Doppler Shift Anyone?
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Guest
Doppler Shift Anyone?
I was just reading some of the comments on what should be added, and I was surprised that no one mentioned Doppler Shift of the visual light. This would be a cool effect, especially when you transverse the galaxy. Keep up the excellent work.
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diogo
Re: Doppler Shift
I said that in the old Bboard we had, not only about Doppler Shift, but also the relativistic distortion of the images when travelling.
I?d be willing to code it and present the code in the forum if someone could chew me out the calculations for the doppler shift and relativistic distoprtion alterations when travelling at high speeds.
I?d be willing to code it and present the code in the forum if someone could chew me out the calculations for the doppler shift and relativistic distoprtion alterations when travelling at high speeds.
Re: Doppler Shift
diogo wrote:I said that in the old Bboard we had, not only about Doppler Shift, but also the relativistic distortion of the images when travelling.
I?d be willing to code it and present the code in the forum if someone could chew me out the calculations for the doppler shift and relativistic distoprtion alterations when travelling at high speeds.
there's a linux app that does relativistic distortions of views based on speed of viewer, maybe you could rip some useful code snippets off it.. I *believe* its called lightspeed or the like, If you want I can send you the sources (got it on my linux CD)
bye,
[L]
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diogo
Light beyond the speed of light.
I have an issue regarding the classical formula of the doppler effect.
This formula works fine for speeds up to that of the light. However, in Celestia, we can go way beyond the speed of light. How would the light be seen at these speeds, if at all?
The doppler shift formula results in an imaginary lambda, with a real component which is fixed on -1, and an imaginary component which is lower as the speed increases. What is an imaginary lambda? How would the imaginary component be interpreted?
Also, for high speeds (even below the speed of light), the light we see from the stars would soon fall out of our visible spectrum. However, stars do emmit EM waves on nearly all spectrum frequencies. When increasing speed, EM waves we usually not see would become visible (eventually, we would even see radio waves). Anyone knows where can I find information regarding the EM emission of a star throughout the spectrum according to the stellar type?
Thanks.
Diogo.
This formula works fine for speeds up to that of the light. However, in Celestia, we can go way beyond the speed of light. How would the light be seen at these speeds, if at all?
The doppler shift formula results in an imaginary lambda, with a real component which is fixed on -1, and an imaginary component which is lower as the speed increases. What is an imaginary lambda? How would the imaginary component be interpreted?
Also, for high speeds (even below the speed of light), the light we see from the stars would soon fall out of our visible spectrum. However, stars do emmit EM waves on nearly all spectrum frequencies. When increasing speed, EM waves we usually not see would become visible (eventually, we would even see radio waves). Anyone knows where can I find information regarding the EM emission of a star throughout the spectrum according to the stellar type?
Thanks.
Diogo.
Doppler Shift calculations
The classical doppler equation needs correction from Newtonian to relativistic frameworks. Try substituting
v' = v / sqr(1 + v^2/c^2)
to get a physically reasonable value to input to the doppler equation.
Stars emit light approximately as classical black bodies (ignoring absorption effects, especially in low temperature stars), so you can use Planck's Law to calculate the radiation emitted. (If not handy, you can use the reference at http://scienceworld.wolfram.com/physics/PlanckLaw.html - equation (8) relates wavelength and temperature to emission)
Unfortunately, as indicated here (http://image.gsfc.nasa.gov/poetry/ask/a11115.html) finding the temperature of a star is not trivial, even given the star's spectral type and luminosity class.
Just to complicate things a bit further, after you've gotten all that done, you'll have a spectral curve which you need to interpret as a color to be displayed.
Anyway, hopefully some of that is useful and not discouraging. Good luck!
v' = v / sqr(1 + v^2/c^2)
to get a physically reasonable value to input to the doppler equation.
Stars emit light approximately as classical black bodies (ignoring absorption effects, especially in low temperature stars), so you can use Planck's Law to calculate the radiation emitted. (If not handy, you can use the reference at http://scienceworld.wolfram.com/physics/PlanckLaw.html - equation (8) relates wavelength and temperature to emission)
Unfortunately, as indicated here (http://image.gsfc.nasa.gov/poetry/ask/a11115.html) finding the temperature of a star is not trivial, even given the star's spectral type and luminosity class.
Just to complicate things a bit further, after you've gotten all that done, you'll have a spectral curve which you need to interpret as a color to be displayed.
Anyway, hopefully some of that is useful and not discouraging. Good luck!
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Guest
Aberration and time dilation
In addition to everything Kotetsu said, to really do it right, you'll want to display the relativistic distortion of images. This is commonly known as the aberration of starlight:
http://www.mathpages.com/rr/s2-05/2-05.htm
(Be careful: the first page on this that Google pops up seems to be the work of a crackpot. The one I listed looks good.)
