Time Dilation: Cells Divide on Earth & Travel to Sun

[atomqwerty]

Homework Statement

Two cells that divide on Earth each 10s start a travel to the Sun at v = 0.85c (Distance earth-sun: 1.5·10^11 m). How many cells should exist when the rocket they travel in carshes with the Sun?

Homework Equations

Time dilation: t=t₀/sqrt[1-v²]

being t₀ the time from a 'rest' sytem.

The Attempt at a Solution

My results are:

10 seconds on Earth mean 18.9 seconds on the rocket, due to time dilation, thus it will be less divisions by the time a person on Earth watches the rocket crashes with the Sun. So:

2⁵⁹ cells (From system Earth) = 5,77·10¹⁷ cells
2³² cells (From system Rocket) = 4 294 967 296 cells

Is this correct? Thank you.

 

[Doc Al]

No, not correct. First things first: How long does the trip take according to Earth observers?

 

[Andrew Mason]

It appears you are using 590 seconds for t₀. How do you determine that?

What is your answer? You have given two different ones.

AM

 

[atomqwerty]

It appears you are using 590 seconds for t₀. How do you determine that?

What is your answer? You have given two different ones.

AM

Yes, I used 590 seconds, obtained: t = [distance earth-sun)/(speed of light), that is the time that the rocket takes to reach the sun for an oberver on earth.

Because of time for each observer is not the same, a person on Earth will measure 2⁵⁸ divisions and another one on the rocket (in which the cells are) will measure 2³² divisions - I forgot to say that in the beginning there was 2 cells. ten seconds later, will be 2², at 20 seconds will be 2³... and son on.

Thanks

 

[atomqwerty]

No, not correct. First things first: How long does the trip take according to Earth observers?

According to Earth observers: 588,24 s. In this time will be more divsions from Earth than from rocket, due to the time for a single division in rocket is not 10 secds like on earth, but 18,9 seconds.

I'm a little confused


Thanks

 

[Doc Al]

According to Earth observers: 588,24 s. In this time will be more divsions from Earth than from rocket, due to the time for a single division in rocket is not 10 secds like on earth, but 18,9 seconds.

OK, I see what you're saying and I understand your answers now. (You had labeled both answers as "From system Earth", which threw me off.)

The way I'd state it would be that the travel time according to Earth observers is 588 s. Thus, due to time dilation, the travel time according to the rocket clocks would be 588/1.9 s.

Good!

 

[atomqwerty]

OK, I see what you're saying and I understand your answers now. (You had labeled both answers as "From system Earth", which threw me off.)

The way I'd state it would be that the travel time according to Earth observers is 588 s. Thus, due to time dilation, the travel time according to the rocket clocks would be 588/1.9 s.

Good!

Ok! I already fixed that! Thanks, I've understood the problem!