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I know the atmospheric pressure on Mars is less than that of Earth, and so is its gravity. However, I know that the deeper you go (e.g. in a cave or a hole that is dug), the more atmospheric pressure you would experience. How deep would you have to go on Mars (e.g. below the surface) for the atmospheric pressure to be equal to the pressure we experience on the surface of the earth?

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Nasa has a atmospheric model of mars: $$0.699 *e^{-0.00009 h} $$

A naive application of this model, solving for a pressure of 101 kPa, gives a depth of -55 km.

The Armstrong limit depth (at which water boils at body temperature) is -24km

The model assumes constant temperature, and gravity (it doesn't correct for the fact that at 55 km below the surface you would be well into the martian mantle and the temperature would be very much higher, and deep enough for a measurable difference in gravity). There's no "goldilocks depth" at which you would only need an oxygen supply.

These depths are not achievable with current technology. The deepest mines on Earth are about 4km deep, and even the Kola superdeep borehole only managed 12km

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    $\begingroup$ The main problem of the deep mines are: 1) elevated temperature 2) water incursions. None of them would be a problem on the Mars. $\endgroup$
    – peterh
    Commented Aug 9, 2018 at 10:40
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    $\begingroup$ Do you know about the temperature profile in the martian mantle? $\endgroup$
    – James K
    Commented Aug 9, 2018 at 12:33
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    $\begingroup$ Here is a paper about the temperature profile of the upper soil. The mantle, I don't know, but I suspect it might elevate with a smaller gradient to until around 3-4000K in the center. $\endgroup$
    – peterh
    Commented Aug 9, 2018 at 12:36
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    $\begingroup$ Plants don't need 101kPa - the partial pressure of $\rm CO_2$ in the athmosphere of the Earth would be far than enough for them. It is 0.035% of 101kPa, which is 35Pa. The athmospheric pressure on the Mars is 600Pa. Only the $\rm CO_2$ is far more than enough for plants. Maybe another limit is that water shouldn't boil on the temperature what the plants need to live. $\endgroup$
    – peterh
    Commented Mar 16, 2019 at 21:20
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    $\begingroup$ It may not be possible to go much deeper than 7 km below the Geoid of Mars (the ground zero altitude all our measurements of Mars average atmospheric density, temperature & wotnot are calculated for) What's the deepest a trench could theoretically be dug on Mars?. $\endgroup$
    – Pelinore
    Commented Nov 30, 2019 at 21:34

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