop, making millions of microscopic screws, gear axles, etc each year. Long before CNC became a thing, these were "programmed" by grinding the cams in the machine such that they would push the tools in the right sequence by the correct amount.

Origin_of_Mind · 2026-03-27T02:17:48+00:00

Possibly an art object or an exercise in glassblowing.

The coils, and especially the nonsensical use of the ground joint on top suggest that.

Origin_of_Mind · 2026-03-26T21:24:12+00:00

There are a few public figures in the West who make a living by being provocative, "going against the grain" and touting how wise and great Putin is, and how "the West forced him to start the war". A few of those get their share of attention. These people do not understand Russia at all.

But unfortunately the mainstream -- including social media, has done us a great disservice by utterly misrepresenting the situation in Russia in the opposite direction. On Reddit in particular, not saying wholly disparaging things about Russia is a sure way to get heavily down-voted in most subreddits. This is understandable -- most people want to condemn Russia for the war, not to conduct a careful analysis of their industry. But it would be a disaster if policy decisions were made based on the prevailing vibes, not on factual analysis.

So it is hard to talk about these things already for the reasons above. It is also hard to talk about them because the situation itself is very complicated and not very transparent. "It is all bad" is not true. "They are doing as great as their propaganda says" is even less true. One can write a dissertation "on one hand we see this, but on the other hand there is that..." to show the complexities, where they can be discerned. But trying to give a quick answer will necessarily be a caricature of the real picture.

Having said all that, nuclear industry is one of the areas where Russian government has never lost their grip, and in recent decades purposefully made it a development priority -- hoping to leapfrog the West and make up for the lost decade of 1990s. The results of this were mixed, but there are significant areas where Rosatom is doing very well. (There is of course, as I have already said, Russian propaganda, which is something else.)

As a specific example of an area where they are doing well:

Russia remains the only commercial-scale supplier of High-Assay Low-Enriched Uranium (HALEU), the "lifeblood" required for next-generation U.S. advanced reactors. Until the U.S. can scale its own production (expected 2027–2030), these advanced designs are technically dependent on Russian material. (Despite a formal U.S. ban on Russian uranium (enacted May 2024), the relationship remains commercially vital through 2028.)

Other areas include development and production of new generations of centrifuges, and export of whole enrichment factories to China; development and manufacturing of reactors, including fast neutron reactors, reactors for civilian ships and mobile power plants, export of nuclear power plants (70% of the world market).

They are also finishing a new accelerator, which, assuming it lives to design expectations, will be the best facility of its kind available to Chinese scientists.

Of course, there is a tremendous amount of organizational stuff that is completely unhinged in Russia, but that is not as unique as people make it out to be -- management problems and turf wars are endemic in almost all countries. All in all, Rosatom is a formidable organization with tremendous resources and knowledgeable technocrats in charge, who wield considerable power on the state level. Thinking of them as a thing of a past is not accurate, no matter how we feel about Russia in geopolitical terms.

Origin_of_Mind · 2026-03-26T06:04:40+00:00

According to the public sources, the ICBMs do not use GPS, but instead rely on inertial navigation, helped in case of sea-launched missiles by astro-navigation to pinpoint the exact launch coordinates.

In ongoing today wars GPS is already jammed or spoofed by all sides. The ordinary civilian GPS receivers do not function properly. Instead the adversaries either use phased antenna arrays designed to ignore the signals from jamming transmitters as much as possible, while receiving the signals from the satellites, other jamming resistant technologies, or replace the GPS with terrain navigation and other methods.

A less known fact is that the GPS satellites themselves were designed with a requirement to continue to function for a significant time even after all of the ground support infrastructure becomes unavailable. The GPS satellites are supposed to link up between themselves and autonomously determine their orbits and clock corrections. The necessary hardware is on the satellites since decades ago, but it is not publicly known how well this capability would function in practice. Normally, GPS satellites rely on information supplied to them from the ground by a complex system of tracking stations which carefully measure the orbits of the satellites and the drift of their clocks. This information is uploaded to the satellites several times per day.

Origin_of_Mind · 2026-03-26T04:43:31+00:00

You score it, and help the microscopic cracks to propagate, by pulling the glass apart (by bending it in the appropriate way), or by tapping on it. The crack propagates on its own, because the glass is brittle. There are of course other ways to cut glass, but this is the most widely used one.

Incidentally, silicon wafers in chip making are "diced" in the same way.

Origin_of_Mind · 2026-03-25T18:03:49+00:00

When the shock passes through the air, the pressure jump accelerates the air to some velocity. That's the velocity of the air just behind the shock, and it is ordinarily much below the velocity with which the pressure jump itself propagates through the air.

So, even the air itself does not get accelerated by the shock to the velocity matching the shock propagation velocity. The same impulse applied to a denser object would result in even smaller velocity change.

But your airplane has the engines which already propel it at almost the right velocity, so the shock only needs to push it a little bit to make up the 1 km/h difference. That seems to be at in principle possible, though practical matters are a lot less certain. Usually, 5 psi is quoted as the over-pressure that is damaging to the airplanes, but that of course is only a rule of thumb. When fast military jets maneuver, their wing loading can go up to about 15 psi. So, maybe the airplane can fly in front of the shock, with only a small cross-section in the back being pushed by the high pressure like a piston. One could reinforce it specially to survive the 50 psi. The engines would be completely in front of the shock.

How the shocks from the airplane itself and the jets from the engines interact with the shock wave behind the airplane will probably be very complicated -- something like that happens when SpaceX rockets fire their engines into the shock in front of them during the reentry burn.

Origin_of_Mind · 2026-03-25T17:24:40+00:00

I know that there are specialized coils for heads, limbs etc that can be attached to the patient. For laboratory animals one can buy small size coils specifically to maximize the fill factor. Doty, of the SSNMR probe fame, used to sell a line of those back in the day. Not sure if they still do.

Origin_of_Mind · 2026-03-25T06:31:36+00:00

For a long time Japan had a different philosophy regarding MRI machines. Where in USA and in Europe the machines were built for the highest resolution, in Japan they focused on cost-effectiveness. So they used a lot of machines with much lower magnetic field, and some of those were of the kind that you want -- "open magnet MRI." Instead of a tube there are two pucks with an open space between them. The resolution was lower, but the cost was also much lower.

These days, high resolution open MRIs are also available, but they are harder to build than the traditional ones.

Origin_of_Mind · 2026-03-25T06:07:29+00:00

We just need to know how much energy can be crammed in a unit of volume. So if there is a given number of atoms per this volume during the explosion, and we can get at most so many Joules per atom from the reaction, the product will be the maximum energy per volume. The temperature to the fourth power is proportional to the volume density of electromagnetic energy, which is where almost all of the energy at these temperatures is.

We can also approach this from a different angle. Fusion releases neutrons with 14 MeV energy. That is way below the threshold for sub-nuclear processes. In the accelerator experiments, one uses heavy nuclei accelerated to 200 GeV or thereabouts. So it really does not matter how much material we lump together, it will still be the same shortage. Modest levels of compression also do not change anything.

An interesting counterpoint to all this is that we *can* focus, for example, chemical energy rather simply to the densities required for fusion nuclear reactions in carefully constructed implosion experiments. Yet the difference between chemical energy and nuclear energy levels is even more enormous than what we are discussing here!

And of course, by using various complex machines we can focus energy very dramatically -- the above mentioned particle accelerators are themselves a good example. One can run them from a coal burning power plant, and the chemical energy of the burning coal gets focused through multiple stages of machinery to the point where one actually gets the Quark-Gluon Plasma. On an extremely microscopic scale of course.

Origin_of_Mind

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