Minimize the trip time from Earth's perspective?

Question

Here's a challenge problem I thought up relating to interstellar travel at relativistic speeds.

Your spaceship is in Earth orbit. You want to journey to Proxima Centauri, which is 4.22 light-years away, then return to Earth. Your ship is capable of traveling at any speed between 0 and c, the speed of light. If you make the journey at close to the speed of light, time dilation will cause many years to pass back on Earth. However, if you travel extremely slowly, the trip will take a long time.

What fraction of the speed of light do you travel to minimize the amount of time that passes on Earth during your round trip to Proxima Centauri?

10 points to the first correct answer!

Part 2: How much time will pass on board the ship during the 8.44 light-year trip?

Part 3: How much time will pass on Earth?

Answer 1

This is probably the first time that I answered a question before you or Bekki. Finally, I can actually earn some points!


1). Travel at roughly .709c

2). Ship time: 11.912 years

3). Earth time: 16.891 years


I'm also taking Lorentzian length contraction into effect, so our answers may differ slightly. However, all answers should be around .7c

Answer 2

*Part 1*: It seems to me that time will elapse the same on earth regardless of the speed of the spaceship so to minimize the time duration would be to travel as close to the speed of light as possible to complete the trip as fast to eliminate time of the trip. So .999...c would be my answer. I don't really understand what part 1 is asking because It looks more like some sort of judgment rather than thinking mathematically.

*Part 3*: Part 3 more convenient to answer first. I don't know it it's alright to solve with newtonian physics but I don't know relativity that well.
D = RxT (neglecting any sort of accelerations that the spaceship would be subject to during travel)
8.44(c x 1year) = .99c x T; T is roughly 8.53years.
8.53 years is the time that would appear to someone in an inertial frame not traveling near the speed of light, like on earth. *So 8.53 years would pass on earth during the trip*.

*Step 2*:
t = t(duration for astronaut)/sqrt(1-v^2/c^2)
ta = t/sqrt(1-v^2/c^2)
ta = 8.53yr x sqrt(1-(.99c)^2/c^2))
ta = 1.2yr
*So 1.2 years would pass on the spaceship.*

I'm not sure if all of this work is correct because we never covered relativity in my physics class all that I know is from reading the chapter on my own and I don't think I understood it entirely.

Answer 3

Your Open QuestionShow me another > Choose a best answer q APRIL MMember since: December 20, 2005
Total points: 200 (Level 1)
Points earned this week:
--% Best answer

APRIL M
S Your trip to space``(e) ( =) (mc) (sq)?
How fast can you excel to light speed. double that time, cause you gots to slow down~!` add that to your 8.44 yrs thats how long you'll be gone from earth. Now! quote to me! Einstein's. theory of relativity, cause I cant find my copy at home. And I , can figure the time on board for you. But, what are you going to do with the infinite mass and the size you will obtain according to the same formula! MAYBE WHEN YOU REACH NEAR LIGHT SPEED, AND ARE SO INFINITELY LARGE!! YOULL BE THERE ALREADY. SO MAYBE THE TRIP WILL TAKE ONLY THE TIME TO REACH LIGHT SPEED TO DECELERATE AGAIN,,HAVE FUN ON THE TRIP DONT FOR HEAVENS SAKES FORGET TO WRITE US!! NA NU NA NU( !!V!!) PS....JUST SO YOU CAN HEAR MEEEE.. ...MAY THE FORCE BE WITH YOU ~~

Additional Details

3 minutes ago
OPPS~! FORGOT MY COFFEE` SO FORGIVE ME YELLING IN YOUR EARS
JUST SO YOU DONT FORGET PLEASE DONT FORGET TO TAKE YOUR MEDS ON THE TRIP~`GOD SPEED FROM SOME HERE ON EARTH,, PS, HOWEVER, IT SURE WOULD BE KIND OF NICE TO TAKE THAT TRIP TOO,,,

6 minutes ago - 3 days left to answer. - 0 answers - Report Abuse
You can't answer your own question.

Answer 4

The leading question has to be--who the hell wants to go to Alpha Centauri? and in answer to age--hey, 29 forever.