Even things on dead planet like the moon can't survive indefinitely because meteors either striking it or dusting it, even if we etched the moon with nuclear blasts contour would get fuzzy and disappear over million years.
One option would be to put in one Lagrange point some high quantity of radioactive material. You'd need to pick quantity and material well tho, because material with short hair life would cool off to get and become just a rock and materials with too long half life would be very hard to detect due their low emissions.
Give it a shape nature would have had time to replicate like an empty cylinder and it would likely be the best way to leave artifact for million years into the future. Won't be able to store any meaningful information beyond "someone was here" and future people coming to bertrand teapot style of argumentation against God would have a hell of a shock upon rediscovery
Almost all of the moon's surface is older than the ~500MYA scale we're talking about. It has the occasional impact, like Earth does, but the overwhelming majority of those craters you see are from the early bombardment. The dark splotches visible on the near side, the maria, are mostly flat volcanic plains laid down toward the end of that period about 3BYA, and are visibly lacking in craters.
That’s the large impacts. The Moon gets hit by ~2800 kg of meteor material per day, though this likely has been decreasing over time.
It’s about one ‘bullet’ going ~38,000 mph per 379 square kilometers. But times 365 days a year you’re at 1 bullet per square km/year. Over 500 million years that’s 500 bullets per square meter which would heavily damage if not outright destroy any structure and cover it in lunar dust.
PS: The 38,000 mph issue is hard to conceive of assuming similar weight it’s ~2,500 times the kinetic energy of a 9mm bullet. Military rail guns are aiming for Mach 7+ which is ~1/40 the kenetic energy of a similarly massed meteor.
Yeah, but those aren't going to destroy a structure, just put holes in it the way they put little holes in the surface. You can look at the moon landing videos and see surfaces that have been consistently flat and undisturbed at scales greater than cm for billions of years.
It kind of depends on what you mean by structure. Buildings would not survive. The great perimids would look like odd hills after this stuff.
Moon is x impacts per day * 365 days * 500 million / 37.9 million square kilometers = 4815 days worth of bombardment per km squared. Each day represents 2800 kg so each square meter gets hit with ~ 13.5 kg if stuff going 17,000 m/s.
1/2 Mass * velocity squared. 13.5 kg * 17,000^2 = 1950750000j or 1/2 a ton of TNT per square meter. Except the force is conctrated in one direction so it’s closer to 1 to 3 tons of TNT for every single square meter.
Now it’s diffent because these impacts don’t happen at the same time. But they also don’t happen from a single direction so taller structure would be hit along their surface.
(Edit: this was written to respond to your original comment about the Sears tower, not the one that you have up now which is about ancient egyptian physics or something. I'm too lazy to type up another response. I'll just leave it at "you're wrong" and depart)
> But if you put say the sears tower there 500 million years ago it would not be recognizable as a structure
That's just not true. Look at the Apollo 11 photos. Those exposed rocks are 3+ billion years old (six times older than the timescale we're talking about) and they're certainly not covered in a mound of dust. A 500m-scale structure on the moon would absolutely still be standing, absent really really bad luck.
Look at the size of those rocks. Fist sized chunks of rubble are not a structure. After the surface solidified it was continuously bombarded and broken into tiny fragments. That same thing would happen to buildings on those time scales.
Picture a cooling pile of molten rock that’s solidified, now you can’t pick that up. You can only pick up fragments that are blown apart and looking at those pictures their are plenty of fragments you need to dig to find the solid rock.
Additionally, useful surface structures probably would be made in part of lightweight materials transported from Earth; a useful base would likely be largely subsurface. There's no particular reason why an entrance to such a base need be durable or monumental, or even directly visible with human eyes (or artificial aids thereto) from many kilometres above (let alone from Earth).
Apart from radio beacons and similar navigational aids, there's good reason to think a predecessor terrestrial spacefaring civilization would see very differently from mammals closely related to humans.
(Along those lines, one can imagine a predecessor Earth civilization whose leading species is comfortable in a temperature or pressure that humans could not tolerate, and that their comfortable working conditions would drive the location and composition of a lunar base for them. Even our own species had (and has) mountain-dwelling civilizations in environments challenging to subtropical coastal people. If they had been in the Space Race, mountain-dwellers might have had some advantages in needing to haul around less atmosphere (being comfortable with a higher cabin altitude), and they're the same species as the first Americans and Soviets in space.)
One option would be to put in one Lagrange point some high quantity of radioactive material. You'd need to pick quantity and material well tho, because material with short hair life would cool off to get and become just a rock and materials with too long half life would be very hard to detect due their low emissions.
Give it a shape nature would have had time to replicate like an empty cylinder and it would likely be the best way to leave artifact for million years into the future. Won't be able to store any meaningful information beyond "someone was here" and future people coming to bertrand teapot style of argumentation against God would have a hell of a shock upon rediscovery