Red/Blue shifting question

[Louella]

Okay, so, light coming from an object that is moving, will vary in colour, depending if the object is moving away from, or towards the observer.

So a star moving away from Earth will appear red, a star moving towards Earth will be blue.

Here are two ships, A and B, and also two observers, 1 and 2.

A and B are moving in the same direction, at the same speed.

Top situation, A illuminates B with a yellow laser. Is it still yellow to B ? but red to observer 2 ?

Bottom situation, B illuminates A with a yellow laser, Is it still yellow to A ? but blue to observer 1 ?

Does it change if A and B are now moving at 0.1c ?

If the ships are moving fast enough, and A suddenly slows down, then uses its yellow laser to warn B of something, does that risk B getting hit by X-Rays ?

[N_las]

Yes, in the top situation, B will see yellow light, while 2 will see red light.

And in the bottom situation, A will see yellow light, but 1 will see blue light.

The situation doesn't change if A and B are moving at 0.1c

EDIT:

Motion is relative, so if you want to know what happens only between ship A and B, you can always consider both as stationary (If they move in the same direction with the same speed).

And yes, if A stops suddenly and warns B via its yellow laser, B can get a small dose of X-Rays from that, if he is moving fast enough (in relation to A)

Edited February 2, 2015 by N_las

[Louella]

Thanks.

Was trying to wrap my brain around some stuff with spaceships with lasers on them. Things like simple tactics and manoeuvres.

if A is trying to escape B, then if A suddenly slows down, a yellow laser aimed at B would then be effectively a blue laser, BUT it means that yellow lasers from B aimed at A, would also be effectively blue, right ?

[N_las]

Yes, exactly. But if the involved relative velocities are so high, that you can blueshift a yellow laser into something dangerous, the surrounding starlight and the interstellar medium will be a much bigger problem than your laser.

[Mr Shifty]

If your speed is much less than c, the light will be subject to classical Doppler shifting, with the wavelength shift z=ÃŽâ€ÃŽÂ»/λ₀ approximately equal to the ratio β=v/c. When you're going nearer to c, you have to deal with the time dilation and aberration effects due to relativity. In a purely radial direction (directly toward or away from the observer), aberration isn't a consideration, and you have z=[(1+β)/(1-β)]-1. For 0.1c, z=0.22 or more than twice as much wavelength shift as predicted by classical mechanics.

EDIT: You'd have to be going about 0.97c to shift yellow light up to X-rays. Keep in mind that if you could decelerate at 1000g's, it would take about 8 hours to decelerate enough to open up this large a speed gap between the vessels. Hopefully your vessels are more than 8 light-hours apart. (Note this is farther than Pluto ever is from the sun.)

Edited February 2, 2015 by Mr Shifty