Is interstellar flight possible in the near future in a way that would keep our civilization alive? I mean is it practically possible to obtain technology that would enable us to travel to nearby habitable earth-like planets to keep our civilization alive?
For example, consider this design for NASA’s Star Trek-style Space Ship, the IXS Enterprise. Do you know any good site which goes into detail on both latest practical and theoretical development of this interstellar flight?
Answer
The link you posted refers to a design which would supposedly make use of faster than light travel. After reading this, I immediately stopped reading, since this is not possible. I don't care if it's a NASA-affiliated person who says this, it is simply misguided!
Before continuing, I should draw your attention to the fact that I will not be discussing the Alcubierre drive, a highly speculative method of achieving very fast space travel which I personally think is more based on wishful thinking than anything else. Instead, I will stick to methods of travel that to not depend on manipulating spacetime in an exotic way.
A different question is whether it might be possible without using faster than light travel, although the answer is almost certainly still no. From this wikipedia article we learn that the closest possibly habitable planet would be around 12 light years away. This means that, traveling at $c=299792.458\ \frac{\text{km}}{\text{s}}$ one would take about twelve years to get there.
Let's assume a best-case scenario, where this planet turns out to be absolutely perfect - with minimal issues pertaining to adjustment to a different atmosphere etc. - while we also ignore any logistical issues like building enough spacecrafts to transport a significant number of humans (note that these issues alone will probably already make moving to a different planet an infeasible plan in a realistic scenario!). Let us just focus on the travel time.
From some further wikipedia research (notably here and here) we can conclude that our fastest (unmanned!) spacecrafts currently have a speed around $20\ \frac{\text{km}}{\text{s}}$. Let us, for the sake of discussion, assume that we can significantly improve on this "in the near future". Say some great technological breakthroughs occur that allow us to improve the speed of our spacecrafts by over an order of magnitude(!) to about $v_\text{sc}=300 \frac{\text{km}}{\text{s}}$ - this number is chosen somewhat arbitrarily; it makes comparing to the speed of light easy. Then, our estimate time of arrival would be
$$\text{ETA}\sim 12\ \text{year}* \frac{c}{v_{\text{sc}}}\approx 12*10^3\ \text{years}$$
As you see, we might experience some trouble here, too ;) In short, I think it is safe to say that we will not be able to move to a different planet in the foreseeable future.
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