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So there's this planet that, several decades earlier, suffered a massive famine and drought that made habitation impossible. Everyone still alive on this planet died, except for 2 escapees, both of which have just recently died. The planet is around the size of Earth's moon and, at its peak, had a population of around 5 million. The planet's civilization was culturally and technologically based on Ancient Egypt and the entire planet is a desert.

So here's what's happening now: The drought on the planet has long since ended. The government of Ishgabangaloodoo (a planet with Victorian British culture but Star Wars-level technology) has decided that someone needs to be around to maintain this planet's culture and prevent the planet from being used as a smuggler hideout. They sent a team of archaeologists to the planet, where they got DNA samples from some of the mummified corpses.

If the Ishgas were to clone, say 1,000 of these people, assuming that most genetic defects are edited out of the clones' DNA, how long would it take for this planet to repopulate to its historical 5 million?

Note: the inhabitants of this planet have essentially human physiology.

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    $\begingroup$ You might want to take a look at minimum viable population discussions. From what I remember, 1000 people might not be enough genetic diversity, so you may need more. But, alternatively, you could do some genetic "fixing" to eliminate some genetic issues so they never crop up. $\endgroup$ – Andon Oct 26 '18 at 14:36
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    $\begingroup$ Also worth noting, but again outside the scope of the question, is that these clones would have to be taught, somehow, the culture and technology of the dead peoples. $\endgroup$ – Andon Oct 26 '18 at 14:37
  • $\begingroup$ I'm assuming that planet ___________ is populated by pretty much human people rather than freakish alein nightmares? $\endgroup$ – Ummdustry Oct 26 '18 at 14:57
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    $\begingroup$ @Ummdustry actually it's populated by anthropomorphic animals, but they have basically human physiology and lifespans so that's not really relevant to the question. $\endgroup$ – The Weasel Sagas Oct 26 '18 at 15:02
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    $\begingroup$ It's worth noting also (if you need a political reason) a regular imperial population has the potential to one-day become a threat to Ishgabangaloodoo (See America and Britain) whereas a bunch of dog-people with sticks probably won't become a threat anytime soon, and if there's five million of them they can probably make pirates at least think twice $\endgroup$ – Ummdustry Oct 27 '18 at 16:25
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Let's assume a 1.1% population growth rate per annum (this is by no means unreasonable as it's Earth's current growth rate, but, you could go as low as -100 and as high as 2 or maybe 3 depending on what your story needs).

We then have a simple geometric series.

Population (Year N+1) = 1.01* Population (Year N)

Or

Population (Year N) = 1.011^N * 1000

To find what year you reach five million people we simply rearrange

N = Log base 1.011 ( 5000000/1000 )

Which equals 779 years, roughly. I'm also assuming that your clones are adult so you might want to add on eighteen years for that. You could also accelerate this process a lot either by having a higher growth rate or more clones.

For example, a 2% growth rate, with 5000 initial clones, would yield just three hundred years.

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