alien astronomers would have been able to detect the Great Oxidation Event on earth spectroscopically, determine the planet is hospitable to life, and embark on a invasion/colonization campaign. they have had somewhere between 850 million and 2.5 billion years to travel. (when could oxygen have been detected? would the alien astronomers have had to wait for all other oxygen sinks (oceans, rocks) to be exhausted before they began to see oxygen accumulating in the atmosphere?) assuming the aliens had to travel 50,000 light years (halfway across the galaxy) and took 1 billion years, that's 15 km/sec, same speed as New Horizons, easily achievable with conventional rockets, no exotic sci-fi propulsion necessary. invading from Andromeda is not that much more difficult, requiring 750 km/s or 0.0025c (assuming galaxies don't move, which is false over a billion years).
several possibilities why we haven't been invaded (trying to explain the Fermi paradox):
- there are a great many other worlds with detectable oxygen and other biomarkers indicating that they are hospitable to life, so earth does not especially stand out as an invasion target. next generation telescopes may soon be able to confirm or eliminate this possibility.
- it is difficult to observe that earth is hospitable to life. maybe there are only a few lines of sight not obscured by gas and dust of the Milky Way, and those lines have not overlapped with aliens' telescopes. does the earth need to eclipse the sun to do spectroscopy? if so, that limits the lines of sight even further.
- there is no other intelligent life in the Local Group.
- building starships, warships, and colonization fleets that can survive billion-year journeys is difficult.
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