Last week, I summarized the assumptions that I’m making about any planet to which humans might eventually travel. Note that this would include Earth, if a generation ship traveled with a constant acceleration long enough to reach a significant fraction of the speed of light, such that the time dilation effect returned them to an Earth significantly older than the ship itself. In fact, this is the premise that I will use as the basis for the spaceside part of the site – that the journey both begins and ends at Earth.

This week I’m listing some of the assumptions about the journey on which humans would travel to get to such a planet. At some future point, I’ll speculate or provide my ideas and opinions about the ship – what it might look like, how it might be constructed, what source it might use for internal power, the propulsion system, provision for artificial gravity, and other relevant problems that would have to be solved. This week, however, I want to describe some assumptions about the journey and the people on it.

#### Physics Considerations

First, which direction do we go, and what path do we follow? Because the Milky Way Galaxy (the one in which Earth is located) is basically disk-shaped, it probably makes sense to travel a path more-or-less perpendicular to the galactic plane in order to minimize the chance of running into anything. Let’s **assume that a course could be found that would allow the ship to travel in a straight line away from, and then back to, Earth, without encountering anything with which it might collide.**

Next, a consideration that instantly comes to my mind about the trip is “how fast and how long?” Because we want to use time dilation to let significantly more time pass on Earth than on the ship, the answer to “how fast” is “very fast, but depends on how long it can be sustained.” More on that in the next paragraph. The answer to the question of “how long” is “fairly long, but depends on how fast we can go.” So, this becomes a problem of two related variables. However, while the “how long” depends i part on “how fast,” it also depends on some unrelated assumptions, such as how much longevity and reliability we can build into such a ship with today’s (21st century) technology. I’ve settled on an **assumption of a total journey time of 1000 years**, composed of a 500 year long outbound segment followed by a 500 year long return segment. These two 500 year long segments would be composed of a 250 year long acceleration followed by a 250 year long deceleration. (Yes, I know, both are technically “acceleration,” but I think this makes it clearer.) So, the ship begins to accelerate away from Earth orbit on a path basically perpendicular to the galactic plane, accelerates in a straight line for 250 years, decelerates along that same line for 250 years (at which point it is momentarily stationary), then begins to accelerate back along the same line in “reverse” – that is, back toward Earth – for 250 years, and finally decelerates along that line for 250 years at which time it falls back into Earth orbit.

It is important at this point to acknowledge that acceleration and speed are different. The minimum speed that the ship needs to sustain in order to achieve at least the minimum desired time dilation is a calculation for another time. Any acceleration that is applied long enough will achieve and then exceed that minimum speed. So, the acceleration is one of the assumptions I’m going to make, with some more-or-less informed guessing. A few calculations might help in thinking about this, and the following sites are interesting and informative:

- Earth gravity: 9.81 m/s²
- Speed of light: 299,792,458 m/s
- A helpful website for velocity calculations: https://www.calculatorsoup.com/calculators/physics/velocity_a_t.php
- Our velocity after 250 years at 0.01g: 773,950,000 m/s (but this is faster than the speed of light, so not possible)
- Our velocity after 250 years at 0.001g: 77,395,000 m/s (or approximately 26% of the speed of light, but is this fast enough?)

Note that the above calculations ignore any effects of relativity, other than time dilation, as velocity increases. There is almost certainly some maximum practical limit to the velocity we can attain, even with constant acceleration.

At this point I’m going to **assume a constant acceleration of between 0.01 gravity and 0.001 gravity.** That’s a pretty wide range, and we’ll narrow it down later. For now, we’ll just **assume an acceleration that will provide a time dilation effect of, say, 10 to 1 (or greater)**, so that Earth ages at least 10,000 years while the ship makes the journey of 1000 year.

#### Human Factors

Another important consideration for the journey is to avoid a situation where a single failure, accident, or malicious act kills the entire population on the ship. The best way to do this – I think – is to partition the people on the ship into many identical “containers.” That is, divide the ship into separate physical sections that are self-contained, self-sufficient, identical in construction and environment, and isolated from each other. That way, if a “mad scientist” (or just some mutation) creates a virus that kills everyone in a section of the ship, the people in the other sections survive to complete the journey. This works similarly for a failure or accident. Also, this allows the society in each “container” to develop independently, which should provide a good diversity of approaches to civilization.

Finally, how many people are initially needed in each “container” in order to provide a viable population for 1000 years? And, what is the estimated population at the end of the journey (we’ll need to determine what the reproduction rate might be)? We’re probably looking at having 40 to 60 generations during the journey, and each container will need to be large enough to support the eventual estimated maximum population.

Estimates of how many people are required to sustain a society vary widely. The following articles provide some interesting and thoughtful commentary:

- https://en.wikipedia.org/wiki/Tristan_da_Cunha
- https://worldbuilding.stackexchange.com/questions/3/what-is-the-minimum-human-population-necessary-for-a-sustainable-colony

While it appears that the absolute minimum might be as low as 15 (we are ignoring the Biblical accounts of 2 (Adam and Eve), and 8 (Noah and his wife and their three sons and their wives) because of the different lifetimes recounted for them vs out current lifetime norms), and the widely regarded “minimum for 10 to 20 generations” is 160, I think we’d want to have a few more than that – let’s say 320. Now we need to consider how fast – if at all – the population will grow, in order to determine the required size for each of the “containers” in the ship. Relevant reading can be found at:

- http://biology-pages.info/P/Populations.html
- https://creation.com/biblical-human-population-growth-model
- https://www.dummies.com/education/science/environmental-science/the-environmental-science-of-population-growth-models/
- http://monkeysuncle.stanford.edu/?p=933

We will revisit this question at some future point, and perhaps try to come up with some justifiable estimates. For now, I’m going to **assume an initial population in each “container” of 320, with at least 200 of them being of “reasonable” reproductive age (say, 20 to 35 years old) and more-or-less equal numbers of males and females**. Further, I’m going to **assume that over the 1000 ship-year journey, the population of each “container” increases to and stabilizes at 3200**.

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