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View Full Version : The Speed of Light, Acceleration and Alpha Centauri. And one more about a Black Hole



RalofTyr
2010-May-26, 03:24 AM
A few questions.

Now, it takes a certain amount of time to accelerate to near light speed due to technological and human toughness reasons.

Basically, how fast could a space craft accelerate too while going to Alpha Centauri? Consider that it would also have to slow down so it may not be able to reach top speed (near the speed of light).

Also, I know the trip would take four years Earth-time, but to the people on board the craft, could seem like four years to them. How long would a trip seem to them?


I'm thinking, that, if humans are ever able to reach near the speed of light, then although a trip to another star, say100 light years away, wouldn't be impossible for the astronauts to reach the star and not die of old age due to time dilation.


Black Hole: Say you were sucked into a Black Hole Singularity; would you be traveling so fast that time might just stop, preventing you from smacking into the Inner Singularity at light speed?

Jens
2010-May-26, 03:54 AM
Now, it takes a certain amount of time to accelerate to near light speed due to technological and human toughness reasons.

This has been asked from time to time, and I'm sure somebody can give you a quick calculation.


Also, I know the trip would take four years Earth-time, but to the people on board the craft, could seem like four years to them. How long would a trip seem to them?

No, it wouldn't take four years Earth time. It would take much longer, because of the time required for acceleration. The trip would be shorter for people on board, but still would be a while, because it would take a long time to accelerate, as I said.



I'm thinking, that, if humans are ever able to reach near the speed of light, then although a trip to another star, say100 light years away, wouldn't be impossible for the astronauts to reach the star and not die of old age due to time dilation.

If you could get close to the speed of light quickly, then the astronauts could get there without dying of old age. But this would require unknown technologies.



Black Hole: Say you were sucked into a Black Hole Singularity; would you be traveling so fast that time might just stop, preventing you from smacking into the Inner Singularity at light speed?

Well, you'd be torn apart before that. Time would be running slower for your toes than for your head. Plus you wouldn't smack into anything, I think. You would just be sucked into it.

WayneFrancis
2010-May-26, 05:32 AM
For back of the napkin calculations lets say you accelerate at just 10m/s or just over 1g.
Light speed is 299,792,458 or roughly 300,000,000/s
So to get to near light speed you would have to accelerate for 30,000,000 seconds.
There are 31,556,926 in a year so it would take about a year to get to that speed.
So we have 1 year accelerating and 1 year decelerating
Distance covered while accelerating for the year is found by the formula
D = (V1 + V0)*t/2
where V0 is your starting speed
V1 is your ending speed and t is your time
Well this simplifies to V1*t/2 or 300,000,000m/s * 15,000,000s = or 4,500,000,000,000,000 or 4.5x1015
roughly 1/2 a light year. So during acceleration and deceleration 1ly out of the 4ly would be accelerating or decelerating. this is from the reference frame of us on Earth
The other 3 ly would appear to those on board as almost instantaneous, accelerating up to c would make the 4ly distance undergo a length contraction, if a ship was travelling at .99c past Earth towards AC then to the ship AC would appear just over 1/2ly away but then the Earth wouldn't look spherical either.
Even with dilation effects most of the acceleration/deceleration would happen to the crew as normal.
With out going into the complexity of calculating time dilation over a long period of acceleration I'd estimate that those on board would experience the trip to be about 1.5 years
To those on Earth it would appear to have taken about 5 years.

This is ignoring the fuel issues, minor facts/curiosities and some other SR effects that for a back of the envelope calculation don't need to be considered.

astromark
2010-May-26, 05:59 AM
Great... I knew that if I waited some maths expert would come to your rescue... Gold medal to Wayne...

So if you in a spare moment could develop faster than light speed transport we could... go to those 100 ly away star systems in just a few y's...

As for the black hole question... avoid them.

grant hutchison
2010-May-26, 07:44 AM
Black Hole: Say you were sucked into a Black Hole Singularity; would you be traveling so fast that time might just stop, preventing you from smacking into the Inner Singularity at light speed?No, time dilation only happens in the coordinates of other observers. You reach the singularity in a finite amount of your own proper time.

Grant Hutchison

Cougar
2010-May-26, 01:24 PM
The other 3 ly would appear to those on board as almost instantaneous.

Thanks for working the figures, Wayne. This bit differs from my understanding, though... which is: the clocks on board would appear to those on board to be running normally.

Grashtel
2010-May-26, 01:24 PM
(bolding is mine)


roughly 1/2 a light year. So during acceleration and deceleration 1ly out of the 3 would be accelerating or decelerating
The other 3 ly would appear to those on board as almost instantaneous. Even with dilation effects most of the acceleration/deceleration would happen to the crew as normal.
with out going into the complexity of calculating time dilation over a long period of acceleration I'd estimate that those on board would experience the trip to be about 1.5 years
To those on Earth it would appear to have taken about 5 years.
I think you have gained a light year or two there.

korjik
2010-May-26, 03:14 PM
Thanks for working the figures, Wayne. This bit differs from my understanding, though... which is: the clocks on board would appear to those on board to be running normally.

