It will take between 1 and 6 million years for humans to travel 100 light years. If you wanted to travel 100 trillion light-years away, you could make the trip in 62 years. By the time you arrived, the Universe would have changed drastically. Most stars would have died long ago, and the Universe would have run out of usable hydrogen.
Leaving a living and thriving universe billions of years ago, you would never be able to come back. If you were to travel at 0.25°C, it would take 400 years for the astronaut, but 413 years for the observer. At 0.9°C, it would take 111 years for the astronaut and 254 years for the observer. Proxima Centauri is 4.2 light-years from Earth, a distance that would take about 6,300 years to travel with current technology.
Such a journey would span multiple generations, with most of the humans involved never seeing Earth or its exoplanetary counterpart. To ensure a healthy crew arrives at Proxima Centauri, reproduction between crew members would be necessary throughout the trip. If you were moving away from Earth, the star must be closer than 60 light-years and it would take less than 75 years to reach it. To easily express such large distances, the light-year was used as a unit for measuring astronomical distances.
If you wanted to travel with a constant acceleration of 1G and then decelerate to the edge of the observable Universe, it would take many years to reach your destination. From your close perspective at the speed of light, everything appears to move incredibly slowly due to relativity. Space is compressed in the direction in which you travel, so you don't travel as far as stationary observers see you traveling. In 1676, Danish astronomer Ole Rømer calculated an estimate of the speed of light while trying to create a reliable astronomical clock for sailors on the high seas.
Forty years later, he used a mile-long depressurized corrugated steel tube to simulate a nearby vacuum and obtain a better measurement, which was only slightly lower than the accepted value of the speed of light today. With an acceleration rate of 1G for years, billions of light-years can be traveled over a human lifetime. It took almost a decade for New Horizons to get from Earth to Pluto, which is just 4.6 light hours away.
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