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183. Problem 2.23 (R) The radius of our galaxy is
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,
or about
We
have to answer (a) whether, in principle, a person can travel to the edge
of our galaxy in a normal lifetime; (b) and calculate the constant
velocity needed to make the trip in 30 years (proper time).|
Solution: Click For PDF Version (a) If the spaceship carrying the person to the edge of the galaxy travels with speed very close to the speed of light, although the time period measured by the observer on the Earth will far exceed the normal life span yet the proper time that is the time shown on the watch of the traveller can be a normal period comparable to the lifetime that is about 30 years or so. So the answer to the first part of the problem is in affirmative.
(b) We will now calculate the speed with which the spaceship should travel with
respect to the Earth so that the proper time of 30 years is measured as
where
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years
by an observer on the Earth. Let the speed of the spaceship with respect to the
Earth be v. We will find v from the time dilatation relation
. We
therefore have