They would. The trip would seem shorter tho. At sufficient dilation, the apparent distance would be very small

danscope
2010-May-26, 06:12 PM
There is no free lunch. And there will never be any engineering scheme that will allow you to take enough fuel to accelerate you at one g for a
year abd later descelerate you at 1 g for a year. That's a whopping amount of fuel. Diminishing returns,people.
Real physics and numbers get in the way real fast. Sorry.

korjik
2010-May-26, 06:18 PM
There is no free lunch. And there will never be any engineering scheme that will allow you to take enough fuel to accelerate you at one g for a
year abd later descelerate you at 1 g for a year. That's a whopping amount of fuel. Diminishing returns,people.
Real physics and numbers get in the way real fast. Sorry.

I dont think anyone here has even brought up engineering.

Hornblower
2010-May-26, 07:22 PM
In a thought experiment, we could solve the fuel problem and have the spacecraft go out a thousand lightyears and back, and have the crew live to tell about it, if my understanding of time dilation on board is correct. Back on Earth, our human species might have evolved beyond recognition. The crew might end up in a zoo.

Don't take this as gospel. I am only speculating about what happens on Planet Earth in this adventure.

WayneFrancis
2010-May-27, 12:23 AM
They would. The trip would seem shorter tho. At sufficient dilation, the apparent distance would be very small

Thanks Korjik, Yes I didn't explain that well. During most of the trip, to those aboard, the distance would appear to be ~4 light years. But when they approach c it would appear to them that Alpha Centauri is rushing towards them. When they slow down the opposite would seem to happen.

WayneFrancis
2010-May-27, 12:24 AM
(bolding is mine)

I think you have gained a light year or two there.

That should have read "1ly out of the 4..." thanks....

WayneFrancis
2010-May-27, 12:34 AM
There is no free lunch. And there will never be any engineering scheme that will allow you to take enough fuel to accelerate you at one g for a
year abd later descelerate you at 1 g for a year. That's a whopping amount of fuel. Diminishing returns,people.
Real physics and numbers get in the way real fast. Sorry.

Hence my last line of "This is ignoring the fuel issues,..."

WayneFrancis
2010-May-27, 12:53 AM
In a thought experiment, we could solve the fuel problem and have the spacecraft go out a thousand lightyears and back, and have the crew live to tell about it, if my understanding of time dilation on board is correct. Back on Earth, our human species might have evolved beyond recognition. The crew might end up in a zoo.

Don't take this as gospel. I am only speculating about what happens on Planet Earth in this adventure.

Actually humans would have evolved bugger all for a trip that was 1000ly if you could accelerate and decelerate at 10m/s. Essentially if, from an external reference frame, the ship keeps an acceleration rate of 10m/s up to just under c, again ignoring the fuel requirement, then almost all trip will be a matter of under 2 years + (original distance * time dilation). To those on Earth the trip would end up being the distance + a little under 2 years. So a 1000ly trip would only take the ship ~1002 years. The people on the ship would be 2 years older and 50 generations would have passed on Earth. Not enough time for Evolution to do much about anything.

CaptainToonces
2010-May-27, 04:54 AM
Actually humans would have evolved bugger all for a trip that was 1000ly if you could accelerate and decelerate at 10m/s. Essentially if, from an external reference frame, the ship keeps an acceleration rate of 10m/s up to just under c, again ignoring the fuel requirement, then almost all trip will be a matter of under 2 years + (original distance * time dilation). To those on Earth the trip would end up being the distance + a little under 2 years. So a 1000ly trip would only take the ship ~1002 years. The people on the ship would be 2 years older and 50 generations would have passed on Earth. Not enough time for Evolution to do much about anything.

1,000 years. Not enough time for traditional biological evolution, but as we are witnessing, once a civilization reaches a certain level of advancement the changes come rather rapidly...

And I assume when you say 10 m/s you mean 10 m/sē which would be an ideal acceleration rate since it could also be used to simulate Earth gravity for the colonists.

WayneFrancis
2010-May-27, 06:23 AM
1,000 years. Not enough time for traditional biological evolution, but as we are witnessing, once a civilization reaches a certain level of advancement the changes come rather rapidly...

And I assume when you say 10 m/s you mean 10 m/sē which would be an ideal acceleration rate since it could also be used to simulate Earth gravity for the colonists.

Yea I guess but we'd probably still be genetically compatible but most would probably have some hi-tech prosthetics .

yes, I meant 10m/s2 thanks

wolf1728
2010-May-28, 04:10 AM
And if anyone wanted to calculate the time dilation or other relativistic effects, go to this calculator:
http://www.1728.org/reltivty.htm