<p>The answer is <strong>no</strong>.</p>
<p><strong>Explanation</strong>:</p>
<p>No atmosphere is equivalent to all molecules being able to evade to space (This happens on planets with low gravitational force). Thus also <span class="math-container">$H_2O$</span> molecules will evade and I guess that many molecules already evaded during the frozen state of the planet due to <a href="https://en.wikipedia.org/wiki/Sublimation_(phase_transition)" rel="nofollow noreferrer">sublimation</a>. So this could be the end of this answer.</p>
<p>But let's suppose for a moment, even if it is not realistic, that an atmosphere could form. Top of atmosphere power received from the sun is around <span class="math-container">$S_0 = 1368 \, \frac{\text{W}}{\text{m}^2} $</span> (<span class="math-container">$S_0$</span> being the solar constant). Assuming earth is a blackbody we can equate power received from the sun and power radiated from the hypothetical earth (see also <a href="https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law" rel="nofollow noreferrer">Stefan-Boltzmann law</a>).</p>
<p><span class="math-container">$S_0(1-\alpha) \pi r^2 = \sigma T^4 4 \pi r^2$</span></p>
<p><span class="math-container">$\alpha = 0.6$</span> is the albedo, <span class="math-container">$\sigma = 5.67 \cdot 10^{-8}$</span> is the <a href="https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_constant" rel="nofollow noreferrer">Stefan-Boltzmann constant</a>, <span class="math-container">$\pi = 3.1415$</span>, <span class="math-container">$T$</span> is earths surface temperature and <span class="math-container">$r = 6371 \, \text{km}$</span> is earths radius. Simplifying and rearranging yields</p>
<p><span class="math-container">$T = \left(\frac{S_0(1-\alpha)}{4\sigma}\right)^{\frac{1}{4}} \approx 222 \, \text{K} = -51.15°\text{C}$</span>.</p>
<p>Taking a look at the phase diagram you provided, we see that at <span class="math-container">$222 \, \text{K}$</span> and low pressure water naturally occurs as gas. Given the assumption that an atmosphere could indeed form (for some magical reason someone increases gravtiy) the answer is <strong>yes</strong> an atmosphere could form.</p>

CC BY-SA 4.0
2021-02-24T23:27:30.933Z
2021-02-24T23:27:30.933Z
Joscha Fregin
<p>Phase change of water at different pressures and temperatures tell us that with no atmospheric pressure 200 Kelvin (minus 73 Celcius) is enough to turn ice into vapor directly</p>
<p>Wouldn't that suggest that solar insolation at the distance of earth to the sun heating potential is enough to kickstart the hypothetical ice planet to a waterworld with an atmosphere? Even when averaging day/night?</p>
<p><a href="https://i.sstatic.net/91JS8.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/91JS8.gif" alt="enter image description here" /></a></p>

<climate-change><geophysics><climate><climatology><thermodynamics>
Is it possible to kickstart an hypothetical frozen earth with 0.6 ice albedo to an earth with an atmosphere, with just the sun at current distance?
MP1
# Is it possible to kickstart an hypothetical frozen earth with 0.6 ice albedo to an earth with an atmosphere, with just the sun at current distance?

(Asked by: username_0 on 2021-02-23)

Phase change of water at different pressures and temperatures tell us that with no atmospheric pressure 200 Kelvin (minus 73 Celcius) is enough to turn ice into vapor directly

Wouldn't that suggest that solar insolation at the distance of earth to the sun heating potential is enough to kickstart the hypothetical ice planet to a waterworld with an atmosphere? Even when averaging day/night?

[![enter image description here](https://i.sstatic.net/91JS8.gif)](https://i.sstatic.net/91JS8.gif)

**Tags:** climate-change, geophysics, climate, climatology, thermodynamics


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## 1 answers

### Answer by username_1 on 2021-02-24. Score: 2 | Accepted answer

The answer is **no**.

**Explanation**:

No atmosphere is equivalent to all molecules being able to evade to space (This happens on planets with low gravitational force). Thus also $H\_2O$ molecules will evade and I guess that many molecules already evaded during the frozen state of the planet due to [sublimation](https://en.wikipedia.org/wiki/Sublimation_(phase_transition)). So this could be the end of this answer.

But let's suppose for a moment, even if it is not realistic, that an atmosphere could form. Top of atmosphere power received from the sun is around $S\_0 = 1368 \, \frac{\text{W}}{\text{m}^2} $ ($S\_0$ being the solar constant). Assuming earth is a blackbody we can equate power received from the sun and power radiated from the hypothetical earth (see also [Stefan-Boltzmann law](https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law)).

$S\_0(1-\alpha) \pi r^2 = \sigma T^4 4 \pi r^2$

$\alpha = 0.6$ is the albedo, $\sigma = 5.67 \cdot 10^{-8}$ is the [Stefan-Boltzmann constant](https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_constant), $\pi = 3.1415$, $T$ is earths surface temperature and $r = 6371 \, \text{km}$ is earths radius. Simplifying and rearranging yields

$T = \left(\frac{S\_0(1-\alpha)}{4\sigma}\right)^{\frac{1}{4}} \approx 222 \, \text{K} = -51.15°\text{C}$.

Taking a look at the phase diagram you provided, we see that at $222 \, \text{K}$ and low pressure water naturally occurs as gas. Given the assumption that an atmosphere could indeed form (for some magical reason someone increases gravtiy) the answer is **yes** an atmosphere could form.


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