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Fleeing the solar system

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It's the height of humanity's space-colonization golden age when casual interplanetary travel has become possible and humans have either colonized or established large space stations around nearly every planet in the Solar System. Then, humanity is beset by the sudden onslaught of an unknown alien aggressor that quickly lays siege to Earth and Mars, leaving the spacers who occupy the Asteroid Belt and the various stations past the orbit of Jupiter as the only surviving members of humanity.

Acting quickly while the aliens are busy finishing off their planet-bound brethren, they fashion asteroids and existing space stations into massive starships and promptly leave the Solar System, forming a "Great Fleet" comprised of hundreds of kilometers-long and/or wide seed ships spaced many AU apart relative to each other that occupy almost a light year's worth of volume. It is in this Fleet that they hope to leave unnoticed and spread out into other solar systems to rebuild, traveling for thousands of years, ships breaking off from the Fleet only when they've arrived at a potentially habitable solar system.

Could this work? Could millions or even billions of people actually flee the solar system unnoticed by any alien aggressors, or would they be caught and either shot down by relativistic projectiles or tailed for multiple AU until the faster alien ships get into firing range? Knowing that there's little to no stealth in space, how could they leave unnoticed and stay unnoticed as they commence their centuries-long journey through interstellar space?

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This post was sourced from https://worldbuilding.stackexchange.com/q/58446. It is licensed under CC BY-SA 3.0.

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