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AndrewJ
2009-Jul-30, 07:47 PM
I am trying to devise an example of starlight travel time and throw in a bit of relativity.

I was thinking something like "yonder is Sirius seen on Earth tonight as it was in the last days of Clinton's presidency whereas close by is Betelgeuse seen as it was in the days of Tamerlane and may have supernovaed in the meantime". (One might use Altair and Deneb depending on the time of the year).

Would it be true to add that if one somehow travelled to Betegeuse at very close to c then whenever you looked back you'd measure Earth as closer to you than the distance you would simultaneously measure between Earth and Sirius? Or does that stuff only work inter-galactically? Never 100% confident.

I think it's good to keep SR in mind but you don't want to get it wrong and look like a pillock.

grant hutchison
2009-Jul-30, 08:46 PM
I'm not sure quite what your question is, so I apologize if this doesn't address it.
In the instantaneous coordinates of your travelling spaceship, you'd measure the distance between Betelgeuse and Earth as being much reduced. But at any time the proportion of the distance you had travelled would be the same, whether you measured it in your coordinates, or someone at home on Earth measured it in theirs.

An interesting effect occurs if you make the journey under continuous acceleration, turning over at the halfway point to decelerate towards your destination. The shrinkage of distances fore and aft in your own coordinates offsets your recession from home, while compounding your approach to your destination.
During the first half of the journey, home therefore recedes very slowly, while your destination approaches rapidly. At turn-over, you are half-way between home and destination, and the distance between them is much reduced. As you begin to decelerate towards your destination the change in your coordinate system now slows the approach of your destination, while increasing your rate of recession from home.

I made a graph of one such journey some time ago: it's here (http://www.ghutchison.pwp.blueyonder.co.uk/relativity/starflight.jpg). The distance travelled is just over 98 light-years, acceleration and deceleration are at 1g. The journey takes 100 years according to Earth's clocks, but only nine aboard ship. When the ship turns over at the half-way point, it is travelling at 0.9998c, and the distance between home and destination is just two light-years in the coordinate system of the ship.

Because Betelgeuse and Sirius are in approximately the same part of the sky, I'd guess that when you were travelling towards Betelgeuse you'd also find the distance to Sirius much reduced in your coordinates. If you can find a star that's offset at right angles to your direction of travel, then its coordinate distance from Earth wouldn't change during the journey.

Grant Hutchison

astromark
2009-Jul-30, 09:11 PM
Do not go to Betelgeuse... you may well encounter the shock wave of its nova event. That would be 'unfortunate'.:(
Thank you Grant for this most excellent answer to which my understanding of such has gained some credibility... :) I also note that Andrew has helped me as this post will be quoted in my attempt to explain distance and relativity to a room filled with school children ....mark

grant hutchison
2009-Jul-30, 09:22 PM
Thank you Grant for this most excellent answer to which my understanding of such has gained some credibility... :) Pleasure. :)
Just to add some detail to the business of Betelgeuse and Sirius.

If you're heading for Betelgeuse, you're heading roughly out along the celestial equator at 6 hours right ascension. Your coordinates will be shortened along that direction and in the opposite direction (towards 18 hours RA), but unchanged at right angles: the great circle linking 0 hours and 12 hours RA through the celestial poles.
Because Sirius is just a little off to one side as you head for Betelgeuse, it will be involved in the coordinate shrinkage to almost the same extent as Betelgeuse.

Grant Hutchison

AndrewJ
2009-Jul-30, 10:41 PM
In the instantaneous coordinates of your travelling spaceship, you'd measure the distance between Betelgeuse and Earth as being much reduced. But at any time the proportion of the distance you had travelled would be the same, whether you measured it in your coordinates, or someone at home on Earth measured it in theirs.

Iím just hoping to show that distance and light travel time are so not absolute that a comparison as seen from Earth could even be reversed as seen from another reference. I'll need to ponder the acceleration-deceleration scenario for a little while.


