Orbits decay, often at a plannable rate. Eventually it crashes back to earth and becomes an archeological relic for future explorers. I bet you could even design the sattelite to burn specatularly (in many colors) on the way down so it's more likely to be seen and sought after.
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.
Those are called ballistic projectiles, and you cannot place one in a precise orbit. You need upper-stage guidance, admittedly just for the placement of the satellite, but you still need electronics. Though, that being said, I'm now curious how you intend to store large-scale data without any use of electronics.
I'm struggling to think of a suitable "analog format," maybe help me out? Silicon tablets of runes? Analog is unscalable here, no matter how cheap launch systems are.
