> You could put in an orbit that would have a predefined reentry in the future.

it isn't clear what you mean by this, but there's no picking where something will reenter hundreds of years in the future. if you just want to ensure that it will reenter, sooner or later, that's easily done.

> Design the satellite to survive reentry and somehow safely land in a way that relies on a mechanical system that wouldn't degrade like electronics in space would.

chunks of satellites are far more likely to survive reentry already than you might expect. i expect it would be feasible now to produce an insert sphere filled with information etched on nickel-superalloy plates that would survive uncontrolled reentry and impact with the earth's surface.

i'd suggest storing the information in something covered with retro-reflectors, and dropping it onto the moon's surface, though. need more delta-V to get it there and retrieve it, but it'd be a simpler object to construct, and then later deconstruct.

You can't do this on a long term scale with something that's below geostationary orbit, because random solar flares and solar phenomena cause expansion and contraction of the earth's atmosphere at unpredictable times. If you have a satellite in an orbit that is low enough to gradually degrade through atmospheric drag (even if it's a very high-LEO orbit or molniya orbit that won't reenter for an estimated 300 years), the exact time that it will re-enter can't be predicted with any confidence. At least not if you are talking about a very long time scale. Short-term (3, 5 or 7 year time scale) orbit degradation of things in LEO is predictable based on orbital height and known atmospheric density at a given altitude, but beyond that any re-entry predictions become much more fuzzy.

for reference: https://arxiv.org/abs/1305.0233

If you want to put something in orbit that will stay in a predictable location, you don't want it to re-enter at all, you want to put it in an orbit that is high enough to not be affected by atmospheric drag on a geologic time scale. Something slightly beyond geostationary will still be there in 200,000 years.

Though, it would most likely end up in the ocean since the majority of the earth's surface is covered by water.

Orbits only really decay due to atmospheric drag. Other tiny bits of cosmic, rarified gas can slow the spacecraft on a long timescale, and solar radiation pressure can perturb an orbit (occasionally dramatically, if the Sun is unhappy), but the effect is far smaller than constant drag. If a small satellite is orbiting Earth at a high enough altitude which was calculated to consider the broader gravitational system (Earth's natural satellites, the Sun, and fainter perturbations from nearby celestial objects have to be factored in), orbit can be designed to be stable on a long, long timescale. Millions of years, or more.

The real fly in your plan's ointment would be exposure to space, which sucks a lot for electronics.

I was thinking in the case the civilization lost access to a lot of basic data. Then finding the magic satellite without magic radar, maybe without even knowing about the magic satellite amongst all the other satellites up there.

Depends on your definition of 'findable', I suppose.

Flight 370 wasn't found after "the most expensive search operation in aviation history[1]" performed by a multinational effort over almost three years. There are distinctions to quibble about, sure, and there are things that could be done to make things not designed to shuttle meatbags around easier to find.

But the area comprising the middle of the not-stuff you reference is big.

[1] https://en.wikipedia.org/wiki/Malaysia_Airlines_Flight_370#S...