Fire Planet as a light/heat source for my planets

Question

Whoops! Looks like I screwed up somewhere in my calculations, so I edited the question's calculations and corrected it.

What you are seeing here now is a extremely edited version of the original question, which was too long.

So, basically, I was looking for a alternate light/heat source for my science-fiction novel which I am planning to write. I didn't rely on stars due to some reasons that I omitted from the original question. So, I came up with this concept.

The Vulkan System

So, in this starless (but not geocentric in any way) system, there is surprisingly a planet that actually emits light (and heat) to its own planets, this planet is known as Vulkan. I will go into depth about this planet.

Vulkan

Vulkan is a Super-Earth, with about 15 Earth masses, and is a rocky planet, and a density of 5.51g/cm³, with a radius of about 15,715 km.

Vulkan has deep oceans that extend up to 20 km deep below. This ocean will play a major part in the emission of light by Vulkan (indirectly). Vulkan is actually a ocean-world, with no land, but it has oceans that are moderately deep.

Due to Vulcan's stupendous mass, this means that the core would be much more hotter than that of the Earth. I am too lazy to do the calculation, but it seems that it would be close to the temperatures of Saturn's core. The core is a mix of iron, nickel and other heavy elements, including radioactive uranium, that heats up the core even further, due to radioactive decay heat.

Vulkan's has an extremely dense atmosphere, at about 50 bars at sea level.

Its atmosphere is divided into 3 parts.

• Troposphere- This layer of the atmosphere extends up to 35 km in height, intersected by a cold trap. The composition of this layer is 75% oxygen, 23% carbon dioxide and traces of water vapour, argon etc. This layer contains a narrow cold-trap that condenses water back into clouds, and raining back to Vulkan.

• Stratosphere- This layer is composed of ethanol and methane, and is also known as the "combustion zone".

• Thermosphere- This layer is composed of hydrogen gas. As hydrogen gas is opaque to thermal infrared waves, it can trap heat and keep Vulkan warm. However this layer is extremely tenuous compared to the rest of the atmosphere.

The Vulkan Cycle

Here is how Vulkan emits light and heat. I will show this process in a really crappy diagram, but try to explain as much as possible in the text, but TL;DR it is the burning of methane and ethanol-richstratosphere, that releases the heat and light:

This occurs largely due to 3 organisms-

• Aetherates- They are thermosynthetic organisms that consume carbon dioxide and water to produce glucose and oxygen, with just heat. These Aetherates clump around hydrothermal vents on Vulkan's ocean floor, and form tall spires ranging to more than 20km in height, to trap the heat of the hydrothermal vents within them. They are not affected by Vulkan's strong gravity as they are buoyed up by the water beneath them. They can resist the intense pressures, as they have unique structures in their body, similar to deep-sea creatures here on Earth.
• Firemakers- These are Facultative Aerobes, that are in a symbiotic relation with Aetherates. They take some of the excess glucose from the Aetherates, in exchange for protection. These organisms decompose glucose into ethanol. They have an inbuilt mechanism that prevents them from dying due to too much ethanol production.
• Anaetherates- These are anaerobic organisms that decompose dead Aetherates, Firemakers into methane. They are obligate anaerobes that reside beneath the sea-floor of Vulkan. This methane is released in the form of bubbles.

The Aetherates, release oxygen into the atmosphere, by absorbing carbon dioxide from the atmosphere. The oxygen is sucked up into the combustion zone by massive updrafts powered by the heat of the combustion occurring in the atmosphere.

But at the same time, the Anaetherates and Firemakers release massive amounts of ethanol and methane into the ocean. The ethanol evaporates from the ocean, whereas methane bubbles out from the ocean floor towards the surface. These two combustible substances are also carried up into the atmosphere by the updrafts occuring. This constant supply of ethanol and methane from the ocean ensures that the combustion zone remains stable and burns for a long time.

Meanwhile, the water and carbon dioxide, being heavier than air, form massive parcels of air that sink down towards the surface. The water condenses in the cold trap, whereas the carbon dioxide falls into the ocean air, where the Aetherates act upon it to produce oxygen gas, which is again carried upwards by updrafts.

