Kerbol's Habitable Zone

[CaptRobau]

I've been trying to calculate Kerbol's Habitable Zone to see if it'd actually be in one like Earth is, or whether it should be a dead block of ice. Haven't had much luck. I'm no math hero, so all the formulas out there aren't help me find the answer anytime soon. Would anyone else be able to calculate this?

[AceMgy]

At 0.009 solar masses it's barely a star, if at all. Would most likely be a brown dwarf and not the nice, yellow, sun-like star we see in game.

[allmappedout]

Alternatively, we can assume that Kerbol has one Solar mass, since the entire universe is so much smaller than ours...?

[AceMgy]

Alternatively, we can assume that Kerbol has one Solar mass, since the entire universe is so much smaller than ours...?

That's an idea, but re-normalizing all the units would make the particulars of nuclear fusion tricky. Unless you shrink everything down including the atoms and their respective forces, in which case the universe isn't different at all, size is relative to something.

Gonna get my astrophysics book out to find out some particulars about this "star," as it would still give off some heat at 9.25 Jupiter masses.

Edited June 19, 2013 by AceMgy

[AceMgy]

So, it certainly is a brown dwarf, but at 9.25 jupiter masses it's not one of the lucky few that's able to fuse deuterium or lithium. This means it has no internal heat source, and it's simply radiating energy left over from it's formation. Therefore its temperature and thus color change with its age, becoming more cooler and more and more infrared in color as time goes by. Given it's mass it would probably be considered a sub-brown dwarf. I can't find any good models for calculating the temperature of such an object, so I'll just go with an example:

ULAS J003402.77−005206.7 is a brown dwarf discovered in 2007 that is estimated to be between 500 and 700K in temperature and between 15 to 36 Jupiter masses. So it's still a bit larger than our Kerbol. Using Wien's displacement law to calculate color from temperature, we find it would be about 5.8 micrometers wavelength of light. This puts it in the infrared area of the spectrum.

Let's just assume that Kerbol has this star's temperature, and see where that puts us.

Let's use the wiki values for the radius of Kerbol and Kerbin, and assume there's no albedo (because I don't know what it is). The temperature of Kerbin if Kerbol is 500K would be:

T(Kerbin) = T(Kerbol) * sqr( Radius(Kerbol) / 2D) Where D is the semi-major axis of Kerbin.

I get approximately 49K. Chilly. Remember that this is assuming a perfect blackbody and no albedo (adding that in would make it colder).

It's becoming abundantly clear that Kerbol can't be getting it's energy from nuclear fusion. I think a more "Kerbal" theory is that Kerbol is a perfect mix of liquid fuel and oxidizer burning furiously bright. It wouldn't last too long, but would explain why the Kerbals have limitless rocket fuel at their disposal if their solar system formed mostly out of that.

And if anybody finds fault with my math, tell me. It's been a while.

[stupid_chris]

The sun in KSP is a real physical joke seriously. It's diameter is a third of the Sun's but it's .09 solar masses its quite ridiculous. I think the mass is this low so that the gravitational calculations make sense for each planet's orbit but it looks like a normal star because orbiting such a brown dwarf would be pretty damn boring. I'd say we should give an estimate mass according to it's diameter and this should make more sense, but I think we'll have a bunch of roasted Kerbals. Ace, what would your equations give for a ~.4 solar masses red dwarf?

[AceMgy]

The sun in KSP is a real physical joke seriously. It's diameter is a third of the Sun's but it's .09 solar masses its quite ridiculous. I think the mass is this low so that the gravitational calculations make sense for each planet's orbit but it looks like a normal star because orbiting such a brown dwarf would be pretty damn boring. I'd say we should give an estimate mass according to it's diameter and this should make more sense, but I think we'll have a bunch of roasted Kerbals. Ace, what would your equations give for a ~.4 solar masses red dwarf?

Just a second. I have to look all this up because it's been two years since I've taken astrophys.

Edit: Alright. A main-sequence star of 0.4 solar masses would have a radius of 0.48 solar radii and be classified as an M2 star. This makes it about half the diameter of the sun instead of your predicted third because star diameter doesn't scale linearly with mass.

