Is My Understanding of Basic Relativity Concepts Correct?

[fasterthanjoao]

Right.

Some simple questions, I want to make sure I'm not making stupid mistakes before moving on. I have the questions and my answers, If you tell me that I got them incorrect, i'll run through my working or something (if there could be any..).

1/ How fast must you travel towards a red light (650nm) for it to appear green (525nm)?

Can this just be treated as length contraction?

My Answer: 1.78x10^8m/s.

2/ How great must the relative speed of two observers be for their time-interval measurements to differ by 1%?

My answer: 4.2x10^7m/s.

3/ A distant galaxy is moving away from the Earth such that each wavelength is shifted by a factor of two; what is the speed of the galaxy relative to us?

can this just be treated via length contracion?

4/ A particle moves north at 0.8c, what is this particles speed as measured by an observed traveling south relative to the Earth at 0.5c?

5/Two spaceships of proper length 100m are traveling towards each other, each at a speed of 0.8c, measured on earth.
(i) how long is each ship as measured by the terrestial observer?
(ii)how long is earch ship when measured from the rest-frame of the other?


Thats all the questions I have just now. My idea is that, since I haven't done relativity for ages I should try to brush up on this simple stuff before my new course starts. tomorrow I'm hitting the library for a textbook, sigh.

 

[Doc Al]

1/ How fast must you travel towards a red light (650nm) for it to appear green (525nm)?

Can this just be treated as length contraction?

No. This, and #3, are examples of the relativistic Doppler effect.

 

[fasterthanjoao]

relativistic Doppler effect.

I'm remembering something about the redshift parameter (z) being the change in wavelength over the 'rest'-wavelength?

I think I've followed on from that:

v/c = ((z+1)^2 - 1)/((z+1)^2 + 1)?

is that what I'm looking for? thanks for the response by the way.

(+sorry for the lack of `tex, I'm on the verge of not thinking straight enough to use it.)

 

[Doc Al]

Look here for a discussion of the relativistic Doppler effect: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/reldop2.html