Calculating Time Dilation for Travel to Alpha Centauri

[daenku32]

Say I travel to Alpha Centauri (4.35 light-years from the Sun) AND back to Earth at 50 percent of speed of light.

How much time would the clock on my spaceship and a clock on Earth record me to have taken?

 

[Pengwuino]

Is this a homework question?

 

[daenku32]

Nope. In 28 with 3 kids. I'm just trying to self-educate myself on my spare time (the little I have).

 

[dicerandom]

Even if it isn't a homework problem you won't learn anything by someone simply telling you the answer, as I'm sure you know. So I'll try and give you a push in the right direction, if you have any problems with specifics just post back here and we can work them out.

Basically what you want to do is lay down what's happening in whatever coordinate system is easiest. In this case it's easiest to lay things down in the Earth's system. Say that both frames start out at the Earth at t=0, x=0. The guy in the spaceship is going to head off to the star at the given speed, so you can work out the distance and time at which this happen in Earth's frame. Likewise you can work out the time at which he returns to Earth. You can then use the Lorentz transformation to convert the coordinates of each event in the Earth's frame into the coordinates of the space ship's frame.

 

[JesseM]

As a shortcut, you could also just use the time dilation formula, $$t \sqrt{1 - v^2/c^2}$$. So, for example, if someone was moving at 0.8c for 60 minutes in my frame, then I could predict that their clock would only elapse $$60 \sqrt{1 - 0.8^2}$$ = 36 minutes in my frame.