# I Relativistic doppler shifted blackbody color?

1. Sep 3, 2016

### Artlav

I'm trying to render the sky as it would appear from a starship moving at some large part of the speed of light.
Geometry was straightforward, but colors are the problem.

How would the doppler effect change the color of a star?
The expectation is that the stars behind are red and the ones ahead are blue.

At first i tried to apply doppler shift ( gamma*(1-(v/c)*cos_ang) ) per-channel to the RGB value of the star color, with rather colorful but odd results of violet stars ahead and red-to-black ones behind.

Then i found out that the black body radiation is doppler shifted to the same extent as if it's temperature was altered by the same doppler factor.
So i tried to use the stars' temperatures as the input, since converting temperature to RGB is much easier than shifting arbitrary RGB.

This, however, produced a rather bland view of slightly red stars behind and slightly blue stars ahead.
Further, applying the intensity correction (doppler factor to the power of 4) made the stars fade behind, and be bright-white ahead, with almost no visible color change.

So, the question is - which of these are more correct?

The last one is the blandest one, but it seems to be the most correct as far as i can tell.

The first one is the most colorful, but it assumes that the stars emit nothing but visible light, while you'd expect that the invisible light would be shifted into our visibility range, and blackbody temperture accounts for that.

Even better, are there any reference images of correctly rendered sky at relativistic velocities? The Google finds many, but most are pop science kind of stuff that doesn't account for most of the effects.

2. Sep 3, 2016

3. Sep 3, 2016

### Artlav

I take the frequencies of red, green and blue, doppler shift them, convert each result back to RGB, then mix in the same proportion than in the original.
This gives odd results for random colors, but works ok for near-white ones the stars tend to have.
If you know of a better way, i'd like to know it.

4. Sep 3, 2016

### pervect

Staff Emeritus
If you can, get a hold of "In search of the ’’starbow’’: The appearance of the starfield from a relativistic spaceship". http://scitation.aip.org/content/aapt/journal/ajp/47/4/10.1119/1.11834

At one time it wasn't paywalled, but nowadays you'll probably need to go to a library - I think most libraries will still be able to obtain a copy for a nominal charge, and a good college library might even have the paper and way to print it for a nominal fee per page.

There were some discussions of the paper on PF at one time, as well.

5. Sep 4, 2016

### Artlav

Starbow, hm?
Oddly enough, that's exactly the kind of an effect i got at first, and felt that it's pretty, but unrealistic.

Got the article, it's pretty much exactly what i was looking for.
Turns out i got most of the things right on the second try, except for the intensity factor - it's not there when using temperatures, and human eye response stuff.

Thank you for pointing it to me.

Here are some images i got as a result.
I'll probably leave the starbow version as an option - it's a game, so pretty-but-unrealistic is allowed.

At 0.5c, looking left, with the galaxy behind for emphasis.
Starbow version: http://i.imgur.com/4PWVWsB.jpg
Real version: http://i.imgur.com/tuxgswL.jpg
Standing still reference: http://i.imgur.com/BPitOSM.jpg

At 0.9c, looking mostly forwards.
Starbow version: http://i.imgur.com/XA6w8d2.jpg
Real version: http://i.imgur.com/o82hVZA.jpg
Standing still reference: http://i.imgur.com/IQxvbMO.jpg

6. Sep 4, 2016

### pervect

Staff Emeritus
I like the images. I personally find the artistic ones more appealing than the accurate ones, for whatever it's worth. But the abstract of the paper did mention that they didn't find a starbow either.

The earliest reference I know of for the term starbow was the noevella "The Gold at the Starbow's End" by Fredrick Pohl.

I was looking for the old PF discussion (I didn't find it), but I did find a question on another site: http://physics.stackexchange.com/qu...tic-beaming-which-power-of-the-doppler-factor

Perhaps that was you?

7. Sep 4, 2016

### Artlav

Real physics, ye cruel thing, you took away my starbow?
( Going perpendicular to the galaxy at 0.8c )

No, certainly not. I only got the idea to add relativity a few week ago.

8. Sep 5, 2016

### m4r35n357

There is a seemingly little-known resource that I have just rediscovered a link to. Anyone interested in getting into visualizing SR should take a look. It is from the author of Real Time Relativity.