# Planet illuminated by blue-shifted relic radiation

Are there realistic circumstances that a planet would be accelerated (either artificially or naturally) to the speed at which relic radiation becomes so blue-shifted that the planet is illuminated so as if it were in a habitable zone?

I also wonder the following:

• Will such planet be in constant danger of impact by small bodies who at these speeds can be a danger to the whole planet's population?

• Will not distant stars and galaxies become luminous enough so that their ionizing radiation to become dangerous to the planet's life?

• Will not such planet quickly slow down due to cosmic medium?

• What will happen if such planet impacts an intergalactic gas cloud or enters a galaxy?

• What do you mean by relic radiation? The Cosmic Microwave Background? – Tim B Nov 5 '14 at 18:17
• @Tim B yes, of course – Anixx Nov 5 '14 at 18:17
• Is this planet orbiting a star? – HDE 226868 Nov 5 '14 at 19:42
• @HDE 226868 no. – Anixx Nov 5 '14 at 20:44
• @Anixx Are my tag edits okay? – HDE 226868 Nov 5 '14 at 22:48

I wouldn't know what would accelerate the planet this much without destroying it as a side-effect. Not to speak of any life on it. But I can say that if it manages to, I expect some serious side-effects.

For the record: high-relativistic speeds are pretty crazy. If I neglected or misinterpreted one of their effects, well, this is just a best shot without spending too much time, since nobody else seems to give this a serious try.

## Illuminated habitat at solar spectrum

When moving in the vastness of space, the CMB (cosmic microwave background) actually makes up the majority of incoming radiation. This site has a nice plot and some explanation on that. So, at least in terms of energy, starlight won't be the major factor there.

Now, as to a habitat, I think this will go bad if I understand black-body radiation correctly. I will ignore incoming particles for now and tackle a basic problem of the question: both the CMB and our sun are following Planck's black-body radiation. This means that, if we want to get the spectrum that the sun emits, we have to use a black-body source corresponding to the same temperature, or else the shorter wavelengths' intensities will drop significantly, giving us less visible light, and more infrared and beyond. Red- or blue-shifting black body radiation doesn't change its properties, only its temperature. So, to get the kind of light we have, a large portion of the forward-facing sky (before aberration) would radiate with the intensity of the sun!

The sun has a solid angle of just $7 \cdot 10^{-5}$ as seen from Earth. If the equivalent of something on the scale of a quarter of the sky is a black body at solar temperature, this giant sun would burn the planet. This rules out having light as on Earth, we'll have to go to longer wavelengths.

To make the power of our incoming CMB equal to that of the sun on Earth, we can equate the incoming intensity times solid angle of both of them. (Again, I am assuming aberration just compresses the light into one direction, and work with the undistorted sky for now.) This way, we can calculate the black-body temperature the CMB would have to replace the sun in heat output. Using the Stefan-Boltzmann law for the scaling of power with black-body temperature, we get $T^4 \pi = T_\odot^4 A_\odot$, where $T$ is the desired temperature, $T_\odot$ the sun's temperature, $A_\odot$ solid angle, and the $\pi$ is the equivalent of a quarter of the sky.

(The value for the corresponding effectively illuminated sky is just a rough guess, but should be good enough. See the comment by verlaner. Note that the visible image of the sky may be heavily distorted due to the aberration of light, bundling the incoming light into the forward direction.)

With $T_\odot = 5800\text{K}$ and the solid angle from the previous paragraph, this gives $T = 398\text{K}$.

That's merely about $125^{\circ}\text{C}$. This black-body temperature is far too low to give the desired illumination, but already heats the planet at the full power the sun would yield.

## Velocities

I have the feeling that the idea to blue shift the CMB into the sun's spectrum is not healthy in general. Let's say the CMB magically doesn't harm us, but we need it to have the solar spectrum, to see just how much velocity this is.

The CMB has a peak wavelength of about $1\text{mm}$. The sun is at $0.5\text{µm}$. So you want to get a factor of about $2000$ in frequency.

The relativistic Doppler effect gives a frequency ratio of $\sqrt\frac{1 + \beta}{1 - \beta}$, where $\beta = \frac vc$. This yields something like $v \approx 0.9999995c$.

Let's calculate the kinetic energy per mass at this velocity.

$$\gamma = \sqrt{\frac 1{1 - \beta^2}} = 1000$$

$$E_\text{kin} = mc^2 (\gamma - 1) \approx 9.0 \cdot 10^{19} \frac{\text J}{\text{kg}} = 90 \frac{\text{EJ}}{\text{kg}}$$

So, severe time-dilation aside, obstacles are bad. One gram of infalling mass would have a yield of $90\text{PJ}$, which is roughly 1500 Hiroshima bombs. I guess it's safe to say that dust and meteorites will be a much bigger threat for this planet. Also, if the planet is quickly slowed down due to collisions, nobody would want to live on it. ;)

Assuming it is as large as Earth, the planet is sweeping up volume at $r^2\pi c \approx 3.8 \cdot 10^{22} \frac{m^3}{\text{s}}$. If it passes through a molecular cloud with $10^7 \frac{\text{hydrogen molecules}}{\text{m}^3}$, this yields about $10^{23} \text{W}$. For comparison, our sun inputs about $10^{17}\text{W}$. This doesn't sound healthy.

