Updated 1 Nov 26
I have recently come across a couple of items online based on the elapsed time for occupants of a spaceship accelerating at 1g to traverse cosmic distances.
First a video, Something Terrifying Would Happen If a Spaceship Constantly Accelerated at 1G Through Space..., on YouTube channel ExoSci, posted 27 Sept. The audio refers to an article, but which? Could it be this one, How long does it take to travel through the Universe at 1g?, posted by Ethan Siegel on Big Think just the day before? Too soon surely, but perhaps Siegel had posted something similar earlier. Astonishingly, he concludes: All destinations within the reachable Universe are achievable in 25 years, maximum. Of course, that is for the occupants of the spaceship and is a consequence of relativistic length-contraction over the cosmic distance travelled.
For some reason, this made me remember an amazing fact I first came across many years' ago - if the Earth were to be squeezed as a cylinder of 1 square metre cross-section (maintaining its density), its length would equal the diameter of our galaxy!
Let's check:
- the radius of the Earth is 6.4 million metres
- therefore its volume is ~ 10^21 cubic metres
- with a cross-section of 1 square metre, the cylinder would have a length of 10^21 metres
- one light year is about 10^16 metres, so that makes the squeezed Earth 100 thousand light years in length
- our galaxy is believed to be 100 to 150 thousand light years across, so the assertion is roughly correct!
Why stop there? What if we were to reduce the cross-section of the cylinder to 1 square centimetre? There are 10,000 (100 squared) of those in a square metre, so the squeezed Earth would now be 10,000 times longer than before, so 1000 million, or 1 billion light years in length!
What if we were to reduce the cross-section of the cylinder further to just 1 square millimetre? There are 100 (10 squared) of those in a square centimetre, so the squeezed Earth would now be 100 times longer than before, so 100 billion light years in length! That's about the diameter of the observable universe!
(We could also dial back and increase the cross-section to 1 square kilometre, in which case, the cylinder would stretch to about one millionth the diameter of the Milky Way, i.e. to one tenth of a light year, about the distance from the Sun to the inner edge of the Oort Cloud).
Conclusion: the (observable) universe is vast, but not unimaginably vast. (And 'just' a million Milky Way galaxies placed side-by-side will span it).