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## Homework Statement

Alpha Centauri, the closest star to Earth, is 4.3x10^6 m away. How long would it take a spaceship to reach the star if it were travelling at 0.999c?

## Homework Equations

I did get the answer as 0.2a....and the textbook also said it would take about 2 months,

I do not understand what the a represents/stands for and how the textbook got 2 months from 2a.

Also, I do not why I had to find tm and then to?

## The Attempt at a Solution

ts = d/v = 4.3 x 10^16/0.999c =

*s*

*1.43x10^8*tm = ts/√(1-v^2/c^2

=

**1.43x10^8**/√(1-(0.999c)^2/c^2

= 3.19 x 10^9 s

tm =

**4.5a**

__THE ANSWER KEy gets the same answer till the part above but then the answer key starts doing more calculations afterwards(below) which I do not get__ts = tm√1-v^2/c^2

=

**4.5a**√1-(0.999c)^2/c^2

__ts = 0.2a__the textbook gave 0.2a but also said it will take two months to reach the star and that is what I do not understand.

Thanks for your help.

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