However, I have a query: when the two astronauts clambered back into the capsule, via some kind of step ladder (..?)
Yes, the ladder on the LM is one of its prominent features. The television camera on Apollo 11 captured the crew climbing back aboard via the ladder, except that Armstrong tried to see how far up the ladder he could jump.
how did the capsule manage to take off again
By lighting the ascent engine. Practical liquid-fueled rocketry has been a thing since the 1940s.
and in the right direction?
By steering. Inertial guidance and reaction control have been a thing since the 1950s. Stellar navigation has been a thing since before the Pyramids.
It's pointed out that there is more computer technology in one's smart phone than in the entire banks of computers at NASA at the time.
Why would you need any computer at all for any of this, especially?
Nowadays it's trivially easy to obtain the answers to all the elements of your question by connecting your computer to other computers and use software to search a vast amount of material stored on them. But it's not as if you were completely unable to do that before computers. You just did it differently.
If you wanted to see a picture of the Apollo lunar module and figure out how to get in and out of it, you could have found that out from any number of the old books I have on my shelf and at least some which would have been found in any reasonably large community library. There would have been several books on rocketry and navigation. You would have found these books using a card catalog that contained subject classifications. You would have been assisted by a human librarian who was specially trained to help locate information. Computers eventually made those tasks easier, and in many cases fundamentally changed how we did therm. But it's not as if we just
didn't do them before.
Now because it was harder in, say, 1980, for Joe Rando to rediscover the solutions the Apollo engineers came up with, not many people did it. So it was understandable that a lot of people at that time didn't know the details of how it all worked. No doubt many just took it on faith. But curiously, others handled that ignorance by declaring from their ignorance that it must therefore have been impossible. Then out of that same ignorance they proposed to instruct others on that purported impossibility.
You've done what many others have done. Because you have access to people you reasonably believe might know the answers, you've asked a particular question. I gave you brief answers above. I'll go into more detail tomorrow. I can give a spontaneous lecture on any of the specific points you've asked about. And, in fact, I have—sometimes while sitting in the California desert surrounded by scorpions. But whether you intended to or not, you let some of that, "It doesn't seem possible," sneak in.
The ascent stage only needed to get in roughly the same orbit...
Correct. It was the command module pilot's responsibility to steer
his ship to pick them up, wherever they ended up. He memorized and practiced something like twenty different orbital mechanics scenarios that matched what engineers imagined could go wrong.
The ascent trajectory was flown in so-called open-loop mode. Once its gyroscope was aligned using the alignment optical telescope, the ship just flew a preprogrammed set of directions in 3D space. The program is something like, "Go straight up for ten seconds. Then pitch this far over and fly for 30 seconds. Then pitch over a little bit more and fully for 48 seconds." And so forth. At the end of that, you would be in
some orbit. How did they know that? Because some guy with a slide rule and a basic understanding of Newtonian physics was able to figure out where in space a ship would be if it followed those dirt-simple steps. Your state vector when the engine cuts off uniquely determines your orbit via basic math.
Now of course the ship was integrating its position as it went, but it wasn't using that integrated position to adjust the trajectory. That would have been closed-loop. Keeping it open-loop keeps the solution very simple. Simple solutions have less to go wrong. It's counterintuitive, but reliably getting the ship to an orbit—
any orbit—is safer. It breaks up the ascent into two phases in between which is a stable, safe condition wherein the crews can pause, observe, analyze, and come up with a solution to any problems that arose.
...and then radar was used to home in.
Specifically a procedure invented by (wait for it) Edwin Aldrin. It was his PhD dissertation at MIT. In its purest form, all you need is line of sight to the other ship. You first achieve a coelliptical orbit with the other ship. Then you keep the passive ship stationary against the stars by adjusting your own ship's position. Aldrin provided all the math in his dissertation to prove this works. He also demonstrated it on his Gemini mission.
