Long before the solar wind was discovered scientists calculated other factors which affect how long a planet can retain its atmosphere. They included the velocity of the air particles in the exopshereexosphere, the upper atmopshereatmosphere of the planet, and the escape veloctiyvelocity of thhethe planet - not, repeat not, its surface gravity. The velocity of the irair particles in the exosphere depends on their temperature, which is often very different from the temperauretemperature of he atmosphere at the surface.
And Dole uses that formula to calculate how fast a world loose gas enough to bring the total amount down to 1/e, or 0.368, of the original amount of that gas, based on the ratio of ththe escape velocity of that world divided by the root-mean-square velocity of the gas in the exosphere.
Table 5 on page 35 shows that if the ratio is one or two the amount of gas will fall to 0.368 of the original amount instantly, while if the ratio is 5 it will take about 100 million years for the amount to fall to 0.368 of the original amount, and if the ratio is 6 it will take about infinite tie for the amount of htethe gas to fall to 0.368 of the original time.
Dole descrribesdescribes 6.25 kilometers per second as 5 X× 1.25, so the root-menamean-square velocity of atomic oxygen at 1000 K should be 1.25 kilometers per second, and a world with an escape velocity of 6.25 kilometers per second could retain 0.368 of an original amount of atomic oxygen for about 100 million years. And thus a world with an escape velocity of 7.50 kilometers per second take aninfinitean infinite time for for atomic oxygen to fall to 0.368 of the original amount.
Earth has an escape velocity of 11.186 kilometers per second, which is 1.49 times 7.50 kilometers per second, the escape velocity necessary to retain 0.368 of atomic oxygen forever at 1000 degrees K. Since the exosphere temperatures of Earth get up to 2000 K, the root-mean-square velocity of atmoic oxygennatomic oxygen the exosphere is faster than 1.25 kilometers per second, and the ability of Earth to retain atomic oxygen is somewhat less than it would if the maximum exosphere temperature was only 1000 K.
Venus has a surface gravity of 8.87 meters per second persper second, 0.904 that of Earth, and an escape velocity of 10.36 kilometers per second, 0.92615 that of Earth. The escape velocity is a higher fractonofraction of Earth's than the surface gravity is.
So if atomic oxygen in the exosphere of Venus had a temperature of only 1000 K, and thus a root-mean-square velocity of 1.25 kilometers per second, the escape velocity of Venus would be 1.3813 times as much as necessary for it to take an infinite time for the amount of atomic oxygen to be reduced to 0.368 of the original amount.
Of course the exopshereexosphere temperatures of Earth get as high as 2000 K and htethe temperatures in the exopshereexosphere of Venus might be hotter than 2000 K, so Venus probably looses atomic oxygen by escape into space faster than Earth does.
If atomic oxygen in the exospherexosphere of Mars has a temperature of 1000 K and thus a root-mean-square velocity of 1.25 kilometers per second, the ratio of the escape velocity, 5.027 kilometers persecondper second, divided by the root-mean-square velocity of 1.25 kilometers per second, would be only 4.0216.
According to table 5 on page 35, a ratio of 4.0 would mean that the amount of a gas would wall to only 0.368 in a few thousand years. Suppose that a ratio of 4.0216 would cause a drop to 0.368 of htethe original amount of a gas to take as long as 100,000 years, which seems too long a time,ut but I will use it. In that case Mars would retain 0.1354 of the original amount in 200,000 years, 0.498 of the original amount in 300,000 years, 0.183 of the original amount in 400,000 years, 0.0067477 of the original amount after 500,000 years and so on.
Mars wold retain 0.0000455 of the origianloriginal amount after 1,000,000 years, 0.000000002 of the original amount after 2,000,000 years, and so on. Thus Mars would have to have to produce or acquire atomic oxygen rather rapidly to replace it as fast as it looses it,and clearly doesn't replace atomic oxygen as fast as it loses it.
Oxygen is usually in molecular form, O2O2, whihwhich as a molecular weighitweight of 32,t twice that of atomic oxygen, 16. Atomic oxygen is usually the the result of ultraviolet light breaking up moleculsemolecules of O2O2, or water, H2OH2O, nitric oxide, NO, Carbon dioxide, CO2CO2, etc. Mostof Most of the compundscompounds likely to be found in planetary atmopsheresatmospheres contain oxygen and either solids or gases as light or lighter than oxygen. So the ultraviolet light breakesbreaks up molecules in the Martian atmosphere into atoms whicharewhich are either solid or escape rapidly into space.
So it is my opinonopinion that that Venus and eArthEarth have escepeescape velocities enabling them to loose gases by escape into space very,v eryvery slowly. Mars has an escape velocity low enough that it loses gases into space much faster than they can be replacedsreplaced, which is also hurried by the solar wind. Earth and Venus mostlmostly lose gases by the solar wind and other processes which are much slower than gravitation escape in my opinonopinion.
AdnAnd here is a link to a Wikipedia article discussing various processes of atmospheric loss.