# Relativity and time dilation ... how's that work again?

October 22, 2013 3:50 PM Subscribe

I am writing a story with science fictional elements, and I am finding whatever practical knowledge of time dilation I ever had has dissolved into the mists of time. Help me out?

Let's say there's a spaceship traveling from earth to a system 20 light years away. Right now, "today", it's about halfway through the journey. Let's say it accelerated up to 0.9 C pretty early on, and is now coasting along at that speed.

How much time has passed for those aboard the spaceship?

How much time has passed for people on earth and/or the destination system?

How much time will have passed aboard the spaceship, the earth, and the destination system when the spaceship completes its journey?

How would this change if the ship were traveling at 0.95 C? At 0.99 C?

Does how much time the ship spends accelerating affect these answers, and if so, how?

OK, now let's say earth is sending a stream of information to the ship at the speed of light. Assuming halfway through the journey, 0.9 C:

How long ago was the information the ship receives "today" sent from earth?

How much time had passed on earth since the spaceship launch when the message the ship received "today" was sent?

How would these answers change for 0.95 C and 0.99 C?

How would these answers change if the stream of information was coming from the destination system rather than from earth?

All right, now let's say that sometime after the first spaceship was launched -- let's say when it's a quarter of the way through the journey -- a second spaceship was launched from the destination system on an intercept course. For it to meet the first spaceship at the "halfway point":

How fast would it need to be going, compared to the first ship?

How long ago, in the time frame of the destination system, did it launch? In the time frame of earth? In the time frame of the first ship?

If there's no way for a ship going at sublight speeds to meet the first ship at the halfway point under the conditions stated, what parameters would need to change to make that possible?

Thanks in advance!

Let's say there's a spaceship traveling from earth to a system 20 light years away. Right now, "today", it's about halfway through the journey. Let's say it accelerated up to 0.9 C pretty early on, and is now coasting along at that speed.

How much time has passed for those aboard the spaceship?

How much time has passed for people on earth and/or the destination system?

How much time will have passed aboard the spaceship, the earth, and the destination system when the spaceship completes its journey?

How would this change if the ship were traveling at 0.95 C? At 0.99 C?

Does how much time the ship spends accelerating affect these answers, and if so, how?

OK, now let's say earth is sending a stream of information to the ship at the speed of light. Assuming halfway through the journey, 0.9 C:

How long ago was the information the ship receives "today" sent from earth?

How much time had passed on earth since the spaceship launch when the message the ship received "today" was sent?

How would these answers change for 0.95 C and 0.99 C?

How would these answers change if the stream of information was coming from the destination system rather than from earth?

All right, now let's say that sometime after the first spaceship was launched -- let's say when it's a quarter of the way through the journey -- a second spaceship was launched from the destination system on an intercept course. For it to meet the first spaceship at the "halfway point":

How fast would it need to be going, compared to the first ship?

How long ago, in the time frame of the destination system, did it launch? In the time frame of earth? In the time frame of the first ship?

If there's no way for a ship going at sublight speeds to meet the first ship at the halfway point under the conditions stated, what parameters would need to change to make that possible?

Thanks in advance!

Best answer: The equation for time dilation is t_s = t_0 * sqrt(1-v^2/c^2). By my calculations, time is running 2.29 times more slowly for them (3.2 and 7.1 for 0.95c and 0.99c)

We'll assume that the Earth and destination system have synchronized their clocks by the usual methods.

As far as Earth/destination system is concerned, it takes the ship just over 11.1 years to get halfway. As far as the ship is concerned, it took about 4.8 years to get halfway.

The data stream question is pretty simple. The halfway point is 10 light years away. It would take the data 10 years (from the pointer of view of Earth/destination) to get there. So, when you are at that point, you see data that is 10 years old.

The intercept question is also simple - the intercept can't happen. The second ship would have to travel faster than the speed of light. If you want them to be able to meet then you have to move the intercept point and/or the launch time of the second ship. Note that this question also has nothing to do with time dilation.

posted by It's Never Lurgi at 6:11 PM on October 22, 2013 [1 favorite]

We'll assume that the Earth and destination system have synchronized their clocks by the usual methods.

As far as Earth/destination system is concerned, it takes the ship just over 11.1 years to get halfway. As far as the ship is concerned, it took about 4.8 years to get halfway.

The data stream question is pretty simple. The halfway point is 10 light years away. It would take the data 10 years (from the pointer of view of Earth/destination) to get there. So, when you are at that point, you see data that is 10 years old.

The intercept question is also simple - the intercept can't happen. The second ship would have to travel faster than the speed of light. If you want them to be able to meet then you have to move the intercept point and/or the launch time of the second ship. Note that this question also has nothing to do with time dilation.

posted by It's Never Lurgi at 6:11 PM on October 22, 2013 [1 favorite]

Here is a description of a program that does all the calculations you need, and a link to download it.

posted by Sophont at 7:01 PM on October 22, 2013

posted by Sophont at 7:01 PM on October 22, 2013

Wolfram Alpha has a time dilation calculator

posted by xueexueg at 7:13 PM on October 22, 2013 [1 favorite]

posted by xueexueg at 7:13 PM on October 22, 2013 [1 favorite]

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posted by thelonius at 5:55 PM on October 22, 2013