Having radar helps, but isn't strictly necessary. It simplifies the "keep the line of sight" problem. Having a digital computer helps, but it isn't strictly necessary. You can use a side rule: the little Pickett six-incher. If you can't see the stars, you can use a sextant. The AOT could function as a sextant. And it also helps to have a highly-skilled pilot in your "passive" vehicle who can maneuver
his ship to correct for out-of-plane errors and put it in a coelliptical orbit with you.
Not gonna lie, it took a lot of effort to convince senior engineers that lunar orbit rendezvous would work. Far from being a rickety, chancy thing, the equipment and procedures were actually quite over engineered to make sure the ascent and rendezvous would work.
Ground control also knew exactly where both the CM and LEM were (especially the CM via ground based radar).
Because Armstrong didn't land exactly where planned, they weren't exactly sure where
Eagle was. But it didn't matter, because it wasn't the LM's job to be accurate. It was the LM's job to be reliable.
The CSM tracking was accomplished mostly by passive methods. When the ship goes around the far side, its ongoing radio signal is lost. When it re-emerges, the signal is reacquired. The precise timings of those events over many orbits gives you an incredibly accurate picture of its orbit. The Doppler shift in the carrier as the ship is in the parts of its orbit where it's traveling toward or away from Earth further refine that understanding.
The computers were also specialized units that didn't have fancy graphic displays and the like; they were very well suited to the task.
Uniquely suited. The argument that Apollo spacecraft were impossible because their computers were impossibly weak compared to modern computers carries a number of wrong presumptions. You don't furiously compete your way to the Moon. You mostly just sit there and let gravity do its thing.
I can remember when my washing machine didn't have a computer in it. Did that mean I spent my childhood wearing dirty clothes? Well, I kind of did, but for reasons having nothing to do with the availability of automatic washers. Back then, automatic washers used a cam drum timer. You may remember those. You pulled out the knob, turned it to a specific position, then pushed it in. Over the course of the cycle, that drum turned slowly via clockwork. Valves opened. Motors whirred. Pumps chugged. Those were all operated by a set of cam wheels on the common shaft. As the cam turned, cam followers would open and close circuits. The shapes of those cam wheels were all prearranged by the Maytag people to implement the program. Some operations could start and stop the camshaft. For example, when the Water Inlet Valve cam rotated so as to open the valve, it stopped the wheel until the water level sensor tripped and allowed the cam to proceed.
It's a purely electromechanical computer. It was quite highly reliable. Looking backwards, it's exactly the same kind of mechanism that operates the Linotype typesetter developed at the end of the 19th century. Similar principles were used in the fire control computers in World War II battleships. There is a whole wonderful vocabulary of mechanical control and computing systems that was highly developed by, say, 1960. There were also electrical analog computers that could do things that digital computers today still can't do. Looking forward, the Saturn V's ground launch sequencer was a cam-drum operated device. It was eventually replaced by a digital GLS for the shuttle program. And the engineers who designed the command module's earth-landing system (the parachutes, etc.) didn't fully trust digital technology. They used electrical relays and electromechanical control techniques because we (the engineering community) had generations of experience in those systems.
The point is that if you
have a computer, you can certainly use it. But just because you decide to design a solution using a digital computer doesn't mean there aren't or weren't other ways to do it. Nowadays it's cheaper and easier to use digital control circuits in almost everything. And as such the solutions look quite different than they used to, and can often provide a lot more features. But don't confuse convenience with necessity.
In the 1960s, the notion of an embedded digital control wasn't all that different than it is today. It's a lot different than understanding a general purpose computer such as the one I'm writing this on and the one you're reading it on. An embedded system—then as now—was merely one piece in a larger system. It served the system. When I hire new people who come up through a computer science education path, this is something I have to teach them right away. The platform does not serve your software; your software is a component in a larger system. You build the computer part of a thing to do nothing more than operate the thing. And you can use techniques in that software that you woudn't do for a general purpose computer.