It's rather simple to look up that such main sequence stars have an effective temperature of 3520K.

Now I can calculate the temperature of Kerbin orbiting such a star, but I have two choices. Use the measured radius of Kerbol ingame, or use the theoretical radius of an M2 star on the main sequence. Since very careful observations by our Kerbal astronomers (written down in pen no less) have confirmed Kerbol's radius to be 261,600 km I'm going to go with that, as it'd be pointless to do this for a wrong value.

Same calc as before, gives 345 K, or about 72 degrees C. Conceivable considering I didn't factor in albedo of Kerbin which would cool this temperature down.

But.... If you used the theoretical values, you get approximately 390 K , or 117 degrees C. A bit too hot to save with albedo.

But this is all pointless since we know the values for Kerbol's mass and radius (again, written down in pen no less)! So let's drop this arbitrary fixing of Kerbol's parameters and figure out just what this object is and how it works like true scientists.

We can work this equation backwards to estimate Kerbol's effective temperature. Assuming Kerbin has an average temperature of 20 C (or 293 K), we can find Kerbol's effective surface temperature:

T(Kerbin) / sqr( Radius(Kerbol) / 2D) = T(Kerbol)

That gives me an effective temperature of 2988 K (or just about 3000 K considering this is just a rough approximation). So it's an object with 0.009 solar mass, 0.38 solar radii, and a temperature of about 3000 K. That puts it way off the main sequence, but that just makes it more interesting. Let's figure out what materials / heat source could make an object such as that.

Edited June 19, 2013 by AceMgy

[TheTriniFlyer]

Well, I just did some 'rudimentary' calculations (Very Rudimentary, to the Effect that I can be wrong, so please correct me if I am) and I figured out that Kerbol's Circumstellar Habitable zone According to:

Mass: ! Kerbol cannot support nuclear fusion !

Radius: About 19 500 000 KM which is near Duna

Luminosity: About 1.2 AU which past Eeloo

Edited June 19, 2013 by TheTriniFlyer

[stupid_chris]

Seriously, seeing it this way, I can only come to the conclusion Kerbol isn't a natural object. And then it comes to my mind that the Forerunners in halo were known to be able to control stars somewhat by either giving an object enough energy to initiate nuclear fusion. It's a bit far fetched but the only logical conclusion I get is that it's not natural.

[Spatzimaus]

You pretty much have to ignore the specifics of astrophysics for this game, even though the general concepts are fairly accurate. Yes, Kerbol's mass is an order of magnitude too low for nuclear fusion, but that's because of the game's scaling in other areas, with everything 10 times smaller than normal but 100 times less massive. This makes everything 10 times denser than their counterparts in reality, but the surface gravities remain comparable. The problem is that there are simply no minerals in reality dense enough for that to work; Kerbin's density is 58.5 g/cm^3, which is almost three times denser than lead. You'd have to have degenerate matter making up most of each planet and moon, and that's just not going to work.

So yeah, Kerbol's way too small to be a real star, and that makes the original question of habitable zones difficult to answer.

[Tommygun]

Can you just look up what the habitable zone is for our solar system and divided that by the games 1/11th scale?

[Schweehog]

Can you just look up what the habitable zone is for our solar system and divided that by the games 1/11th scale?

I've heard 1/6th, 1/10th, and 1/11th now. Which is it?

[Tommygun]

I've heard 1/6th, 1/10th, and 1/11th now. Which is it?

HarvesteR has said 1/11th.

[Spatzimaus]

I've heard 1/6th, 1/10th, and 1/11th now. Which is it?

It's about a 10.6:1 ratio. The easiest place to see that is Kerbin, which is supposed to be a direct translation of Earth (with identical surface gravity); Earth's mean radius is 6371 km, Kerbin's is exactly 600.

[JackleOfSparta]

Well you have to remember that the Kerbal Universe has its own elements.......

[Spatzimaus]

Well you have to remember that the Kerbal Universe has its own elements.......

Nope, just different names for the usual ones.

