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The objective is to launch a crewed spacecraft to lower Earth orbit. Except the perigee must be higher than 100km altitude, there is no other constrain on the orbit parameters. The emphasis is that the launch itself is not planned in advance.

If an organization that is capable of sending people into orbit (NASA, Roscosmos, CNSA, ULS, SpaceX, etc.) starts working today, how long will it take to have a launch?

Mys_721tx
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It depends.

I don't know anything about the chinese agency so I'll focus on Roscosmos

It takes about 2 years to build a new Soyuz (Mir era data).

However what would happen is that we'd repurpose a scheduled vehicle for the emergency mission.

Since we launch about 4 Soyuz a year, this mean that on average, a Soyuz should be ready within 45 days, at most 90 depending on the date of the next scheduled launch.

Of course, there is probably room for corner cutting and extra hard work. Especially if you are ready to send a rescue vehicle for the rescue vehicle.

If you needed to send one today (October 19 2016)... You'd be lucky since Soyuz MS-02 is already on the launchpad. Few hours to go !

The 3 months figure is really an average: next launch will be just one month from now:

Antzi
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  • "on average, a Soyuz should be ready within 3 months" Wouldn't the average be half the time between two consecutive launches, because on average you will be smack in the middle between two launches? So on average, a Soyuz should be ready within 45 days? Three months would be the worst case, being the case if the emergency launch is needed and that need materializes immediately after the previous launch commits. – user Oct 19 '16 at 10:56
  • @MichaelKjörling You are right. I was only thinking about the "maximum average" Edited. – Antzi Oct 19 '16 at 11:00
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    "Of course, there is probably room for corner cutting.... Especially if you are ready to send a rescue vehicle for the rescue vehicle." If you already have a rescue vehicle ready for the rescue vehicle, can't you just go ahead and launch the rescue vehicle's rescue vehicle right now? – Dan Oct 20 '16 at 04:30