Time Dilation and Proper Time: Calculating the Effects of Relativistic Travel

[NUFC]

1. Homework Statement [/b]
Just need some help getting started on what looks like a rather simple problem!

A rocket travels to a star 5 light years distant, observers on the star time the journey at 6years. I need to find the time recorded on a clock aboard the rocket and the distance to the star in the rockets reference frame.

Homework Equations

t(observer) = t(rocket) / Sqrt 1-v^2/c^2 so i can rearrange for t(rocket) but the problem i have is that there are two variables missing t(rocket) - the one i need to find and v the velocity of the rocket. This also prevents me from calculating the Lorentz Factor using the normal LF eqn.

The Attempt at a Solution

I have (sort of) calculated the LF by using 6years / 5 light years = 1.2 ie trying to find the ratio between the distand and observed time then applied taht to the 10light years to get 8.33 for proper time on the rocket.

But I am sure this is incorrect, any guidance would be appreciated, thank you.

Please also accept apologies if this is not worded correctly, this is my first post.

 

[Cyosis]

What is the speed with which observers on the star see the rocket come towards them?

 

[NUFC]

That is part of the problem the question does not give the speed of the rocket. I did originally think that it may be simply the actual distance of 5 ly against the 6years observed time, ie 5/6 = 0.83c but regarded that as too obvious!

 

[NeoDevin]

That is part of the problem the question does not give the speed of the rocket. I did originally think that it may be simply the actual distance of 5 ly against the 6years observed time, ie 5/6 = 0.83c but regarded that as too obvious!

That is correct. That is the speed as seen by the observer.

 

[NUFC]

thank you for that, it shows you shouldn't dismiss something because it looks too obvious - doh!

if i use the velocity from observers viewpoint (0.83) and rearrange the time dilation eqn for t(proper) ie the time on the rocket clock [t(rocket) = t(observer) * Sqrt 1-v^2/c^2] will this then give me the correct proper time. Rearranging and substituting the values [12yrs* sqrt (1 - 0.83^2 / c^2)] gives me 6.69 years. To get distance in rockets frame of reference Ido I multiply the proper time by say the 0.83 speed or should I be calculating the speed of the rocvket in its reference frame?

Sorry if getting a bit long winded here, just a bit confused by this one!

Thank you.

 

[NUFC]

Apologies but in the equation i have just posted i have used 12 years it should in fact be 6 years which gives a proper time of 3.35 years.

 

[NeoDevin]

or should I be calculating the speed of the rocvket in its reference frame

The speed of anything in it's own reference frame is zero.

 

[NUFC]

i see what you are saying. but does this mean i am on the right lines by assuming that if i calculate the LF in the frame of the observer it also applies to the rocket? I apologise but i really cannot get my head around this for some reason.

 

[NeoDevin]

Yes, the speed of the observer with respect to the rocket is the same as the speed of the rocket with respect to the observer (though direction is opposite). The Lorentz factor depends on the square of the velocity, so is independent of direction.

 

[NUFC]

Ah ha, i follow now. Thank you very much for your help, much appreciated.