<p>ChatGPT told me this:<br />
&quot;Mars likely experienced the magma-ocean stage very early in its history, shortly after its accretion around 4.6 billion years ago.&quot;</p>
<p>This is hard to digest.  The planet's temperature was growing as<br />
<span class="math-container">$ ΔT = Δt\; \frac{\textstyle H}{\textstyle C_p}\;\;  ,$</span></p>
<p>where <span class="math-container">$H$</span> and <span class="math-container">$C_p$</span> are the radiogenic heating and specific heat capacity.</p>
<p>In the literature, I saw the numbers</p>
<p><span class="math-container">$H = 3.5 \times 10^{12}$</span> W/kg<br />
<span class="math-container">$C_p = 1200$</span> J/(K kg)</p>
<p>(though in the early Solar System the value of <span class="math-container">$H$</span> could have been up to four times higher).</p>
<p>This indicates that, after accretion, at least several hundred million years were needed to heat up the planet to a thousand or two K.</p>
<p>If my estimate is correct, how could the magma-ocean stage start shortly after the accretion?</p>

CC BY-SA 4.0
2024-07-09T20:17:26.987Z
Have you included heat from gravitational potential energy released as result of accretion
James K
CC BY-SA 4.0
2024-07-09T23:02:25.773Z
@JamesK Can this effect heat up a planet to a thousand K? I would be surprised if it were possible. Please correct me if I am wrong.
Michael_1812
CC BY-SA 4.0
2024-07-10T00:25:00.833Z
Maybe "very early" means a small fraction of its current age, a phrase that could be interpreted as a few hundred million years.
Oscar Lanzi
CC BY-SA 4.0
2024-07-10T19:10:31.063Z
@Michael_1812 - back of the envelope order of magnitude thought process: Escape velocity from Earth is 11.2 km/s - this velocity is required to remove something to "infinity". So, for 1 kg of water, the energy is ${1 \over 2} m v^{2}$, or 62 MJ. Heat capacity of water is 4200 J/kg/K, so that 62 MJ would heat water by almost 15,000K (yes, I've ignored changes in heat capacity, phase transitions, etc.).
Jon Custer
CC BY-SA 4.0
2024-07-10T20:45:44.030Z
@JonCuster First of all, many thanks. If you choose to put this comment into an answer, that will enable me to credit it properly. Also, do you really imply that accretion can, by itself and with no help from radioactivity, melt celestial bodies?
Michael_1812
CC BY-SA 4.0
2024-07-10T21:15:24.280Z
@Michael_1812 - consider that the collision of proto-Earth and Theia (generating the Earth-Moon system) likely completely melted both bodies.
Jon Custer
CC BY-SA 4.0
2024-07-10T21:28:40.680Z
@JonCuster Thank you again. Some food for thought...
Michael_1812
CC BY-SA 4.0
2024-07-11T18:30:06.340Z
Just because ChatGPT said something does not mean it's true.  I was at a concert last night where the opening act said they asked ChatGPT how many times they had performed there and it said once.  The venue had records of 3 times.  I suggest finding any sort of research paper that suggests a Mars magma ocean and go from that as your starting point.
Stuart Robbins
<mars><planetary-formation><accretion>
How soon after the accretion did Mars experience the magma-ocean stage?
Michael_1812
# How soon after the accretion did Mars experience the magma-ocean stage?

(Asked by: username_0 on 2024-07-09)

ChatGPT told me this:  
"Mars likely experienced the magma-ocean stage very early in its history, shortly after its accretion around 4.6 billion years ago."

This is hard to digest. The planet's temperature was growing as  
$ ΔT = Δt\; \frac{\textstyle H}{\textstyle C\_p}\;\; ,$

where $H$ and $C\_p$ are the radiogenic heating and specific heat capacity.

In the literature, I saw the numbers

$H = 3.5 \times 10^{12}$ W/kg  
$C\_p = 1200$ J/(K kg)

(though in the early Solar System the value of $H$ could have been up to four times higher).

This indicates that, after accretion, at least several hundred million years were needed to heat up the planet to a thousand or two K.

If my estimate is correct, how could the magma-ocean stage start shortly after the accretion?

**Tags:** mars, planetary-formation, accretion
> **Comments:**
> **username_1**: Have you included heat from gravitational potential energy released as result of accretion  
> **username_0**: @JamesK Can this effect heat up a planet to a thousand K? I would be surprised if it were possible. Please correct me if I am wrong.  
> **username_2**: Maybe "very early" means a small fraction of its current age, a phrase that could be interpreted as a few hundred million years.  
> **username_3**: @Michael_1812 - back of the envelope order of magnitude thought process: Escape velocity from Earth is 11.2 km/s - this velocity is required to remove something to "infinity". So, for 1 kg of water, the energy is ${1 \over 2} m v^{2}$, or 62 MJ. Heat capacity of water is 4200 J/kg/K, so that 62 MJ would heat water by almost 15,000K (yes, I've ignored changes in heat capacity, phase transitions, etc.).  
> **username_0**: @JonCuster First of all, many thanks. If you choose to put this comment into an answer, that will enable me to credit it properly. Also, do you really imply that accretion can, by itself and with no help from radioactivity, melt celestial bodies?  
> **username_3**: @Michael_1812 - consider that the collision of proto-Earth and Theia (generating the Earth-Moon system) likely completely melted both bodies.  
> **username_0**: @JonCuster Thank you again. Some food for thought...  
> **username_4**: Just because ChatGPT said something does not mean it's true.  I was at a concert last night where the opening act said they asked ChatGPT how many times they had performed there and it said once.  The venue had records of 3 times.  I suggest finding any sort of research paper that suggests a Mars magma ocean and go from that as your starting point.  

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## 0 answers

