Question

Is it possible, in principle, for you to travel to the center of the galaxy, which is 23,000ly away in your lifetime? Explain, using both time dilation and length contraction arguments. If your spaceship can go a maximum of v = 0.990c, will you make the one way trip in your lifetime? Let’s assume you have 80 years.

Answer 1

In context to time dilation:

My lifetime of 80 yrs. must be dilated by a factor , where v = speed of the spaceship = 0.990c and c is the speed of light.

Calculating this factor:

Given, my lifetime in a rest frame or proper life time to be

So, from the time dilation relation, my dilated lifetime would be:

So, due to time dilation, my lifetime would be

So, distance that can be travelled over this lifetime (t = 567.4 yrs) = vt.

Now, speed of light,

1 light year = distance travelled by light in 1 year, i.e.

Time taken to cover 23000 ly

This time is much greater than my lifetime even after time dilation and hence, it is not possible to make one way trip during my lifetime.

In context to length contraction:

The distance to the centre of the galaxy must be contracted by a factor where v = speed of the spaceship = 0.990c and c is the speed of light.

The proper length i.e., the distance to the centre of the galaxy,

So, from length contraction relation, the general length after contraction would be:

Time taken by the space ship to travel the distance:

This time is also much greater than my lifetime even after length contraction and hence, it is not possible to make one way trip during my lifetime.

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