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The device needed is a monitoring system. Aliens leave a probe on Earth or orbiting Earth, which typically lies dormant, but it awakes every 1,000 years or so to check life's status on Earth.

There's a clock hooked up to a pebble-bed reactor. The clock could take the form of a series of gears. Each subsequent gear will rotate at a slower rate than the previous gear. Once the last gear completes one revolution the pebble-bed reactor is triggered — pebbles are released from their repositories. The reactor then turns on and the monitoring devices are powered. Once a report has been generated, a signal containing it is broadcast to the alien's home star system. So, overall, the reactor runs for a short time. It then shuts down for 1,000 years until it's time for the system to send another report.

The reasoning for using a pebble-bed reactor is that the reactor depends on the pebbles' geometry. If the fuel pebbles aren't packed closely together, then the reactor is not critical, and fuel is not consumed — or consumed at a much lower rate.

It may take ~250 kilowatts for a data rate of 1000 bits per second per Project Longshot for a probe sending data from Alpha Centauri to Earth.

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    $\begingroup$ Do you just want to know about the power situation? Or do you want to know about environmental effects that could affect the reactor? $\endgroup$
    – SRM
    Commented Dec 30, 2020 at 5:09
  • $\begingroup$ @SRM The power situation is probably more relevant. $\endgroup$
    – Daniel
    Commented Dec 30, 2020 at 5:11
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    $\begingroup$ The classic problem with "millions of years" questions on Earth is that the surface changes a whole lot over millions of years. The dormant probe my find itself washed into the sea, melted by a surprise volcano, smashed by a tsunami, sunk deep into a swamp, eroded by sandstorms, squashed under a glacier, etc. $\endgroup$
    – user535733
    Commented Dec 30, 2020 at 5:30
  • $\begingroup$ Redundancy could solve that. If there's ~25 probes chances are there's going to be at least one which makes it to a geologically stable area. $\endgroup$
    – Daniel
    Commented Dec 30, 2020 at 5:37
  • $\begingroup$ pebble bed reactors still rely on steam spinning a turbine and no turbine is going to last thousands of years, consider RTG batteries instead. $\endgroup$
    – John
    Commented Dec 30, 2020 at 18:15

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You have two major issues here, even for a redundant implementation:

  1. Spontaneous decay of the reactor fuel. As you state, the pebble bed reactor rely on the packing of the pebbles to be operative. If the employed fuel is naturally radioactive, over the thousands of years it is supposed to work will change its concentration in the pebbles. Unless you can provide fresh pebbles at every cycle, this will sooner or later stop the reactor from working because the concentration of the fuel will be too low.
  2. Wear and tear of the gears triggering the reactor. Wheels and gears spinning for thousands of years are hard to manufacture, maintain and keep in working condition, no matter how slow they are supposed to spin.
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    $\begingroup$ This is an important frame challenge. The concept of the pebble reactor is fine, but nothing we know of needed for its existence will last millions of years. The fuel goes stale. The gears wear. The reactor walls rust. The electrical wires used to send the signals go brittle and turn to powder. The more we handwave those other conditions the less it matters what kind of reactor you use. The reactor design, itself, is not enough to justify the time span. $\endgroup$
    – JBH
    Commented Dec 30, 2020 at 7:39
  • $\begingroup$ @JBH I agree. Any reactor that is not complex enough to include a self-diagnostic and repair mechanism falls afoul of this challenge. A reactor complex enough to include such diagnostic and repair facilities probably [IN MY OPINION] has a continuously operating reactor to keep those facilities running far more regularly than every 1K years. If you assert that by some tech magic those facilities are not needed, I think we are into tech magic that is outside today's physics regardless of reactor type. $\endgroup$
    – SRM
    Commented Dec 30, 2020 at 10:11

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