The hydrogen-layer, acts as a greenhouse gas. Since hydrogen is opaque to infrared radiation, this helps lock in some of the heat on Vulkan. But since the hydrogen layer is comparatively tenuous compared to the rest of the atmosphere (~0.5 bars-0.0000000.... bars), not too much heat is trapped. This ensures that Vulkan doesn't turn into a Venus-like steamy, crushing environment, while at the same time ensuring that Vulkan doesn't freeze into a iceball planet. Since most of the oxygen gets used up in combusting the ethanol and methane, there is virtually no risk of the hydrogen catching fire and igniting. The hydrogen layer is simply hot, but not burning. Furthermore, Vulkan's intense gravity holds the hydrogen in place, and prevents it from escaping.

A cold trap exists, but as an extremely narrow band about 3-4 km thick, and about 6km above sea level. Since the cold trap is really narrow, there is no thunderstorm formation on this planet, and thus no lightning occurs. Whatever rain occurs is merely a drizzle, or shallow rainfall. The intense heat of the combustion zone prevents tall clouds from forming, as they break apart from the heat. The cold trap, furthermore, is only effective for water. The cold trap simply isn't "cold" enough to condense ethanol back into rain. Even if ethanol manages to be captured by water, or condense, that ethanol is going to be a tiny fraction of the total ethanol produced. The majority of the ethanol combines with the methane, and rises into the atmosphere via updrafts, and burns in the combustion zone. The carbon dioxide and water vapour are then pulled back to the surface by powerful downdrafts.

This "combustion-zone" is what is responsible for producing the heat and light of Vulkan. This zone is where ethanol and methane, after reaching this layer, combust vigourously at intense temperatures, to produce heat and light. The reason why this combustion occurs is due to a reason which would be extremely lengthy, distracting backstory, so it is not included here. This light is completely free of UV rays and other radiation. Also, no stellar winds or flares are produced here.

Vulkan has 9 planets (moons?) orbiting it. These "planets" vary in mass and size. But for now, this is the planet, which shall be focused on in this question, Virgo:

• Virgo is a moon that orbits a extremely compact rocky planet Aquarius at about 500,000 km from it. Its parent planet Aquarius, has 7 earth masses, and a radius of 7800 km which implies an extreme density of about 21 g/cm³. Aquarius (along with Virgo) orbits Vulkan at a distance of 2 million km.
• Unlike its parent planet, Virgo has the exact same density, mass and radius as Earth. It also has the same amount of water as that of Earth. This implies Earthlike gravity, suitable for existence of Earthlike-life. But unfortunately I don't know if Vulkan can radiate enough heat and light to warm up Virgo to temperatures suitable for the existence of Earthlike-life.

The main question focuses, thus, upon Virgo, the moon of Aquarius.

Can Vulkan radiate enough heat/light to heat up Virgo to temperatures suitable for the existence of Earthlike-life? If no, then how should I fix my world?

^Addendum

^{1. Extra info- For those who are wondering where I got my calculations, well, there were a lot of sites from where I gathered, but I mostly used Omnicalculator to calculate size, gravity etcetera}

^{2. No, Radioactive Decay isn't the primary heat source for the planet. Although it indirectly heats Vulkan to habitable temperatures, it cannot emit enough heat and light to keep a close by planet warm enough. Furthermore, Radioactive Decay is going to emit harmful radiation that can destroy life. Hence, I decided not to use Radioactive Decay as the heat source. Radioactive Decay and Primordial Heat from planetary formation are indirect factors in sustaining the Aetherate-Firemaker-Anaetherate Cycle.}

^{3. The heat comes from the combustion of methane and ethanol in the upper atmosphere, which are produced by organisms present in the deep oceans.}

Answer 1

No.

Since fire is (per comments) the main source of the planet's thermal output, we can calculate the total energy available to your system. Let's do a quick order of magnitude estimate. Order of magnitude estimates typically miss the mark by at least a factor of 10 one way or the other, but it'll get us close enough.

Combustion will get you on the order of about 1 MJ per mole of reagents - or about $10^7 J / kg$ counting up the all the oxygen, carbon, and hydrogen moles.

