Calculating Time Dilation for Travel to Alpha Centauri

In summary, the conversation discusses a question about the time difference between clocks on a spaceship and on Earth when traveling to Alpha Centauri and back at 50 percent of the speed of light. The expert suggests using the Earth's coordinate system and the Lorentz transformation to calculate the time difference, or using the time dilation formula as a shortcut.
  • #1
daenku32
2
0
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?
 
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  • #2
Is this a homework question?
 
  • #3
Nope. In 28 with 3 kids. I'm just trying to self-educate myself on my spare time (the little I have).
 
  • #4
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.
 
  • #5
As a shortcut, you could also just use the time dilation formula, [tex]t \sqrt{1 - v^2/c^2}[/tex]. 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 [tex]60 \sqrt{1 - 0.8^2}[/tex] = 36 minutes in my frame.
 

1. What is Alpha Centauri?

Alpha Centauri is a star system located about 4.37 light years away from Earth. It is the closest star system to our solar system and consists of three stars: Alpha Centauri A, Alpha Centauri B, and Proxima Centauri.

2. How long would it take to travel to Alpha Centauri?

The estimated travel time to Alpha Centauri depends on the speed of the spacecraft. With current technology, it would take approximately 137 years to reach Alpha Centauri. However, with advancements in technology, this travel time could potentially be reduced to 20-30 years in the future.

3. Can humans survive the journey to Alpha Centauri?

The journey to Alpha Centauri would be extremely long and challenging, but it is theoretically possible for humans to survive the trip. However, the spacecraft would need to be equipped with advanced life support systems to sustain human life for such a long duration.

4. Is there any other way to explore Alpha Centauri without physically traveling there?

Although physically traveling to Alpha Centauri is currently the only way to explore the star system, scientists have been using telescopes and other instruments to study it from Earth. There are also plans to send unmanned spacecrafts to gather more data and images of Alpha Centauri.

5. Why is Alpha Centauri important for scientific research?

Alpha Centauri is important for scientific research because it is the closest star system to our solar system and could potentially harbor habitable planets. Studying this star system can provide valuable insights into the formation and evolution of planetary systems, as well as the potential for extraterrestrial life.

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