My question is whether Mars just about failed to meet the threshold or missed it by a lot. It's been dry for 3 billion years. How much bigger would it have needed to be to buy it that extra time? Let's say in modern times we turn up and find it has enough CO2 to be as warm as Earth, and has small seas in the lowest lying regions north of the equator.
Based on this chart (I found in a Google image search) it seems that Mars should be about twice as massive to avoid water vapor reaching escape velocity. If Mars is twice the mass then for the same density (although actually it would automatically be more due to being squished by its own mass) it should have an escape velocity of around 6.324km/s. If it had the same density as Earth due to an iron core (though again Earth gets extra density from squishing its core), then the escape velocity should be 6.69km/s. A double massed Mars should probably have an escape velocity somewhere between these two extremes. 6km/s seems to be the threshold for maintaining water vapor at current Martian temperature, though the issue is that having a thicker atmosphere would warm Mars up a lot. If it had enough greenhouse gases to be the average temperature of the Earth at its current semi-major axis then perhaps the escape velocity needed would be more like 7km/s, which could mean a Mars around 3 times the mass (depending on how much we fiddle with the density). I can't factor in the effect of a strong magnetic field.
Is my quick estimate overzealous? Am I missing anything?