Because Betelgeuse and Sirius are in approximately the same part of the sky, I'd guess that when you were travelling towards Betelgeuse you'd also find the distance to Sirius much reduced in your coordinates. If you can find a star that's offset at right angles to your direction of travel, then its coordinate distance from Earth wouldn't change during the journey.

OK, my spiel wonít work with two close stars. Iíll try with a couple that are at more of a right-angle.


this post will be quoted in my attempt to explain distance and relativity to a room filled with school children

If youíre in NZ I guess you could use Canopus as your ďfar starĒ and any closer star at 90 degrees.

Hereís an amended Northern Hemisphere example:

Yonder is Dubhe seen on Earth tonight as it was in the days of Grover Cleveland's presidency whereas this way is Deneb seen as it was in the lifetime of Muhammed . If one somehow travelled to Deneb at very close to c then whenever you looked back you'd measure Earth as closer to you than the distance you would simultaneously measure between Earth and Dubhe.

AndrewJ
2009-Jul-31, 06:41 PM
An interesting effect occurs if you make the journey under continuous acceleration, turning over at the halfway point to decelerate towards your destination. The shrinkage of distances fore and aft in your own coordinates offsets your recession from home, while compounding your approach to your destination.
During the first half of the journey, home therefore recedes very slowly, while your destination approaches rapidly. At turn-over, you are half-way between home and destination, and the distance between them is much reduced. As you begin to decelerate towards your destination the change in your coordinate system now slows the approach of your destination, while increasing your rate of recession from home.

I made a graph of one such journey some time ago: it's here (http://www.ghutchison.pwp.blueyonder.co.uk/relativity/starflight.jpg). The distance travelled is just over 98 light-years, acceleration and deceleration are at 1g. The journey takes 100 years according to Earth's clocks, but only nine aboard ship. When the ship turns over at the half-way point, it is travelling at 0.9998c, and the distance between home and destination is just two light-years in the coordinate system of the ship.

My understanding: whilst accelarating the distance measured to an object you're receding from shortens and so little progress seems to have been made whereas surprisingly great progress is measured regarding an object you are approaching. I guess the crew on an acceleration-deceleration mission would seem to see their destination being sucked into home until half-way when home would seem to rip away and progess to destination become more labored.
If the average speed over the entire journey were say 95% of c would the on-board measured travel time be the same as if the speed were constant at 95% of c for the entire journey?

I know the accelaration scenario was given as a thought experiment but is any such change in velocity in any way possible during an interstellar journey? I can envisage an exotic particle whizzing along at a bit less than c.

Ken G
2009-Jul-31, 07:43 PM
If the average speed over the entire journey were say 95% of c would the on-board measured travel time be the same as if the speed were constant at 95% of c for the entire journey?
No, all you can say is that if the time average of v in the Earth frame is 0.95c, then the time it takes in the Earth frame is the same as if v was constant. But on board, if you fix the on-board time average of v at 0.95c, the on-board time is proportional to a bizarre quantity you might call the "on-board distance", which is the Earth-frame distance contracted by the factor 1/gamma, where gamma = root(1-v2/c2), and v is evaluated whereever you are calculating that contraction factor. That factor isn't constant if v isn't, nor does it average the same way v does. If, for example, you spent half the on-board time at c, and half at 0.9c, you basically wouldn't be spending any time at all at 0.9c, so you'd basically be making the whole trip at c, and the contraction would be great and the on-board time would be essentially zero.


I know the accelaration scenario was given as a thought experiment but is any such change in velocity in any way possible during an interstellar journey? I can envisage an exotic particle whizzing along at a bit less than c.I think the limit is the acceleration a human can tolerate, if the energy problems were magically solved. But for an exotic particle, one can do the acceleration and deceleration very quickly, and most of the trip can be near c, that's exactly what would happen if we pointed the beam of a particle acclerator toward some distant star (and the particles could get through the atmosphere and interstellar medium). Those particles would get to that star in less than a day in their own frame.

AndrewJ
2009-Aug-01, 03:26 AM
Very educational responses, thanks to the three of you. Next summer evening I'm in the yard with someone I'll have my Deneb-Dubhe comparison ready (bottom post 5) and not have to worry I'm going to get caught out.