- #1
Buckethead
Gold Member
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Imagine a mother ship traveling away from Earth at .5c and a shuttle takes off from the mother ship in the same direction of travel at .5c relative to the mother ship. The shuttle fires a blue laser (400nm) to a transparent screen mounted on top of the mother ship as it is traveling away. Due to the Doppler shift of
[itex]1-v/c[/itex] = .5 for v=.5c
the wavelength approximately doubles at this speed causing the blue light to light the screen with a deep red color (around 800nm) . A telescope on Earth views the screen and since the screen is moving away from the Earth at .5c it gets red shifted again to an infrared color of around 1600nm. Between the shuttle and the mother ship the speed is fairly non-relativistic (.5c) as is the speed between the ship and the Earth so I'm just using the simpler form of the Doppler shift to calculate the wavelengths.
My questions are:
1) If the above assumptions about calculating the total Doppler shift is wrong, why?
2) What is the apparent speed of the shuttle as seen from Earth and how do I calculate it?
3) If I use just the apparent speed of the shuttle as seen from Earth in the Doppler formula will the answer differ from my calculation above (assuming my assumptions were correct of course).
Thanks
[itex]1-v/c[/itex] = .5 for v=.5c
the wavelength approximately doubles at this speed causing the blue light to light the screen with a deep red color (around 800nm) . A telescope on Earth views the screen and since the screen is moving away from the Earth at .5c it gets red shifted again to an infrared color of around 1600nm. Between the shuttle and the mother ship the speed is fairly non-relativistic (.5c) as is the speed between the ship and the Earth so I'm just using the simpler form of the Doppler shift to calculate the wavelengths.
My questions are:
1) If the above assumptions about calculating the total Doppler shift is wrong, why?
2) What is the apparent speed of the shuttle as seen from Earth and how do I calculate it?
3) If I use just the apparent speed of the shuttle as seen from Earth in the Doppler formula will the answer differ from my calculation above (assuming my assumptions were correct of course).
Thanks