Question

Using a few additional assumptions, we'll complete a "back of the envelope" calculation. This is a quick-and-dirty calculation that lets us determine if we're on the right track. The calculation will reveal to you a crude estimate of the amount of time it takes to colonize all 100 billion stars in the Milky Way Galaxy if your assumptions are true.

The number of colonized stars at any given time is:

Stars Colonized = (Offspring + 1)timestep

For example, if we produced 2 offspring colonies during every spawning time, the number of stars colonized on the third step would be 33 = 27 colonized stars. We can confirm this with a simple chart:

Target Stars:

100 billion

"Spawning" Time:

74000 years (travel time) + 9000 years (growth time)

"Offspring" Colonies:

10 stars per event

Timestep	Existing Colonies	New Colonies	Total Colonies
1	1 (Earth)	1 x 2 = 2	1 + 2 = 3
2	3	3 x 2 = 6	3 + 6 = 9
3	9	9 x 2 = 18	9 + 18 = 27

Equation

log(TargetStars) Time = log(Offspring+SyawningTime

Sample Calculation

If we want to know at which "timestep" we hit 100 billion stars (our target stars), we simply rearrange the equation to solve for timestep:

log(Target Stars) = log(Offspring + 1) x Timestep

log(Target Stars)/log(Offspring + 1) = Timestep

When we solve this equation, we'll know how many timesteps it takes ... but each timestep is equal to our "spawning" time. So we multiply the timestep by the "spawning" time to get the total actual time it would take to colonize the targeted number of stars.

Using your assumptions, calculate how long it would take humanity to colonize every single star in the Milky Way Galaxy. Years

Answer 1

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