Earth receives order of $10^{24} J$ of work from the sun annually, with a cross-sectional area of roughly $10^8 km^2$.

To duplicate this at a radius of 2 million km we need to put that amount of joules through each spot on that spheric surface annually, which has a surface area of order $10^{14} km^2$, therefore we need $\frac {10^{14} km^2}{10^8 km^2}= 10^6$ times that power output, or $10^{30} J/yr$.

$(10^{30} J/yr)/(10^7 J / kg) = 10^{23}kg/yr$

Let's suppose that instead of oceans, you have pure self-oxidizing liquid fuel compressed to the density of water. 20km deep times the surface area of your planet gets us order of $10^{10}$ cubic kilometers, or $10^{19}kg$ of fuel.

$(10^{19}kg)/(10^{23}kg/yr) = 10^{-4} yr$. That is to say: assuming that the entire biosphere of your planet is rocket fuel, it has enough chemical energy for less than a day.

If we assume that only a few percent of the total mass of the biosphere is combustible, there's probably only enough energy stored up for seconds of the power output desired.

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"But my biological system replenishes the chemicals," you might be thinking.

No, it doesn't. Energy is conserved. To replenish the chemicals, the biological system must do exactly one joule of work for every joule of work the chemicals did combusting, plus some extra to pay for entropy. Of course, it gets to recycle any energy that was radiated back down at the planet and didn't re-radiate back into space as blackbody radiation. (Which is itself problematic since we'd vaporize the oceans, melt the surface, and exterminate all life on the planet forever, but ignore that part, these are magic indestructible microbes.) However, we have only counted the energy that left out into space, never to return. That energy is gone and there's no way to get it back.

I had assumed in my comment that you intended for radioactive decay heating from the planet to replenish the missing energy. However, you wrote: "Radioactive Decay isn't the primary heat source for the planet. Although it indirectly heats Vulkan to habitable temperatures, it cannot emit enough heat and light to keep a close by planet warm enough." We can therefore discard the radioactive heat output of the planet, since you explicitly stated that it can't output the required power, and the first law of thermodynamics requires it to output all of the required power after the first (roughly) $10^{-4} yr$.

The fire planet burns out in much less than a day - or perhaps it smolders dimly rather than burning out all at once, a dull orange speck in the frigid endless night, reflecting coldly off of surface of the solid nitrogen-oxygen snow that coats the lifeless surface of Virgo.

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Suggested takeaway:

When you're working out plausibility of something, first work out the energy balance. How much power do I need and where can I get it? or How fast do I have to reject heat to do this?

Answer 2

I did not read your entire post

I quick-read it. For the record, don't write posts that long.

Can what you describe actually exist? I very much doubt it. Can the planet produce enough light and heat (same thing, BTW¹) to bring Virgo to Earth-like standards?

Probably not

But is that important? Personally, I think the current craze to write "hard science" science fiction is a disservice to the whole of humanity. We find new things about the universe almost daily. That leaves plenty of room for suspension of disbelief.

But why the "probably not?"

It takes an entire G-type star to make Earth the way it is at the distance Earth is from the Sun. The orbit looks concentric, but in reality the barycenter of the orbit is inside the radius of the Sun.

You don't have that. You probably don't realize it, but nothing orbits around Vulkan. It's a massive, wobbly, n-body mass of nasty with a barycenter well outside the radius of Vulkan. The system will be fairly unstable without moving the radius of some of the planets well outside Vulkan's usefulness as a star. But let's ignore that and do some rough math.

Sol is roughly 333,000 times the mass of Earth, which is a distance of 1 AU. Vulkan is roughly 15 times the mass of Earth. Assuming Vulkan's ability to emit light is (and this is the important part) equal to what the Sun can do per-square-meter of surface of the Sun, then Virgo must be (1 AU) * (15 ME) / (333,000 ME) = 45 micro-AU.²

That's only 6,738 km.

To put that into perspective,³ the Moon is 384,472 km from the Earth. That means the distance between Virgo and Vulkan is 1.8% the distance of the Moon from the Earth. Those two will be orbiting around each other at break-neck speeds.

