Interstellar space travel and reference frames

[sr57]

Homework Statement

A spacecraft with its astronaut has a total mass at rest of 10^5 kg. The astronaut is to travel to a star 10 light years away at a speed such that she only ages 1 year in her frame of reference
a) the quantity 1-v/c where v is her speed with respect to Earth is?
b) the total energy required to accelerate the spacecraft from rest to this velocity in units of 10^22 Joules is?

Homework Equations

The Attempt at a Solution

1 year = 356 days = 1.89 x 10^9
I tried converting 10 light years into km
Then tried using v = d/t to find V

 

[alphysicist]

Hi sr57,

Homework Statement

A spacecraft with its astronaut has a total mass at rest of 10^5 kg. The astronaut is to travel to a star 10 light years away at a speed such that she only ages 1 year in her frame of reference
a) the quantity 1-v/c where v is her speed with respect to Earth is?
b) the total energy required to accelerate the spacecraft from rest to this velocity in units of 10^22 Joules is?

Homework Equations

The Attempt at a Solution

1 year = 356 days = 1.89 x 10^9
I tried converting 10 light years into km
Then tried using v = d/t to find V

You did not say what units you converted a year to, but I don't think it's 1.89 x 10^9 seconds.

What did you find when you calculated v using your method? If you change 10 light years into meters, and convert a year into seconds, it looks like your equation will give a speed larger than the speed of light (greater than 3 x 10^8), which indicates this approach will not work.

Here the speed will be large enough that you need to incorporate relativistic effects into your approach.

 

[sr57]

Using relativistic approach:

T = To/square root of (1-v^2/c^2)

T = 10 light years x speed of light/ V --> I'm not sure abt this

To = 1 year = 3.15 z 10^7 seconds

I don't know how to find V when i substitute the numbers

 

[alphysicist]

Using relativistic approach:

T = To/square root of (1-v^2/c^2)

T = 10 light years x speed of light/ V --> I'm not sure abt this

No, that can't be correct because it doesn't have the right units. (time on the left side, distance on the right)

But now that you have the time interval T in the Earth frame of reference, and the length in the Earth frame, you can use your original equation d=vT.


As an alternative, you could have kept everything in the astronaut's frame of reference. You have the time interval To, and you could find the length in his reference frame (it will be contracted). Then you could use d=vT in that reference frame.


This problem is much like the discussion on muon decay which your textbook probably covers; it might be a good idea to read over that to see how they calculate the same motion in two different reference frames.