The best example of that is that wonderful rendezvous radar. The LM computer software had been written, debugged, fine-tuned, and tested. It worked quite well. But then at a late stage in the mission, Buzz Aldrin suggested that they keep the rendezvous radar in standby mode during the descent. This was 1960s electronics. Remember how your old TV had to warm up before it worked? So did the radar. Most aerospace hardware like radars had a STDBY mode that would allow the electronics to warm up before it was needed. Aldrin wanted it warmed up in case they needed to abort the landing. He wanted the computer to have radar data immediately.
Simple, right? Well, no. Unbeknownst to him, the dual power supplies were not synced in standby mode. This caused the radar to report its data to the computer at twice the usual rate. The additional computing power needed to accept and store that data was just enough to make the real-time tasks start to fall behind. This is where you hear the crew say, "1202 alarm." The engineers who built the computer and programmed it had taken it right up to the limits of its computing capacity and tuned the software to run that way. They knew exactly how long it would take the computer to execute certain parts of the code and made sure to stay within the limit. That's perfectly okay in embedded computing. Moreover, the software engineers had been smart: the most crucial real-time tasks were done first and so forth down the line, so that if a 1202 overload occurred, the lowest-priority code would be skipped. The way people approached digital computers for these applications is very different than how most people today encounter computers.
Their computers were well ahead of anything commercially available at the time.
Well, yes and no. By the time the AGC flew, it was fairly old. But it wasn't supposed to be new, flashy, and fast. It was supposed to be reliable. People tell me that their laptop has more computing power than the AGC by several orders of magnitude. And they're right. But what if I put your laptop in a bucket of boiling salt water? What if I put that bucket in a paint mixer and then threw the paint mixer off a building? The AGC would probably still be running.
It's a fascinating bit of computer history. Digital with rope memory and a 16bit word length!
But it only had three bits for the instruction, which was kind of an oversight. So they essentially invented what we would today call a virtual machine. The code is out on Github if anyone is interested.
And of course they were in contact with ground control that could do the big number crunching on their mainframes.
The IBM mainframes at Mission Control were commercial computers, but NASA had tricked them out with all the expensive add-ons. Anyone in 1969 could have had the same setup, if they had deep pockets.
What nobody else had was the CDC 6600 at Lawrence Livermore lab. That was a supercomputer of the day, roughly equivalent to a Pentium 90. All the heavy computations were partially precomputed on this and then the partial solutions stored on tape. If you needed to recompute trajectories or anything like that which required heavy numerical computing, the IBM mainframes started with the closest partial solution and finished the computation. This then gets transmitted to the Apollo onboard computer which doesn't have to do anything more strenuous that keep the ship pointing in the right direction and turn the engines on an off. As I wrote above, you don't have to furiously compute most of the ride.
Find CuriousMarc on YouTube. They have a 20-ish part series on how they completely restored an original AGC. Mike Stewart's channel is also wonderful. He has implemented the AGC at the gate level (i.e., the low-level electronics) from the original plans and has successfully flown a lunar landing with it. He has figured out how to read those old core ropes and has sucked the software out of something like a dozen AGCs in museums and run it. Marc, Mike, and a host of professional electrical engineers have scoured auctions and private collections for old Apollo hardware and have restored much of it to working condition. They just finished the digital telemetry system. Every time they get original documents from the National Archives, they put it out on ibiblio.org, which has now thousands of original drawings.
When we say it would have been easier to just to do it than to fake it, what we mean is that if people can pull old Apollo hardware off junk heaps, old dusty shelves, and musty garages, poke at it according to the original plans (hundreds of thousands of drawings), and
actually get it to work as advertised, then that's quite a lot of effort expended toward something that's ostensibly just a cover story. If the alleged cover story stands up to the efforts of modern engineers to operate it, then it's easier to conclude that it just worked as advertised. Sooner or later the cover story would have to break down if it were all fake. If that point lies beyond "works as advertised," then you clearly don't have a fake.
fbi spy museum by Username Vixen, on Flickr
And if he had known about those other "German experts", I am sure he'd have written a song about them as well; a treasure trove for the satirically inclined!