[Merinsan]

Seriously, seeing it this way, I can only come to the conclusion Kerbol isn't a natural object. And then it comes to my mind that the Forerunners in halo were known to be able to control stars somewhat by either giving an object enough energy to initiate nuclear fusion. It's a bit far fetched but the only logical conclusion I get is that it's not natural.

There is nothing wrong with the Kerbol system. The problem you have is the assumption that this is in our universe. It clearly is not.

The Kerbol system is in another universe, where the fundamental building blocks are different to our own. The speed of light is different.

The gravitational constant is different. Weak and Strong nuclear force is different.

It's the only hypothesis that makes sense.

[XenonSpark]

I think the biggest thing I've learned from this thread is that I should take Astrophysics next semester.

[Brotoro]

Can you just look up what the habitable zone is for our solar system and divided that by the games 1/11th scale?

Not everything scales linearly. The location of the habitable zone will depend on the energy flux from the star, which scales inversely with the square of the distance.

[stupid_chris]

There is nothing wrong with the Kerbol system. The problem you have is the assumption that this is in our universe. It clearly is not.

The Kerbol system is in another universe, where the fundamental building blocks are different to our own. The speed of light is different.

The gravitational constant is different. Weak and Strong nuclear force is different.

It's the only hypothesis that makes sense.

Actually the laws of physics are the same, the only reason we can go faster than the speed of light is because the devs didn't implement it. A parallel universe sounds more far fetched than an experiment by an advanced civilization.

[Moon Goddess]

Actually the laws of physics are the same, the only reason we can go faster than the speed of light is because the devs didn't implement it. A parallel universe sounds more far fetched than an experiment by an advanced civilization.

The fun thing about infinity is that neither are more far fetched than the other, infact that are both statistically true.

Given infinity, somewhere there is an advanced civilization that created the kerbol system, and somewhere there is a parallel universe that is exactly the kerbol system. It's just statistically has to be given an infinite number of universes and an infinite number of systems in each universe.

[stupid_chris]

It's not yet proven that there are multiple universes. Although it's extremely unlikely that there aren't others, it's possible that there really aren't any. but playing with the maths of infinity virtually makes everything possible. Technically, given the universe is big enough, if we go a Googol LY in one direction, we will start seeing repetitions, because after this distance, literally every possible molecular position has been achieved. Meaning there is probably a perfect replica of your dog, molecule for molecule, somewhere in this universe. And a perfect replica of you. And potentially a perfect replica of Earth. And so on. It's a bit trippy.

[Merinsan]

Actually the laws of physics are the same, the only reason we can go faster than the speed of light is because the devs didn't implement it. A parallel universe sounds more far fetched than an experiment by an advanced civilization.

Given that the matter that forms Kerbin is supposedly so dense that it's physically impossible in this universe, I'd say that it's far more far fetched that it's an experiment by an advanced civilization than an alternate universe - it's not a parallel universe, just alternate.

Of course it could be an experiment by an advanced civilization which is doing it by creating a virtual reality simulation like The Matrix, where cosmological constants are not the same as our own universe, but then it's just a computer game.

[stupid_chris]

Given that the matter that forms Kerbin is supposedly so dense that it's physically impossible in this universe, I'd say that it's far more far fetched that it's an experiment by an advanced civilization than an alternate universe - it's not a parallel universe, just alternate.

Of course it could be an experiment by an advanced civilization which is doing it by creating a virtual reality simulation like The Matrix, where cosmological constants are not the same as our own universe, but then it's just a computer game.

I personally see it as all the planets in KSP are actually made by that civilization, not just a simulation. They could, for example, harness a few neutron stars, build radiative shields around and then add a planet surface and voila, a hollow planet with a neutron star in the middle that seems to be way dense than what it should be. Take this general model to build ever planet and You have pretty much the system seen in the game.

Of course none of all of those theories can and probably won't ever be proven, but I personally like the idea We're all free to have our own vision of the game and I won't force anyone to think like me lol

[Brotoro]

Magratheans.

It's even more than 10 characters long, so there's your proof.