Not radio, because this is 1840, but a good attempt with regular materials.
If I was sticking a library on the moon, I would put it on the poles. Unless there is a huge meteorite impact, those will stay in much the same place. If you were looking for something that was put somewhere on the Moon for you to find, this would narrow it down to one of two places.
The next thing you could do is to have some sort of passive reflector, like a set of wires that would show up on round-mapping radar…
Or stick it next to the one the dinosaurs left.
Dammit. Bang goes my working day - I am going to be thinking about this now.
Yeah, just take a so-far unused moon or build a new one, then start going through your library and consider each item.
If you want to keep it, transfer it to the new moon.
If not, consider whether you can donate it to some other galactic civilisation who might get some use out of it and if not, dispose of it responsibly (you don’t want to leave potentially dangerous culturalmaterials floating around).
I suspect that lunar temperature would make electrochemical options tricky, if running at ambient temperature most reactions would slow to a crawl; while if heated by sunlight or system waste heat they could end up well above comfortable operating temperature, having no atmosphere is obnoxious like that(though you might be able to exploit a thermal gradient between a sunlit and shadowed or dark-side area for quite a while before your exploitation equilibrated temperatures and shut down that energy source; not sure how viable geothermal heat pump arrangements in lunar regolith would be).
In terms of locateability your suggestion of a conductive and/or RF reflective structure seems like a very plausible one. In percentage terms there’s a decent amount of metal on the moon; but not in bulk metallic form with suspiciously artificial shape.
As an accessible archive I’m curious about the viability of a radio equivalent of what they have etched on these disks(the small but unencoded pictures telling you about how to interpret the higher density encoded data sections): you’d want a first-stage accessible with as little knowledge and equipment as possible(our hypothetical listener would probably need to know where to point a fairly directional antenna, I suspect that preposterous power would be required if the lunar transmitter was omnidirectional enough for a ‘just point at moon from somewhere in earth’ case to work): have a first stage in something simple and retro like a looping recording in several languages, broadcast as AM audio, describing the encoding of the actually efficient and high speed transmission; with the bulk of the data being sent out over and over on that channel so that anyone who can scavenge enough circuitry to build the receiver out of the nuclear rubble could obtain a copy just by keeping their antenna on target and waiting. No need to actually retrieve the hard copy(indeed, the distance would keep it safe).
The RF beacon would obviously fail for one reason or another long before the disks decay(I’m just curious if a realistic target given the environmental constraints would be 10 years? 100? 1,000?); but being accessible with comparatively modest RF gear would be useful to a lot more hypothetical futures than needing some billions of dollars worth of at least 1970-level rocket science(since any disaster that leaves you with that will be virtually certain to spare some of the terrestrial copies).
Okay, I’m still here. Your radio signal system sound like the “A for Andromeda” signal.
Soppose you had copies of your library and some small solid-fuel rockets. It would probably be easier to emit some regular signal at long intervals, and listen for the same signal echoed back at you. If someone did that, you could send a rocket to the place the signal came from. I would imagine you could harden electronics and keep them underground. If a solid-fuel rocket degrades, as it might, you could use some sort of electromagnetic acceleration.
Why would someone point their radio antenna at the moon, anyway? We might want to generate a very broad band signal, such as a spark pulse, which would show up on most wavelengths. Maybe we direct our signal at points where radio waves are coming from.
How do we generate the electricity? There’s plenty of solar power, but my gut says that the cells would be damaged by the radiation. There are no tides on the moon, as its rotation is locked to the earth. I am tempted to go for some sort of nuclear process, as you can get energy from isotopes with half-lives of millions of years. If you can store it and let it go all at once, you don’t need a lot of power.
