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The Scenario:

  • The Sun is eternal.
  • We are producing much more oxygen than we need.

First off, would the atmosphere grow, or would it just become much more dense?

Given the circumstances, if the atmosphere grows, could it eventually reach the Sun?

What will happen once it gets close enough? Would the Sun burn up all the oxygen leading to Earth, then burn everything on Earth and Earth itself?

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    $\begingroup$ You need to find some aid to appreciate the scale of the solar system. Try drawing it, with the Earth's diameter, the height of the atmosphere on it, and distace from Earth to the sun drawn in correct scale. $\endgroup$ – JDługosz Apr 10 '15 at 1:49
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    $\begingroup$ @JDługosz Assuming we represent the Earth as my 12" globe, the atmosphere (80 km) is about the thickness of a $1 coin, the sun is around 110' in diameter (bigger than the US Capitol dome), and the radius of the Earth's orbit is 2.2 miles (from the Capitol to the Lincoln Memorial). For bonus points, the moon is 3 1/4" diameter (between a baseball and softball) and has an orbit 60' in diameter (a little smaller than the width of the steps of the Lincoln memorial). (Yes I live in DC!) $\endgroup$ – 2012rcampion Apr 10 '15 at 2:49
  • $\begingroup$ Hi Dexus your scenario is very unlikely sun will eventually burn out and currently we have estimated 21% of oxygen in the air increasing this would not make our atmosphere grow or glows lol. If you mean creating infinite oxygen this would violate the conservation of mass, I'll humor you on this, distance from Earth to Sun is 149,600,000 km (diameter of Sun is 1,391,684 km) with this much oxygen molecules and density the Earth will definitely collapse on itself and become a black hole. Now you are killing the Sun instead! $\endgroup$ – user6760 Apr 10 '15 at 3:43
  • $\begingroup$ @user6760 So we have bigger problems then burning up lol. $\endgroup$ – Dexus Apr 10 '15 at 4:02
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    $\begingroup$ The sun already contains oxygen... $\endgroup$ – ratchet freak Apr 10 '15 at 9:20
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Let's calculate the mass of this huge oxygen atmosphere, shall we?

I can use a modified version of the barometric formula to calculate the density at any altitude $h$ above a reference point - in this case, at Earth's surface: $$\rho=\rho_0 \exp \left[\frac{-g_0M(h-h_0)}{RT} \right]$$ where $_0$ denotes a quantity at $h=0$. To find the average value, we have to use a formula: $$f(x)_{\text{avg}}=\frac{1}{b-a} \int_a^b f(x)dx$$ In our case, $a=h_0$ and $b=150,000,000,000$ (both in meters). $\rho$ is a function of $h$, so we have $$\rho_{\text{avg}}=\frac{1}{150,000,000,000-h_0}\int_{h_0}^{150,000,000,000}\rho_0 \exp \left[\frac{-g_0M(h-h_0)}{RT} \right]dh$$ $$\rho_{\text{avg}}=\frac{1}{150,000,000,000-h_0}\int_{h_0}^{150,000,000,000}\rho_0 \exp \left[\frac{-g_0Mh+gMh_0}{RT} \right]dh$$ $$\rho_{\text{avg}}=\frac{1}{150,000,000,000-h_0}\int_{h_0}^{150,000,000,000}\rho_0 \exp \left[\frac{g_0Mh_0}{RT}-\frac{g_0Mh}{RT} \right]dh$$ Using $u$-substitution: $$u= \to du=-\frac{g_0M}{RT}dh$$ $$\rho_{\text{avg}}=-\frac{g_0M}{RT}\frac{1}{150,000,000,000}\int_{h_0}^{150,000,000,000}\rho_0 \exp u du$$ $$\rho_{\text{avg}}=-\frac{g_0M}{RT}\frac{1}{150,000,000,000} \rho_0 \left[\exp u \right]_{h_0}^{150,000,000,000}$$ $$\rho_{\text{avg}}=-\frac{g_0M}{RT}\frac{1}{150,000,000,000} \rho_0 \left[\exp \left[ \frac{g_0Mh_0}{RT}-\frac{g_0Mh}{RT} \right] \right]_{h_0}^{150,000,000,000}$$ $h_0=0$, so $$\rho_{\text{avg}}=-\frac{g_0M}{RT}\frac{1}{150,000,000,000} \rho_0 \left[\exp \left[ -\frac{g_0Mh}{RT} \right] \right]_0^{150,000,000,000}$$ Substituting in some variables, I get $$\rho_{\text{avg}}=-\frac{9.81 \times 0.0289644 }{8.31432 T}\frac{1}{150,000,000,000} \rho_0 \left[\exp \left[ -\frac{9.81 \times 0.0289644 h}{8.31432 T} \right] \right]_0^{150,000,000,000}$$ The tricky bit is temperature, which is not a function of altitude. Even worse, I've estimated that the lapse rate is zero! Okay, well, it's an approximation, so I'll say that $T$ is Earth's average air temperature - 288 Kelvin, according to Wikipedia. Plugging that in, I get $$\rho_{\text{avg}}=-\frac{9.81 \times 0.0289644 }{8.31432 \times 288}\frac{1}{150,000,000,000} \rho_0 \left[\exp \left[ -\frac{9.81 \times 0.0289644 h}{8.31432 \times 288} \right] \right]_0^{150,000,000,000}$$ $$\rho_{\text{avg}}=-7.91 \times 10^{-16} \rho_0 \left[\exp \left[ -\frac{h}{1.19 \times 10^4} \right] \right]_0^{150,000,000,000}$$ At $h=0$, $p_0=1.225$, so $$\rho_{\text{avg}}=-9.69 \times 10^{-16} \left[\exp \left[ -\frac{h}{1.19 \times 10^4} \right] \right]_0^{150,000,000,000}$$ $$\rho_{\text{avg}} \approx 9.69 \times 10^{-16}$$ Pretty low, right? But let's find the mass. given that $r=150,000,000,000$, we get $$M=V \rho_{\text{avg}}$$ $$M=1.37 \times 10^{19} \text{ kilograms}$$ That's only about double the current mass of our atmosphere.

