Time Dilation at 0.97c: Calculating Travel Time to a Star

[Allens]

A certain star is 45.0 light-years away. How long would it take a spacecraft traveling at 0.97c to reach that star from Earth, as measured by an observer:
(a) on Earth?
(b) on the spacecraft ?

i'm not sure how to solve this question... simply i don't know which is tv and which is t0.
i was thinking that the person on Earth would be in rest frame, however relative to the spacecraft the person on Earth would be in tv and the person on the spacecraft would be in the rest frame (t0)... very confused :S

 

[Matterwave]

The Earth bound observer will just measure t=d/v=45ly/(.97c). You can treat him as the stationary observer since the star isn't moving relative to the Earth (as far as this problem is concerned).

The spacecraft bound observer will measure t'=d'/v where d' is the Lorentz contracted distance.

This should be conceptually much simpler than doing the time dilation between t and t'.

 

[Allens]

The Earth bound observer will just measure t=d/v=45ly/(.97c). You can treat him as the stationary observer since the star isn't moving relative to the Earth (as far as this problem is concerned).

umm... can u simply put it into the equation t =d/v ? don't you need to use the time dilation equation? since the observer is not in the same frame of reference to the spacecraft (he is stationary therefore rest frame t0)?

$$<br /> Tv= \time \equiv \frac{t0}{\sqrt{{45 - v^2/c^2}}<br />$$

 

[Matterwave]

Time dilation is only ever used to find the time that passes in ANOTHER frame from your frame.

If I'm on Earth, why would I dilate my own time? I would only dilate the spacecraft 's time.

(If I were on the spacecraft , I would only ever dilate the Earth's time. This leads to the Twin paradox)

 

[Allens]

OHHHHHHHH,, heheheh... i must have had a mental blank :), i get you now,, why would time dilate when your on Earth, when your not traveling at 0.97c the dilation that would occur would be the spacecraft , in which it is in the same frame of reference to 0.97c.

It's actually common sense, why would time dilate for someone that is NOT traveling 0.97c. (different frame of reference)

sorry i completely misunderstood question.

thank you, this was very helpful :D