Yes, Pete actually said they were receding from each other and never mentioned 'centre of mass' - only their relative velocity. I'm waiting to mark Pete's homework, at which point I will reveal my answer (or will have to revise it accordingly).
Don't you agree with the simple equation I supplied for the calculation?
I did read that link. Amazing. I mean the parts I can guess at.
OTOH, a youtube tutorial vid I just watched calculated how much time would have passed here on earth on my arrival back from accelerating away at G for ten years, decelerating for ten, then on return the same procedural way, so a 40 year journey. Wow
Let one of them have velocity v1=v, and the other velocity v2=-v.
The "usual" way to calculate their relative velocity is simply v relative = v1 - v2 = 2v
However, according to the theory of relativity:
v relative = [v1 - v2]/[1 - (v1*v2/c2)] = 2v/[1 + v2/c2] where c2 is the speed of light squared.
Now, apply that formula to your two objects and see what you get!
I tried to follow that, but it is dimensionally inaccurate IMO.
You can't put v2/c^2 and expect it to make sense.
I have been working with E^2 = p^2 x c^2 + m^2 x c^4 tonight.
It's p that is giving me the problem. Because it involves the Lorentz factor.
To be clear, you are making no headway tonight!Clearly no headway being made tonight.
Attached is the physics for the relative velocity of approach.
The only difference compared to the relative velocity of recession is that the + signs in the Lorentz Velocity Transformation become - signs.
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That may be because it is actually v^2/c^2, as I clarified in the post following the one which you quoted.You can't put v2/c^2 and expect it to make sense.
If you get a 'wow' out of that, then you should enjoy 'Tau Zero' by Poul Anderson.
When a spaceship's Bussard ramjet engines run out of control, it continues to accelerate until it attains light speed. For the occupants on board subjective time slows down, but the universe outside ages rapidly - ultimately collapsing in a Big Crunch and being re-born in a new Big Bang.
The Cosmology regarding the ultimate fate of our universe may be out of date, but the book's a darned good read in the relativistic sense.
Tau Zero - Wikipedia
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Haven't come across this one, but I've read many of his novels. He's always been a good read.
The really wowee factor is not the 56000 year thing but say I want to come back to the future just 50 years later. How long would I have to travel then? A couple of weeks??
Now that's got to be doable, no?
There's one way to live for 150 years
Correction: I should have said "it continues to accelerate until it approaches light speed."
Anderson's Tau Factor is the square root term in the above equation. When the speed of the spacecraft (V) approaches the speed of light (c) then the tau factor approaches zero.
As the tau factor approaches zero, the time (t') which elapses on the spacecraft will become smaller and smaller compared to the time (t) which elapses in the universe.
Anderson's Tau Factor is the square root term in the above equation. When the speed of the spacecraft (V) approaches the speed of light (c) then the tau factor approaches zero.
As the tau factor approaches zero, the time (t') which elapses on the spacecraft will become smaller and smaller compared to the time (t) which elapses in the universe.
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Time dilation is a fruitful field for sci-fi writers.
And yes, I'm a big Larry Niven fan.
I'll leave it up to you to experiment with this calculator: Time Dilation Calculator
If you scroll down, you can enter the percentage of the speed of light at which you are going to travel, and the distance you wish to travel in light years.
The calculator will then work out the journey times in years as viewed from the Earth and from the spaceship.
Sorry, I don't see the significance of your question in relation to the topic of time dilation that we were just discussing.
The time you would take to get to where you want to go would depend on the distance in light years you want to travel. That could take years, tens of years or hundreds of years! You would have all that time to accelerate to your near-light speed. We're not talking about simple non-relativistic jaunts to the Moon and back! Maybe you should take some time to use the calculator to which I linked.
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Galu, you are editing your posts so rapidly, I am losing track....
You mentioned the Lorentz velocity transform at some point.
Discopete was talking about two particles at 2/3 lightspeed relative to some central observer.
So v relative = 4/3 divided by 1 + 4/9
Which is 12/9 divided by 9/9 + 4/9 if I follow.
Which is 12/13.
Is that the answer?
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