magine an alien spaceship traveling so fast that it crosses our galaxy (whose rest diameter is 100,000 ly) in only 100 y of spaceship time. Observers at rest in the galaxy would say that this was possible because the ship's speed B was so close to 1 that the proper time it measured between its entry into and departure from the galaxy was much shorter than the galaxy frame coordinate time (~ 100,000 y) between those events. But how does this look to the aliens? To them, their clocks are running normallu, but the galaxy, which moves backward relative to them at speed B~1, is Lorentz-contracted to a bit less than 100 ly across: this is what makes it possible for the whole galaxy to fly by them in only 100 y. Then find the diameter of the galaxy in the aliens' frame, and verify that it is possible for a galaxy moving at speed B with this diameter to passthe aliens' ship completely in 100y.
Imagine an alien spaceship traveling so fast that it crosses our galaxy (whose rest diameter is 100,000 ly) in only 100 y of spaceship time. Observers at rest in the galaxy would say that this was possible because the ship's speed B was so close to 1 that the proper time it measured between its entry into and departure from the galaxy was much shorter than the galaxy frame coordinate time (~ 100,000 y) between those events. But how does this look to the aliens? To them, their clocks are running normallu, but the galaxy, which moves backward relative to them at speed B~1, is Lorentz-contracted to a bit less than 100 ly across: this is what makes it possible for the whole galaxy to fly by them in only 100 y. Then find the diameter of the galaxy in the aliens' frame, and verify that it is possible for a galaxy moving at speed B with this diameter to passthe aliens' ship completely in 100y.
Answer: 0.9999995
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