Atmospheres

 

The atmospheres of the terrestrial planets share some similarities, but also have many differences.

 

 

The atmospheres that these planets retain today is governed by a number of processes. Among these are:

 

1. Loss of high-speed molecules

 

2. Chemical reactions

 

3. Erosion by impacts

 

Loss of High-Speed Molecules

 

In the absence of resistance by air, any object with sufficiently high speed will have enough kinetic energy to escape the gravity of its planet.

 

 where  is the mass of the molecule,  is the mass of the planet,  is the radius of the planet, and  is Newton’s gravitational constant.

 

The actual kinetic energy is given by:

 

 

 

So the condition where these are equal is:

 

 or .

 

In reality, the velocities of the molecules is not at

a single value, but rather a distribution:

 

The average speed is determined by the temperature of the gas and the mass of the molecule being considered:

 

 or   where  is the Boltzmann constant.

 

Note that even if , there will be some molecules at the high-speed tail of the distribution that will have . The usual “rule of thumb” is that if  the gas molecules will not escape quickly enough. Notice that  depends on the composition of the gas molecule  more massive ones move more slowly at a given temperature, and are retained by the planet more easily!

Example:

 

For Earth,  

 

Oxygen (O₂):  

 

Hydrogen (H₂):   

 

So the Earth retains oxygen but not hydrogen. To be more precise, we need to do these calculations at the top of the atmospheres to have the correct temperature.

 

Chemical Reactions

 

One of the most important reactions for altering the composition of the atmospheres of terrestrial planets is sometimes referred to as the Urey Reaction, named for Harold Urey, the Nobel laureate who noted its importance:

 

 

 

There are a couple of ways this can operate. First, carbon dioxide mixed with rainwater will make a weak carbonic acid capable of dissolving silicate rock which then flows into the ocean where it can (with or without the intervention of mollusks) be converted into carbonate rock. Second, carbon dioxide can dissolve directly in fresh water and seawater to accomplish much the same purpose. The net effect is the removal of CO₂ from the atmosphere and store it in rock.

 

 

 

 

 

 

 

 

 

 

Another important reaction for us is the production of ozone from molecular oxygen:

 

 

 

Both molecules combined provide protection form ultraviolet photons capable of breaking the chemical bonds in organic molecules. O₂ covers the higher-energy UV photons from 120-200 nm (0.12-0.20 μm) while O₃ covers the lower-energy UV photons from 200-350 nm (0.20-0.35 μm). Luckily, the solar spectrum declines rapidly at wavelengths shortward of 300 nm.

 

Impact Erosion

 

We have already looked at impacts.

 

 

 

 

Planetary Temperatures

 

The terrestrial planets are heated almost exclusively by light they absorb from the Sun. They also radiate that energy back into space. If these two are not balanced, the planet will rapidly heat up or cool down until it does, achieving thermal equilibrium with its surroundings. The temperature the planet has is that which is necessary to reach equilibrium.

 

Energy Absorbed by a planet:

 

 

 

If we wanted to explicitly use the surface temperature and radius of the Sun (instead of its luminosity) this could also be written as:

 

 

In turn, the planet radiates:

 

 

In equilibrium, these must be equal:

 

               or         

 

More simply:

 

 

 

How do these stack up against the measured temperatures?

 

 

 

Note: the freezing point of water is 273 K, and the boiling point is 373 K, under 1 Atm pressure. Venus is currently too hot for liquid water. Mars is too cold. The Earth is "just right".

 

But WHY are the temperatures of Earth, and especially Venus, higher than what is predicted? Because we have not included another very important effect: the Greenhouse Effect!

 

Greenhouse Effect

 

The greenhouse effect warms a planetary surface by warming the atmosphere above it. Due to the Sun’s surface T, Light from the Sun peaks near wavelengths where the Earth’s atmosphere is transparent, so little heating of it occurs. The light that is absorbed by the ground heats the ground, when then radiates at its characteristic T, which is a lot cooler, and peaks in the IR. Unlike visible wavelengths, the IR is filled with absorption bands due to various molecules. These molecules absorb the IR, effectively depositing that energy in the atmosphere, and warming it. The warm molecules radiate at those same wavelengths that they absorb at, and half of the radiation is back in the direction of the surface of the planet.

 

 

 

 

Here is some more of this:

 

 

 

I found a nice little description, apparently from Channel 4 News in Chicago, which I save, and you should look at the figures here:

 

http://www.physics.uc.edu/~sitko/AdvancedAstro/12-Impacts&Atmospheres/archer.ch4.greenhouse_gases.pdf

Because of the greenhouse effect, we need an additional factor in the equation of equilibrium  one that describes the efficiency (or lack thereof) for the planet being able to radiate away energy. To calculate this term, which we will call , is complicated. For this class we shall just see its effect on the temperature of the planet. Including this term we get:

 

 

 

For NO greenhouse effect, , and we get our earlier expression. But if , you can see that the temperature will become higher than in the case of no greenhouse warming.

 

These effects will determine at which distances from the Sun a planet can sustain liquid water, for example (assuming that the atmospheric pressure also allows it of course!). Here are 3 illustrative examples.

 

 

In the last panel. The value of  is too small for the Earth, and way too large for Venus.

 

Structure of the Atmospheres of Terrestrial Planets

 

Temperature Profile

 

As one goes from the surface to outside the atmosphere, the temperature rises and falls.