## Spaceship travels at .83 c, relativity

1. The problem statement, all variables and given/known data

Suppose our sun is about to explode and we escape in a spaceship toward the star Tau Ceti. When we reach the midpoint of our journey, which takes place at v=.83 C we see our sun explode and, unfortunately, we see Tau Ceti explode as well (we observe the light arriving from each explosion. (there's a part a and b but i understand those parts, so i'll go straight to c and d)

c)In the spaceship frame of reference, how long before we saw the Sun explode did it actually explode? (enter a positive value for times in the past.)

d) In the spaceship frame of reference, how long before we saw Tau Ceta explode did it actually explode?

2. Relevant equations

Δt = $\gamma$(Δt' - v/c2Δx') } S'-->S

3. The attempt at a solution

c) I have worked out an answer using the equation I gave but I'm not sure if its correct.
I said that S is my frame for the spaceship and S' is my frame for the sun.
Δt = $\gamma$(Δt' - v/c2Δx')
so Δt = 1/(sqrt(1-(.83c)2/c2))*((6 years)+(.83c*6c)/c2)
Δt=19.686 years
Δt' = 6 years
So it actually exploded 13.686 years ago?

for part d), i used the same equation but instead used -v
so Δt = 1/(sqrt√(1-(-.83c)2/c2))*((6 years)+(-.83c*6c)/c2)
= 1.823 years
so it actually happened 1.823-6 = -4.171
4 years into the future? This is the main reason why I'm not believing my answer.
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hi harts! welcome to pf!
 Quote by harts Δt=19.686 years Δt' = 6 years So it actually exploded 13.686 years ago?
how can you subtract measurements in two different frames?

(and what do you think "∆" means? )
 Thanks for the reply! OK, I thought I was finding the difference in time between the two frames, which is why I subtracted the change in time from one frame from the change in time in the other frame. Am I misinterpreting the question? "In the spaceship frame of reference, how long before we saw the Sun explode did it actually explode?"

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## Spaceship travels at .83 c, relativity

hi harts!

(just got up )
 Quote by harts Am I misinterpreting the question? "In the spaceship frame of reference, how long before we saw the Sun explode did it actually explode?"
yup! …

both measurements must be made in the spaceship frame …

the time the sun exploded, and the time the light reached the spaceship
 OK I think I understand it now. I know that the sun actually exploded 6 years ago, but because of relativity I have to use a lorentz transformation to figure out how much time it took for us to see it. For part c, I use my equation t'= ((-6 years)-(.83c/c^2)(-6ly))/ sqrt(1-(.83c)^2/c^2)= -1.83 For part d, I use the same equation but use 6 light years for my x value and I got -19.686 years. I guess it just took me a while to understand those lorentz transformation equations. Thanks tiny tim