The best time for our journey to the stars
How long would it take to fly to another star? Longing! But it could be quicker if we take our time.
The search for the "second earth" is one of the major current tasks in astronomy. Somewhere out there there must be planets with similar habitable conditions as here on Earth. Everything we have learned so far about the planets of other stars points in this direction. Such a celestial body has not yet been discovered, but with the ever-improving telescopes it is actually only a matter of time. However, whether we can also visit this world is doubtful.
Apart from science fiction solutions such as drives faster than light or wormholes, then interstellar space travel is a task that takes a long time. There's just too much space between the stars! And if you still want to cross the gigantic voids in space, you should take it easy. That says this mathematical formula:
It comes from the work "Interstellar Travel - The Wait Calculation and the Incentive Trap of Progress", which Andrew Kennedy published in the "Journal of the British Interplanetary Society" in 2006. To understand them, you have to think about scientific progress. Suppose, says Kennedy, we want to travel to Barnard's Star, six light-years away. At a speed of about 150 kilometers per second (more than half a million kilometers per hour) it would take us 12,000 years. Should a generation ship from Earth nevertheless make this long journey, a lot can happen in the meantime. For example, one can assume with some certainty that new and better drives will be developed that will make the journey much faster. After arriving at Barnard's Star, the long-term tour group would probably find that faster spaceships from Earth had already arrived on site.
It would have been better if they had waited a little longer. But how long? This is exactly what Kennedy's formula describes. "t0" is the achievable travel time in the present, "t" is the time waiting before departure, and "h" is the time that elapses between doubling the cruising speed. "T" is then the time that the star flight lasts after this waiting time has expired. Assuming the 12,000 years mentioned above as a guideline for the present and a doubling of the speed every 100 years, then after a waiting period of 637 years one could fly to Barnard's Star in just 145 years. If you waited even longer, you would be there even faster - but this speed advantage is eaten up by the longer waiting time. For the above equation, the 637+145=782 years are actually the minimum: There is no faster way to get to Barnard's Star.
A speed of 150 kilometers per second is a bit optimistic for the currently available technology; we get at most a tenth of this value and that only with small space probes in which a human being has neither space nor could survive for a long time. In addition, it is questionable whether technology really advances so constantly and doubles the speed every 100 years. It could also happen more slowly - or faster. All of these factors (including other complications such as the relativistic effect at very high speeds) are taken into account by Kennedy in the further course of his work. But the basic problem remains: We won't be able to reach the stars any time soon. We either have to fly through space for a very long time or we have to wait a long time and hope that in the meantime someone builds a very fast spaceship.