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I assume that if everyone left the ISS, there is a method that can be used to put people back on it. For example to open the “door” from the outside.

However how long could the ISS remain functioning without anyone on it?

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    $\begingroup$ That's anyone's guess. There's not much function to it if it doesn't have to support astronauts or experiments, so most of it could be switched off and most of the remaining functions can be controlled remotely, including resupply of propellants and orbital reboost maneuvers. Then you'd have to wait for some failure that requires a human hand to fix to happen, to render it unusable. Related: What is the theoretical life of the ISS? and What factors limit the lifetime of an unmanned spacecraft? $\endgroup$ – TildalWave Jan 23 '16 at 16:25
  • $\begingroup$ @TildalWave, so "resupply of propellants" can be done while unmaned. $\endgroup$ – Ian Ringrose Jan 23 '16 at 16:32
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    $\begingroup$ The Russian segment holds propellants on Zarya and Zvezda modules and can use them for thrusters on Zvezda (see ISS Propulsion Module), or use the resupply vehicle's (Progress / ATV) own thrusters for reboost or collision avoidance maneuvers (conjunction analysis is done on ground anyway). See What propulsion methods does the ISS use for station-keeping? Both ATV and Progress resupply vehicles can dock autonomously. Tho it isn't clear if there's gonna be any more ATVs (there were 5). $\endgroup$ – TildalWave Jan 23 '16 at 16:37
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    $\begingroup$ No more ATVs. nasa.gov/content/… $\endgroup$ – Organic Marble Jan 23 '16 at 18:32
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    $\begingroup$ @OrganicMarble For the first batch of 5 yes, but things have changed, including official extension of ISS operations to 2024 since the 5 were ordered. Orion Service Module only covers ESA's share of expenses of ISS operations till 2020, so it's not really excluded that ESA will order more ATVs at a later date. $\endgroup$ – TildalWave Jan 23 '16 at 19:12
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The main factor that would limited unmanned lifetime of the ISS is a breakdown of a critical system. The thermal control system comes to mind: without cooling, you'll get a much wider range of temperatures which can lead to other failures. This is one of the more problematic systems on board as well, requiring regular repairs.

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