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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?

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    $\begingroup$ Have you included heat from gravitational potential energy released as result of accretion $\endgroup$
    – James K
    Commented Jul 9 at 20:17
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    $\begingroup$ @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. $\endgroup$ Commented Jul 9 at 23:02
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    $\begingroup$ Maybe "very early" means a small fraction of its current age, a phrase that could be interpreted as a few hundred million years. $\endgroup$ Commented Jul 10 at 0:25
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    $\begingroup$ @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.). $\endgroup$
    – Jon Custer
    Commented 2 days ago
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    $\begingroup$ 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. $\endgroup$ Commented yesterday

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