Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Titanscape on 07/02/2008 02:59:12

If a laser is aimed at the earth from behind a satellite, blue light, and it is traveling away at 90% light speed, what spectrum is the light when it reaches the earth?

It depends, is it the laser that is moving away from the earth or is it the blue light? If the former then the light will be redshifted using the formula for the Doppler effect, its wavelength can be calculated. On the other hand if it is the light that is moving away at 90% the speed of c, then the colour will remain the same.

If a laser is aimed at the earth from behind a satellite, blue light, and it is traveling away at 90% light speed, what spectrum is the light when it reaches the earth?
λ' = λSqrt[(1+β)/(1β)] = λSqrt[(1+0.9)/(10.9)] ≈ λ*4.36
Blue light has λ > 400 nm then the wavelenght of light arriving on earth is > 400*4.36 ≈ > 1744 nm which is in the infrared.

If a laser is aimed at the earth from behind a satellite, blue light, and it is traveling away at 90% light speed, what spectrum is the light when it reaches the earth?
λ' = λSqrt[(1+β)/(1β)] = λSqrt[(1+0.9)/(10.9)] ≈ λ*4.36
Blue light has λ > 400 nm then the wavelenght of light arriving on earth is > 400*4.36 ≈ > 1744 nm which is in the infrared.
This boy knows his stuff!

On the other hand if it is the light that is moving away at 90% the speed of c, then the colour will remain the same.
Do you mean "the light SOURCE"?
The 'light' would be traveling at c, surely.
The actual thought experiment is not very clear, here.

Yes, the light source is on the satellite, which is traveling away from the earth at 90% light speed. It emits blue light, from a laser. When the light reaches the earth, you have formulated it would be red shifted to infra red?
Also how fast would the photons be traveling in relation to the earth?

Yes, the light source is on the satellite, which is traveling away from the earth at 90% light speed. It emits blue light, from a laser. When the light reaches the earth, you have formulated it would be red shifted to infra red?
Also how fast would the photons be traveling in relation to the earth?
1. Yes, it would be redshifted into infrared; infrared has λ > 800 nm so 1744 nm is certainly infrared (longer wavelenghts are "terawaves", then "microwaves", "radiowaves ecc.)
2. c

If a laser is aimed at the earth from behind a satellite, blue light, and it is traveling away at 90% light speed, what spectrum is the light when it reaches the earth?
λ' = λSqrt[(1+β)/(1β)] = λSqrt[(1+0.9)/(10.9)] ≈ λ*4.36
Blue light has λ > 400 nm then the wavelenght of light arriving on earth is > 400*4.36 ≈ > 1744 nm which is in the infrared.
This boy knows his stuff!
Thank you.

I get lost with β λ etc. They're all Greek to me [:D]

the satellite, which is traveling away from the earth at 90% light speed
I was also confused that you called it a satellite (an object in orbit). At that speed it would be well past its escape velocity!

I get lost with β λ etc. They're all Greek to me [:D]
β = v/c where v is the light source speed with respect to the observer;
λ = wavelenght of light when the light source is stationary with respect to the observer;
λ' = wavelenght of light when the light source is moving away of the observer with speed v;
nm = nanometres = 10^{9} metres (about 10 atomic diametres). Visible spectrum ranges from about 400 nm (violet) to about 800 nm (dark red).

Thank you

Sorry, satellite came to mind, thinking of the look of them, I should have typed, voyager. Or craft.
Interesting replies, thanks.