However, outer space -- outside of galaxies -- has densities below one atom per cubic meter. This strips the six orders of magnitude we need to get it below solar output. I admit I don't have any idea whether this kind of bombardment might deal damage to atmosphere or habitat directly, even if its absolute power isn't high.

Not that any of that is relevant compared to the black-body radiation argument above. All in all, my estimate is that this will not end well, and probably quickly too.

No warranty on correctness. Please comment or edit if you find a mistake.

• Why u take half of the sky? It seems the maximum power will come from the middle. – Anixx Nov 5 '14 at 23:47
• @Anixx you're probably right that that's not exact. Something tells me that it should be $\pi$, the unit cycle area, equivalent to only a quarter of the sky. I'll think about it for a moment. But that would not raise the temperature enough to change the overall result. Frankly, I might not be qualified for doing more than a rough guess; I don't know relativity that well. Time on this planet is passing veeeeeeery slowly and I'm having a hard time imagining photons that come in sideways as they go into the new reference frame. – Vandroiy Nov 6 '14 at 0:09
• @Anixx I think the whole sky is distorted so heavily via aberration that what an outside observer would see coming from the sides would seem to be coming from the front. I'm stopping with the edits for now and leaving some notes. Heck, can I even do the calculations in the second part like this, with all the distortions going on? I don't know. Might have been better to scrap the answer. Maybe I'll get to ask someone who knows more about this. – Vandroiy Nov 6 '14 at 12:51
• +1, definitely seems qualitatively correct. It's worth noting that the blueshift at an angle away from the forward velocity would go with the cosine of the angle $1+z = \gamma (1+v \cos{\theta}/c)$. Using a quarter of the sky for the effective area probably isn't too far off. Also, Wikipedia gives the CMB peak at $1 \textrm{mm}$? – Robbie Rosati Nov 7 '14 at 4:40
• @verlaner: Thanks! Argh... Yea, CMB wavelength is off by a factor two. I'll see that I recalculate. The number was from around the web, where people probably looked at a certain strange plot. See "A Cautionary Word" on link – Vandroiy Nov 7 '14 at 15:09

I'm not going to calculate at what speed the planet would have to move in order for this effect to happen. My guess is that it would have to go pretty darn fast for there to be a substantial difference, but I don't have much to back that up, other than (sometimes faulty) intuition.

Could a planet be accelerated to some incredible speed? Absolutely. Just put it near the supermassive black hole, Sagittarius A*, in the center of our galaxy. I have to add in a picture (from Wikipedia) to illustrate just how much stars are effected near it:
Image courtesy of Wikipedia user Cmglee under the Creative Commons Attribution-Share Alike 3.0 Unported license.

It is thought that intergalactic stars are chucked out of their home galaxies by interactions with a supermassive black hole. Here's a graphic (from Wikipedia) that illustrates this:
Image in the public domain.

I apologize if the graphic take a while to load; it took about 30 seconds on my computer.

These stars are known as hypervelocity stars. They can travel at speeds of about 1,000 km/s - not nearly enough (if Vandroiy's calculations are correct) for this kind of speed. However, I wouldn't me surprised if a galaxy with multiple SMBs (perhaps the result of a few galaxy mergers) could get stars moving a lot faster than that. If this can happen to stars, it can sure happen to planets (note: rogue planets do not necessarily get removed from their star in this fashion). Besides, planets are a lot less massive than stars (many orders of magnitude) and so could possible get boosts many orders of magnitude higher.

Will such planet be in constant danger of impact by small bodies who at these speeds can be a danger to the whole planet's population?

Most likely not. Remember this quote from Douglas Adams:

"Space," it says, "is big. Really big. You just won't believe how vastly, hugely, mindbogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space, listen..."

There aren't a lot of dense areas of celestial bodies. Remember, the nearest star system is the Alpha Centauri system - and that's 4 light-years away! I'd imagine that collisions would be extremely unlikely, although there could be more activity near the galactic center. However, it will probably interact a little with the interstellar medium, though not a serious amount.

What if this thing goes into intergalactic space? Well, it will probably run into the intergalactic medium, some of which is composed of a plasma, possibly made of hydrogen. The planet might heat up a little, which I think is good, for your scenario. There would probably be some interesting atmospheric interactions, too; friction between the atmosphere and the intergalactic medium could heat up the top layers of the atmosphere to an extreme level.

Will not such planet quickly slow down due to cosmic medium?

