Settings formed by Uncontrolled Terraforming of Venus and Mars via Portals

Question

If two circular portals of 2 meter (arbitrary) diameter were created allowing uninhibited flow between surface atmospheres of Venus and Mars, what would be the environmental effects on the two planets?

My thought process was inspired partially by both xkcd and the games Portal and Portal 2. Considering that one must obtain the necessary resources for terraforming a planet either from that planet, a neighbouring astronomical body, or extra dimensional sources, if the portals could exist, they would be a useful means to provide heat/atmosphere/energy to Mars, while venting it to form habitable pockets/domes on Venus. It would be much easier, for instance, to manufacture insulating tiles for Venus on Mars. I was trying to plan out a short story, based on a catastrophic failure of this system, such that transport though the portals is completely unregulated. Just a step by step explanation of how it occurred and what happened would be exciting, unique, and lead to beautiful images in an “epic storm scouring away the surface of the planet” way. It could also lead to an epic adventure of “close that last Earth/Mars portal before the building it is in fails.

Portal definition:

2 circular 2 meter diameter surfaces, each are fixed to a geostationary (there might a better term for that) point on each planet. Both oriented perpendicular to the planet’s surface and fixed in place (think stargate) Orientation relative to the axes/equator/etc of the planet is unspecified and can be chosen at your discretion. Instantaneous transport occurs through the portal in a way that can be modeled as a infinitely thin, indestructible orifice plate. Transport through the portal is free and has no effect on the matter passing through Velocity of particles after, passing through relative to the discharge portal, is the same as it was prior to passing through, relative to the entrance portal. Acceleration/velocity of the two portals relative to each other is technobabbled away.

By my rough calculations the pressure on Venus at the surface is 15000 times higher than that on Mars. As a result about 1.5 tons of air should be going through the portal per second. Due to the composition of the surface of Mars, this should easily cause widespread dust storms. It is, however, negligible to the mass/motion of the planet. It should be able to effect the atmospheres of both planets within a year (reasonable time to get a disaster team there assuming that portals cannot be used to get there for some reason). The finer details of the effects on the planets are more difficult to predict, which is the reason for the question.

Note: I have been using this scenario as a writing/thought experiment with no intent to ever publish anything on this subject. Any concepts developed here are public domain.

Answer 1

Movement of Gases

That's the most obvious thing to happen, which you've accurately identified. Assuming the portals are both on the surface, the air at the portal will have the respective air pressures (with forces acting on that area of the portal given in parentheses):

Venus: ~92 bar (28,902,652.4 newtons)

Mars: ~0.00636 bar (1,998.05293 newtons)

That means the pressure on the Venus side of things is ~14465.4088 times that of Mars. I don't need to do much more math to say that the atmosphere from Venus is very certainly going to initially flow into Mars', not the other other way around. This flow cannot be stopped until the pressures of the atmospheres have equalized or the portals are closed. (Having an automatic shutdown for these portals seems like a good fail-safe!)

Now, given that there is such a large difference in surface pressure and gravity, we need to figure out if the Venusian Atmosphere, when flowing into the Martian Atmosphere, achieves escape velocity. According to Wikipedia, the escape velocity for Mars is a humble 5.027 km/s. If you apply the force from Venus' atmosphere to a mol of its most common particle (carbon dioxide), you get (using dynamic pressure)

$$v = \sqrt{\frac{2q}{\rho}}$$

where

$v$ is velocity of the air

$q$ is the dynamic pressure (in this case 92 bar - .00636 bar = 91.99364 bar)

$\rho$ is the density of the air (for venus, it's 67 kg/m^3)

which yields:

$$v = 524.03042 \text{ m/s}$$

$$524\text{ m/s} << 5,027\text{ m/s}$$

So Venus doesn't have the pressure needed to launch stuff through this portal, through Mars' atmosphere, and into space. (You should be careful where you put your portals, though, because you could theoretically use this to launch things into space with other planetary bodies.)

Once the atmospheres have equaled in total pressure, the atmospheres will then attempt to stabilize their partial pressures until the two planets share the exact same atmosphere. It should be noted that this process will take longer than the total pressure equalization, simply because there is so much air to move from Venus to Mars, that Mars' atmosphere won't get a change to go to Venus until the total pressure is about equal.

Time for a little more math, this time using a more familiar pressure due to depth equation: $$p = \rho \times \text{gravity} \times h$$

knowing that the pressure of Venus and the pressure of Mars will (eventually) equalize, and their densities will be the same, we're left with

$$\frac{g_{\text{Venus}}}{g_{\text{Mars}}} = \frac{h_{\text{Mars}}}{h_{\text{Venus}}}$$

$$\frac{8.87 \text{ m/s}^2}{3.711 \text{ m/s}^2} = 2.39019132$$

So Mars' new atmosphere should be ~2.4 times the depth of Venus' new atmosphere when this terrible pressure-equalization event finally blows over. That's just the bulk pressure. What about partial pressures?

Atmospheric Composition / Chemistry

With these atmospheres being exposed to each other, and knowing that gases attempt to diffuse evenly in the space they're "allowed" to go into, we're looking at a change in Mars' atmosphere, followed by a change in Venus' atmosphere.

If you take a look at the Wikipedia articles for the Venus and Mars, and look at the list of partial pressures, you'd realize that their atmospheres look pretty similar- they're mostly both mostly (>95%) carbon dioxide followed by nitrogen and other trace elements. Mars' atmospheric sulfur content would increase, and Venus would get a few more trace elements, but otherwise the makeup would not be significantly changed.

According to this, one of the problems with Mars is that it doesn't have enough of an atmosphere to hold heat in. The additional carbon dioxide from Venus, though, would help quite a bit, giving it an atmosphere which holds heat in, making it warmer. Not to mention the air from Venus is a hellish 737 K, which will go a long way into making the Red Planet warmer.

I don't know the exact composition of Venus and Mars, so I can't say how much warmer / cooler each planet would become or how fast. I'm willing to say, based off the each planet's relative size and some knowledge of heat capacity, that Mars will heat up more than Venus will cool off. In fact, given enough time, Mars and Venus may eventually reach the same temperature, assuming the portals allow for heat transfer.

Weather Pattern Changes

This is another area of speculation, because Martian weather patterns are not readily available. Also, weather systems are classic examples of chaotic systems, your slow introduction of Venusian Atmosphere may have many, many unforeseen effects.

Locally, though, we know that the denser Venusian Air will spread out until its pressure is roughly that of Martian pressure. We also know that it's much more dense, so the air will spread out (relatively) near to the surface. If the portals were larger, this may result in fixed surface winds, like we see with land and sea breezes.

Answer 2

I will assume that the portals are effectively wormholes, and as such conserve potential and kinetic energy and momentum.

In that case, the net flow of gases will be from Mars to Venus. While the pressure gradient favors the reverse flow, this is overcome several-fold by the difference in the gravity of the two planets (Venus's gravity well being much deeper) and far more so by the fact that Venus is further inward in the Solar System and is thus deeper in the Sun's gravity well. Therefore, the effect will be that Mars loses almost all of its existing atmosphere, while Venus's atmosphere is increased in density by an insignificant amount. To conserve momentum, the planet's orbits will also change by insignificant amounts.

Note that if the portal is only two meters in diameter, it could take a long time for Mars to lose its atmosphere.