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How far could an astronaut travel in a lifetime? Billions of light years, it turns out. But they ought to be careful when to apply the brakes on the return trip.
I'm guessing it must be based on the assumption that the universe stopped expanding and you could keep increasing your travel speed faster than the speed of light. If I understand it right, it assumes your travel speed keeps increasing every second by an additional 28 feet per second.
It's based on a 1g acceleration from a rest frame and probably takes the cosmological constant in to account, as well. Even with constant acceleration the astronaut will never reach the speed of light, but only come arbitrarily close to it. The astronaut reference frame will appear to slow down, however, so even though the astronauts are only moving at about the speed of light in Earth's reference frame, they will appear to live for a very long time. The astronaut will perceive time normally, but length contraction along the direction of motion will make the travel distance as large as it appears to an Earthbound observer.
It's based on a 1g acceleration from a rest frame and probably takes the cosmological constant in to account, as well. Even with constant acceleration the astronaut will never reach the speed of light, but only come arbitrarily close to it. The astronaut reference frame will appear to slow down, however, so even though the astronauts are only moving at about the speed of light in Earth's reference frame, they will appear to live for a very long time. The astronaut will perceive time normally, but length contraction along the direction of motion will make the travel distance as large as it appears to an Earthbound observer.
Right. I saw the 1g acceleration point, but the way it was described: "Accelerating at around 9 meters (28 feet) per second per second -- which would feel roughly like a comfortable 1 g -- a craft could get 99 per cent of the way to the expansion "horizon.", the "per second per second" is a bit awkward. The impression I got from it is that starting out at 28 feet per second, and each second following then increases by another 28 feet per second. Meaning that in 2 seconds, the acceleration will be 56 feet per second. At 3 seconds, 84 feet per second, etc. Maybe I'm wrong though.
I realize time will slow down from the astronaut's reference frame. Actually, time will seem normal to the astronaut, but extremely long from the point of view on Earth. But we're still talking about arriving at destination located within 99% of the universe's expansion horizon which is billions of light years away. But 30-50 years passing from the astronaut's view of time? And that's just one-way.
Right. I saw the 1g acceleration point, but the way it was described: "Accelerating at around 9 meters (28 feet) per second per second -- which would feel roughly like a comfortable 1 g -- a craft could get 99 per cent of the way to the expansion "horizon.", the "per second per second" is a bit awkward. The impression I got from it is that starting out at 28 feet per second, and each second following then increases by another 28 feet per second. Meaning that in 2 seconds, the acceleration will be 56 feet per second. At 3 seconds, 84 feet per second, etc. Maybe I'm wrong though.
I realize time will slow down from the astronaut's reference frame. Actually, time will seem normal to the astronaut, but extremely long from the point of view on Earth. But we're still talking about arriving at destination located within 99% of the universe's expansion horizon which is billions of light years away. But 30-50 years passing from the astronaut's view of time? And that's just one-way.
You're right only in the non-relativistic or Galilean case, where velocity adds linearly. In relativity, velocity is no longer additive and so acceleration no longer is as simple as what you describe. After a time _t_ the Galilean velocity would be _g*t_ whereas the relativistic velocity is actually _g*t/sqrt(1+(gt/c)^2)_. For gt << c, this is nearly identical to gt but as t->infinity the velocity only asymptotically approaches c.
How far could an astronaut travel in a lifetime? Billions of light years, it turns out. But they ought to be careful when to apply the brakes on the return trip.
Off hand I'd say astronauts are only going to go as far as Hollywood makes them go. To be honest though it's not of major importance to me since there are way too many problems to be concerned with and solve here.
However, I do enjoy some of the science fiction and speculation of what the potential could be.
In grad school I was supported by a NASA grant, so friends and relatives sometimes asked if I though manned space flight was worth the expenditure. I had to admit that the money could probably be spent more efficiently in other areas--basic science, applied science, infrastructure--at least in the near term. That being said, though, I argued that NASA wasn't taking money from other areas of science but from the military--just look at the contractors. If we're going to spend billions of dollars developing advanced rocket and jet propelled its nice that some of those craft are peaceful.
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