And that all assumes that your definition for Vulkan allows for a "surface" condition (at the top of the atmosphere) equivalent to the same surface conditions found on the Sun. If you dial the sunlight producing capacity down to 1% of the Sun, then the orbital distance of Virgo just dropped to 67 km.

For the record, I could be completely wrong. Quick-read of the details of Vulkan, rough estimates of what light can do when scaled like you're doing. If I'm wrong, please point it out in comments and I'll correct it as best as I can — but I suspect the basic conclusion won't change.

Gratefully, you tagged your post science-fiction

What I did read of your post was a fabulously detailed account of a perfectly good world! I thought it was fun and innovative. So long as you don't put Virgo some ridiculous distance away from Vulkan (say, a maximum of 0.1 AU), I think the idea meets suspension-of-disbelief just fine. I like the idea!

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_{¹ Heat is not energy. Heat is a convenient measure of the energy state of a mass. Photons have energy. When they scatter around in the atmosphere, some of that energy is passed along to the atmosphere... and the ground... and the plants... causing their energy states to change. You and I interpret that change as "heat." What the sun is emitting is light (photons). The closer you get to the light, the more your own energy state increases. So, when you think about it, your entire question is, "Given the orbital relationship between Vulkan and Virgo and given the production of light on Vulkan as defined and the atmospheric conditions on Virgo as defined, will Virgo be similar to Earth?"}

_{² That's an outrageous simplification that's not really an apples-to-apples comparison. More like apples-to-kumquats. To do that right, you would need to calculate the square acreage of the surface of the sun and compare it to the square acreage of the surface of Vulkan's upper atmosphere (at least!). But I suspect the basic ratio of the rough scribble-it-on-the-tablecloth calculation will be close enough for government work.}

_{³ To really put that into perspective, it's basically the distance from Los Angeles, U.S.A. to Moscow, Russia. Think about that for a minute. The two planets might share atmosphere and generate sufficient heat due to friction.}

Answer 3

I see what you're going for ("fire planet" -- the planet is basically in a non-stop chemical fire, not fusion) and really I have no idea if that's realistic as a heat source to the moons. (I suspect the answer is "no". The total output of heat from the planet, but then fractionally how much of that actually hits a particular moon, and to what extent can it maintain that kind of fire over millions of years.....eh....)

But I feel like you could skip all this and just ask if Virgo can heat itself, and there I think we have good evidence that the answer is yes, with the evidence between Titan around Saturn and Europa around Jupiter.

Europa gets heated by the tidal forces of Jupiter. I'm not sure if Vulkan has enough mass for that but that's probably okay because Titan gets heated by its own core, believed to be rich in radioactive materials (we get some of that on Earth, too).

So all you really need is for Virgo to have perhaps an unusual amount of radioactive materials in its core, and then put it as close as possible to orbiting Vulkan, and between radioactivity and tidal forces, it can heat itself, no emissions from Vulkan required.

"Light" I'm less sure about but maybe the Vulkan idea can still work here: it doesn't need to emit a ton of heat, which implies to me a heck of a nonstop planetary fire, but it does need to emit light somehow. Bioluminescence? Maybe it really does have a nonstop fire in some upper atmospheric level, and that's enough to emit useful light? Maybe Virgo has a lot of bioluminescence?

I feel like you can run with the idea, anyway.

Vulkan has a non-stop fire going on. It Is A Mystery Of The Universe. Virgo is heating primarily internally, but there's "Vulkan-light" during the day (perhaps similar to a full moon on Earth, but really it can be whatever you want).

Answer 4

Ignoring the source of the fuel and oxygen, consider what happens if you do have a layer in the upper atmosphere that's constantly burning bright and hot enough to heat a nearby moon. The planet within is entirely enclosed in this shell of fire with no way to shed heat absorbed from it, and will quickly heat up to the same temperature as the flames. The end result is a ball of molten rock, and the annihilation of any biological activity that might produce fuel and oxygen.

Additionally, combustion can only release energy put into the mix of chemicals using a greater amount of energy from some other source. If that other source is radioactive decay/primordial heat, there has to be enough to produce that amount of heat regardless of any intermediate biology or chemistry.