= Solution
Ancient Martian valley networks, lake basins, deltas, rounded or transported sediments and water-altered minerals show that liquid water was once more widespread than the present cold, low-pressure surface permits. Such evidence motivates a denser early atmosphere and different greenhouse conditions. It does not uniquely establish a continuously warm global ocean: episodic warming, local hydrology and several greenhouse compositions are alternatives that must be tested.
Over <time>, volatile loss to space, declining interior activity and changing surface storage altered the atmosphere. Early intense solar ultraviolet radiation could drive escape of light species; <ion> pickup, <sputtering> and photochemical processes removed additional material. Reduced dynamo activity changed solar-wind interaction, while water and carbon-bearing material could also be sequestered in ice, adsorbed material or minerals. Impacts can both remove and deliver volatiles. The balance is not reducible to one process or to the simple assertion that a <magnetic field> perfectly retains an atmosphere.
Surface ages are estimated mainly by crater size-frequency statistics, calibrated through radiometric ages and an assumed impact history. More heavily cratered ancient highlands and younger, resurfaced volcanic plains demonstrate substantial age differences on Mars. Lunar sample calibration must be transferred cautiously; erosion, burial and secondary craters complicate counting. Martian meteorites and the pre-2018 Curiosity potassium-argon measurement add radiometric constraints, but a mineral age need not equal the age of its final sedimentary deposition.<Measuring the Age of a Rock on Mars by NASA>[2013 Cumberland measurement and distinction between mineral and depositional ages]{ref}
Let $\Sigma=M_{\rm atm}$ denote the printed \b[atmospheric <mass> per area]. An impactor's projected area intercepts a column $m_{\rm col}=\pi R_{\rm imp}^2\Sigma$. The requested model assigns <energy> $m_{\rm col}V_{\rm imp}^2/2$ to atmospheric removal, and equates it to $GM_{\rm Mars}M_{\rm Esc}/R_{\rm Mars}$. Thus
$$
\boxed{M_{\rm Esc}=\frac{\pi R_{\rm imp}^2\Sigma V_{\rm imp}^2R_{\rm Mars}}{2GM_{\rm Mars}}.}
$$
This uses a thin atmosphere, a uniform column, surface escape <energy>, complete useful coupling of that column-energy estimate, and negligible radiative or other losses. It is not a general consequence of the impactor's <kinetic energy>, which would contain the \i[impactor <mass>] instead of the column <mass>. A realistic shock/escape calculation needs a coupling model, impact geometry and atmospheric structure. The expression is evaluated as the stipulated approximate model.
At one bar, $g\simeq3.71\,\mathrm{m\,s^{-2}}$, so $\Sigma=P/g\simeq2.69\times10^4\,\mathrm{kg\,m^{-2}}$ and the total atmospheric <mass> is $4\pi R_{\rm Mars}^2\Sigma\simeq3.89\times10^{18}$ kg. With a \b[<radius>] of $150$ km for the stated diameter,
$$
\boxed{\frac{M_{\rm Esc}}{M_{\rm atmosphere}}
=\frac{R_{\rm imp}^2V_{\rm imp}^2}{8GM_{\rm Mars}R_{\rm Mars}}
\simeq4.38\times10^{-3}\simeq0.44\%,}
$$
corresponding to about $1.7\times10^{16}$ kg. The <pressure> cancels from this fractional estimate. Confusing diameter with <radius> would overestimate it fourfold.
A single such impact therefore does not remove the bulk of the atmosphere in this model. Repeating an identical fractional loss would require roughly $525$ such events for ninety-percent removal, before allowing for volatile delivery or geological evolution. Craters and basins show that bombardment was substantial, but their presence does not establish that the necessary net loss occurred. Heavy-isotope enrichment, including argon and <hydrogen> isotopes, demonstrates selective escape and constrains competing processes. MAVEN had already supplied evidence for substantial space loss by 2017.<NASA's MAVEN Reveals Most of Mars' Atmosphere Was Lost to Space by NASA>[2017 argon-isotope result and solar-driven escape interpretation]{ref} These signatures are not uniquely diagnostic of impact erosion, which can be relatively bulk-like; they should not be presented as proof of impact dominance.
Back to article page