Unless I made an error somewhere - and I very well might have - the gravitational effects on the Solar System will be about nil. Nothing will happen to the Earth, the Sun, the Moon, or anything else. My result conflicts with that of 2012rcampion, though that assumed constant density. See the power of $e^{-x}$ (pun intended)?


The giant extended atmosphere, though, will most likely leave Earth. There's a reason Earth isn't a gas giant - it isn't massive enough. Oxygen molecules at such great distances from Earth can easily fall victim to atmospheric escape, and will soon leave. This envelope would be depleted even if Earth was all by itself.

But it isn't all by itself. There are other nearby bodies, and they would accrete some gas - potentially. Venus and Mercury could move through the sphere, as could Mars. They might each take up some of the oxygen. Most, though, would go to the Sun, or simply float around.

The oxygen wouldn't burn, because a combustion reaction couldn't happen! A typical combustion reaction is $$\text{Hydrocarbon}+x\text{O}_2 \to y\text{CO}_2+z\text{H}_2\text{O}$$ The problem is, there's no fuel! Pure oxygen atmospheres are prone to fire - you only have to look as far as Apollo 1 - but you still need fuel. You'll be hard-pressed to find that. Even near the Sun, where there's a lot of heat, you still won't find much fuel, because while the Sun is rich in hydrogen and helium, there's not a lot of carbon - at least, not relative to the other elements.


Summary

First off, would the atmosphere grow, or would it just become much more dense?

Whoops; I kind of assumed that the extra oxygen was instantaneously placed there. Well, as the others said, it would be extremely difficult to create. So it's rather unfeasible without a bit of handwaving.

Given the circumstances, if the atmosphere grows, could it eventually reach the Sun?

No, because, as I said earlier, it would easily escape from Earth.

What will happen once it gets close enough? Would the Sun burn up all the oxygen leading to Earth, then burn everything on Earth and Earth itself?

Perhaps some will burn, but not a lot. You simply don't have the fuel needed.

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    $\begingroup$ Well explained! +1 $\endgroup$ – Caleb Woodman Feb 18 '16 at 21:04
  • $\begingroup$ Even near the Sun, where there's a lot of heat, you still won't find much fuel, because while the Sun is rich in hydrogen and helium, there's not a lot of carbon - at least, not relative to the other elements. Burn the hydrogen instead? $\endgroup$ – Chieron Jul 5 '16 at 11:29
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The first question is where you're 'producing' the oxygen from. It is a fairly common element on Earth, but most of it is tied up in oxygen containing minerals deep inside the Earth. Liberating that oxygen would radically alter the surface conditions.

Another problem is what happens to the oxygen. Things in oxygen-containing environments typically either rust or burn; that is, they oxidize. In an oxygen-rich environment, both of these things happen very quickly, and tend to deplete oxygen from the atmosphere. Oxygen is the second most reactive element, so it hates to be just floating around (this is why it's all inside of rocks). Only through the continual action of photosynthesis is the oxygen in the atmosphere maintained. The geologic sequestration processes would speed up as you add oxygen to the atmosphere, so you'd need some truly prodigious production mechanism to maintain the large amounts you suggest.

However, there is not enough oxygen to reach the sun. Even if the atmosphere's density remained constant, you'd need to increase the mass of the atmosphere by over a thousand trillion times, to over a billion times the mass of the Earth, or around ten thousand times the mass of the Sun itself.

Before you reached anywhere near that mass, you'd turn the Earth into a gas giant as the thickness and density of the atmosphere increased. At some point, it would become so heated by the compression that it would ignite and turn into a star of it's own right. (Note that a star consisting of mostly oxygen would have a very short lifespan, on the order of a few months or years, as it would behave like the core of a very massive star at the end of it's life.)

So, to answer your points one-by-one:

  • Would the atmosphere grow, or would it just become much more dense?

Both. In fact, the density would increase to around ten billion kilograms per cubic meter as the mass increases to around 10 solar masses (but no more than a couple hundred, at which point the star is so bright the photon pressure blows it apart).

  • If the atmosphere grows then given the circumstances, it will one day reach the sun. Correct?

False. See above.

  • What will happen once it gets close enough? Would the sun burn up all the oxygen leading to earth, then burn everything on earth and earth itself?

The oxygen would burn long before then. Whether it's consumed by regular burning (in a high-oxygen environment, everything becomes highly flammable, even diamonds), rusting the rocks themselves, or by nuclear reactions (turning the oxygen into silicon, then iron, then supernova), no oxygen would ever reach the sun.

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