Possibly - and probably a little bit. There will certainly be interactions with either the ISM or the IGM, which could slow it down a little. If the planet passes through higher-density regions of space (nebulae, gas clouds, etc.), then this will become a bigger issue. Which brings us to our last section.

What will happen if such planet impacts an intergalactic gas cloud or enters a galaxy?

Cool. I'm not sure what would happen here because I don't know if these exist in non-negligible numbers. I can analyze an interstellar cloud, if you want.

Interstellar clouds are regions of space filled with lots of gas and dust. They contain some dense ISM, as well as a lot of hydrogen. Some, such as giant molecular clouds, are the birthplaces of stars. They have a heck of a lot of hydrogen, in its molecular form (H2, I believe, although I'm not positive). How dense are these clouds? Some are very dense. From Wikipedia,

Whereas the average density in the solar vicinity is one particle per cubic centimetre, the average density of a GMC is a hundred to a thousand times as great.

Wow. That's pretty dense. Could that cause some problems for our high-velocity planet? Perhaps. But there could also be some upsides. After all, stars are being born nearby. And gravitational capture is always a possibility. . .

• I'm not so sure "pretty darn fast" and "highly relativistic" have to be on the same scale. We need orders of magnitude of frequency to blue-shift the CMB this much. I gave calculating the velocity for equivalent spectra a shot (see answer) and ended up above 99.9999% of the speed of light. A funny orbit isn't sufficient for that. – Vandroiy Nov 5 '14 at 23:14
• @Vandroiy I'm not talking about a "funny orbit"; I'm talking about enormous accelerations. – HDE 226868 Nov 5 '14 at 23:16
• @Vandroiy Here and here give me figures of $~1,000 \text{ km/s}$. Only about 0.3% of the necessary value, but still quite something. In a galaxy with two SMBs, it's possible that we could get much higher speeds. And remember, there are still many more hypervelocity stars out there. – HDE 226868 Nov 5 '14 at 23:20
• It seems like S2 is the fastest of them, at $5000 \text{km}/\text{s}$. It has its own Wikipedia page: en.wikipedia.org/wiki/S2_%28star%29 But remember that the hard part only begins later; when close to the speed of light, the energy requirement for acceleration increases. Sure, next to an event horizon or a super/hypernova you get a lot of force. However, we're limited by the planet not being destroyed by radiation or tidal forces. I doubt it would withstand the necessary environment to reach high-relativistic speeds. Maybe there is a way I don't know, but the usual sound ugly. – Vandroiy Nov 5 '14 at 23:25
• @Vandroiy It seems that any acceleration that size would have negative effects on the body. But yeah, this planet would be in pretty bad shape. – HDE 226868 Nov 5 '14 at 23:27

Math indicates that the planet would need to be traveling at least 120 km/s relative to a stationary observer (for reference, that's about 15 times faster than the Earth moves around the sun) up to a maximum of around 210 km/s (26 times). I.e. about 0.04% to 0.07% the speed of light.

Odds are, such a planet would not be "stable" (astronomically speaking) long enough to support life. But...

• Yes, it would be in danger of impact from small bodies.
• Distant objects would be blue shifted as well, so your best bet is to make this planet flying off into a void (dark region) of the universe such that all of the visible stars/galaxies would be behind it (and thus redshifted, likely down into the infrared range and beyond). This would also minimize the likelyhood of it crashing into something large.
• Not really, no. I'm sure there's some friction calculations out there for photons, but honestly it's going to be minimal.
• What happens? Very large explosions and death. You're throwing a planet sized body at another planet sized body at incredible speeds. The gas particles entering the atmosphere would likely light up the sky with deadly radiation, think the aurora borealis, except even higher energy.

My guess is that it's unrealistic and could never happen, but it's significantly more plausible than interstellar space flight (FTL travel) and no one has a problem with that. Rational explanation: the planet was flung off from a close-pass with a black hole, sending it into the deep voids of space, stripped from its parent star (stars do orbit black holes at these velocities, so a hyperbolic trajectory could fling off a small body fast enough).

• So slow? Are u sure u did not make any mistake? – Anixx Nov 5 '14 at 21:12
• Uhm. These numbers are impossible. Our sun's galactic orbit already moves at 220 km/s. Our total movement in CMB reference frame is above 600 km/s. You need to be a lot faster for such a strong relativistic doppler effect. – Vandroiy Nov 5 '14 at 21:18
• Given that I linked the page I got the math from...I then found the numbers for the wavelengths of the relic radiation on Wikipedia (1 mm) and applied the multiplication and division. Oh, and orbital speed was supplied by Wolfram Alpha in the computation. – Draco18s no longer trusts SE Nov 6 '14 at 0:33
• The difference in calculated speed between this answer and Vandroiy's one is huge, someone should check the math on both before we assume that one is right over the other :) – Tim B Nov 6 '14 at 9:41