A common mistake made by science fiction writers and popularizers is to think that the universe will just look Lorentz-contracted in the direction of motion. It's actually more complicated than that because you're using finite-speed light rays to see things. The aberration formula in the above source takes that into account.
As for the issue of what to do for speeds greater than c: I wouldn't expect relativistic formulae to give sensible results in this domain, since it doesn't make a lot of sense in relativity to have an observer going faster than light.
So how to avoid spoiling the fun of accurate-relativity mode? I'd say that to really do it right, you want to take time dilation into account. By your own clock, you can in principle go at just under the speed of light and travel anywhere in the galaxy in a short time. It's just that when you come home, a much longer time might have gone by.
This could be accomplished in Celestia by messing with the speed and time/date calculations. The key thing is a factor called gamma:
gamma = 1/sqrt(1 - v^2/c^2)
This is very close to 1 for low speeds, but diverges to infinity as the speed approaches c.
Real-world time (taking into account the usual multipliers) should correspond to a traveler's proper time. But the time/date indicator should show Earth standard time, which would pass at a rate equal to proper time multiplied by gamma.
(What you should see if you look at, say, an orbiting binary star while you're in motion is more complicated because there are also varying light-speed delays. Basically, the apparent rate should vary like the Doppler shift. But that's another story.)
Now, what about speed? The speed that goes into the aberration and Doppler shift formulae, v, is the traveler's speed as measured in an external frame. It's also the speed of the universe as measured in the traveler's frame.
However, it is not the ratio of *external* distance traveled to *proper* time, and the latter is what governs the rate at which Celestia should zip the user around its universe. Call this quantity w. Then
w = v * gamma = v/sqrt(1-v^2/c^2)
v = w/sqrt(1 + w^2/c^2)
As w diverges to infinity, v approaches c.
So in the scenario I'm imagining, if you set "relativity mode" and then travel to Alpha Centauri in 4.3 seconds real time, it's w that is equal to one light year per second. v is some number just a hair under c. We move the user around according to w (and presumably the acceleration controls reflect this), but the speed indicator gives v, aberration and Doppler shift are calculated using v, and the time indicator moves along at a rate scaled by a factor of gamma.
http://www.mathpages.com/rr/s2-05/2-05.htm
(Be careful: the first page on this that Google pops up seems to be the work of a crackpot. The one I listed looks good.)
A common mistake made by science fiction writers and popularizers is to think that the universe will just look Lorentz-contracted in the direction of motion. It's actually more complicated than that because you're using finite-speed light rays to see things. The aberration formula in the above source takes that into account.
As for the issue of what to do for speeds greater than c: I wouldn't expect relativistic formulae to give sensible results in this domain, since it doesn't make a lot of sense in relativity to have an observer going faster than light.
So how to avoid spoiling the fun of accurate-relativity mode? I'd say that to really do it right, you want to take time dilation into account. By your own clock, you can in principle go at just under the speed of light and travel anywhere in the galaxy in a short time. It's just that when you come home, a much longer time might have gone by.
This could be accomplished in Celestia by messing with the speed and time/date calculations. The key thing is a factor called gamma:
gamma = 1/sqrt(1 - v^2/c^2)
This is very close to 1 for low speeds, but diverges to infinity as the speed approaches c.
Real-world time (taking into account the usual multipliers) should correspond to a traveler's proper time. But the time/date indicator should show Earth standard time, which would pass at a rate equal to proper time multiplied by gamma.
(What you should see if you look at, say, an orbiting binary star while you're in motion is more complicated because there are also varying light-speed delays. Basically, the apparent rate should vary like the Doppler shift. But that's another story.)
Now, what about speed? The speed that goes into the aberration and Doppler shift formulae, v, is the traveler's speed as measured in an external frame. It's also the speed of the universe as measured in the traveler's frame.
However, it is not the ratio of *external* distance traveled to *proper* time, and the latter is what governs the rate at which Celestia should zip the user around its universe. Call this quantity w. Then
w = v * gamma = v/sqrt(1-v^2/c^2)
v = w/sqrt(1 + w^2/c^2)
As w diverges to infinity, v approaches c.
So in the scenario I'm imagining, if you set "relativity mode" and then travel to Alpha Centauri in 4.3 seconds real time, it's w that is equal to one light year per second. v is some number just a hair under c. We move the user around according to w (and presumably the acceleration controls reflect this), but the speed indicator gives v, aberration and Doppler shift are calculated using v, and the time indicator moves along at a rate scaled by a factor of gamma.