Go Back   Physics Help Forum > College/University Physics Help > Special and General Relativity

Special and General Relativity Special and General Relativity Physics Help Forum

Reply
 
LinkBack Thread Tools Display Modes
Old Sep 8th 2008, 07:09 PM   #1
Junior Member
 
Join Date: Aug 2008
Posts: 9
relativistic timing

1. The problem statement, all variables and given/known data
A member of a colony on Jupiter is required to salute the UN flag at the same time as it is being done on Earth at noon in New York. If observers in all inertial frames(i.e. any observer traveling at any arbitrary velocity) are to agree that he has performed his duty, how long must he solute for(i.e. seeing you don't know how fast the observer is traveling, what time iterval ensures that the rising of the falg and the saluting are simultaneous for all possible speeds of the observer)? (Distance between the planets is approximately 8 x10^6 km, ignore any relative motion of the planets)


2. Relevant equations

Lorentz Transformation

3. The attempt at a solution

I need help getting started on this. I have no idea what to do at all(partly because of not understanding what the question wants) I'm not sure if I'm suppose to derive an equation, or there is a number answer to this.

I'm totally stuck on the thought process portion and cannot/don't know how to translate anything onto paper.
I know that the arbitrary observer can have velocity from the range of -c to c but I don't know if that means I should end up with two solutions which will give us the time interval.

So any advice on how to begin this would be greatly appreciated. Thanks
jianxu is offline   Reply With Quote
Old Sep 9th 2008, 07:34 AM   #2
Forum Admin
 
topsquark's Avatar
 
Join Date: Apr 2008
Location: On the dance floor, baby!
Posts: 2,856
Originally Posted by jianxu View Post
1. The problem statement, all variables and given/known data
A member of a colony on Jupiter is required to salute the UN flag at the same time as it is being done on Earth at noon in New York. If observers in all inertial frames(i.e. any observer traveling at any arbitrary velocity) are to agree that he has performed his duty, how long must he solute for(i.e. seeing you don't know how fast the observer is traveling, what time iterval ensures that the rising of the falg and the saluting are simultaneous for all possible speeds of the observer)? (Distance between the planets is approximately 8 x10^6 km, ignore any relative motion of the planets)


2. Relevant equations

Lorentz Transformation

3. The attempt at a solution

I need help getting started on this. I have no idea what to do at all(partly because of not understanding what the question wants) I'm not sure if I'm suppose to derive an equation, or there is a number answer to this.

I'm totally stuck on the thought process portion and cannot/don't know how to translate anything onto paper.
I know that the arbitrary observer can have velocity from the range of -c to c but I don't know if that means I should end up with two solutions which will give us the time interval.

So any advice on how to begin this would be greatly appreciated. Thanks
I'm off by a negative sign and I'm not sure why. But here it goes.

I'm going to make the simplifying assumption that the observers' origin is at the Earth at the time that the salute is supposed to be given. Let's synchronize all the observers' clocks with the Earth clock and let t = 0 be when the salute is supposed to be performed. The saluter has to salute somewhat before this time in order for the signal to be received at t = 0 on Earth, so he/she has to salute at t = -L/c where L is the Earth-Jupiter distance. Now an observer moving at speed v sees the salute at:
$\displaystyle t' = \gamma \left ( -\frac{L}{c} - \frac{Lv}{c^2} \right )$

$\displaystyle t' = -\frac{L}{c} \sqrt{\frac{1 + \frac{v}{c}}{1 - \frac{v}{c}}} = -\frac{L}{c} \sqrt{\frac{c + v}{c - v}}$
So as v goes from 0 to c the time t' goes from -L/c to (ahem) minus infinity.

Given the result I strongly suspect our poor saluter is going to have to salute forever (and we can logic that out.) I just can't find a way to get rid of the pesky negative sign.

-Dan
__________________
Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.

See the forum rules here.
topsquark is online now   Reply With Quote
Old Sep 9th 2008, 09:48 AM   #3
Junior Member
 
Join Date: Aug 2008
Posts: 9
thank you for your help. I actually understand what I should be looking for now
jianxu is offline   Reply With Quote
Old Sep 9th 2008, 11:06 AM   #4
Forum Admin
 
topsquark's Avatar
 
Join Date: Apr 2008
Location: On the dance floor, baby!
Posts: 2,856
Originally Posted by jianxu View Post
thank you for your help. I actually understand what I should be looking for now
I'd be interested in how you get the final answer, once you figure it out. That negative sign is driving me crazy!

-Dan
__________________
Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.

See the forum rules here.
topsquark is online now   Reply With Quote
Old Sep 10th 2008, 01:40 PM   #5
Junior Member
 
Join Date: Aug 2008
Posts: 9
yep so we use initial t' = gamma(t - vx/c^2)

what we're suppose to assume is that t' = 0 because all observers have to see the event simultaneously. At this point we know the range of speed an observer can have ranges from -c to c so we just plug that in and solve for t for the two different velocities
jianxu is offline   Reply With Quote
Old Sep 10th 2008, 01:45 PM   #6
Forum Admin
 
topsquark's Avatar
 
Join Date: Apr 2008
Location: On the dance floor, baby!
Posts: 2,856
Originally Posted by jianxu View Post
yep so we use initial t' = gamma(t - vx/c^2)

what we're suppose to assume is that t' = 0 because all observers have to see the event simultaneously. At this point we know the range of speed an observer can have ranges from -c to c so we just plug that in and solve for t for the two different velocities
Ah. Working backward. I like it. Thank you for sharing.

-Dan
__________________
Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.

See the forum rules here.
topsquark is online now   Reply With Quote
Reply

  Physics Help Forum > College/University Physics Help > Special and General Relativity

Tags
relativistic, timing



Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
timing jump onto target helpmeout Kinematics and Dynamics 1 Oct 10th 2015 06:46 AM
Relativistic VS Classic MMM Kinematics and Dynamics 0 May 4th 2015 07:34 AM
Ultra-relativistic and Quasi-relativistic nathanzzf Quantum Physics 4 Jan 4th 2010 04:07 AM
Relativistic Mass Pmb Special and General Relativity 28 Aug 1st 2009 02:02 PM
relativistic confusion physicsquest Special and General Relativity 2 May 26th 2009 11:58 AM


Facebook Twitter Google+ RSS Feed