ATMOSPHERES OF THE TERRESTRIAL PLANETS

The Terrestrial planets are similar to each other in terms of their masses and diameters, and their distances from the Sun. Because of this, it is expected that their atmospheres should share many similar qualities. Despite having several similar qualities, their atmospheres also show significant differences.

Remarks:

• Venus, Earth, and Mars have atmospheres, while there are only traces of an atmosphere on Mercury and the Moon.

• The atmospheres of Venus and Mars are predominantly carbon dioxide while the Earth's atmosphere is 78 % nitrogen and 21 % oxygen

• The Earth is the only planet whose atmosphere contains a significant amount of free oxygen. There is oxygen in Venus's and Mars's atmoshperes, however, it is tied up in the carbon dioxide.

• Venus is essentially void of water, the Earth has abundant water, and Mars shows evidence of water.

• The surface temperatures of the planets vary wildly from T ~ 900 F for Venus to T ~ 70 F for the Earth.

• The atmospheric masses are in the rough ratio of 100:1:0.01 for Venus:Earth:Mars (based on their atmospheric pressures).

There are other differences between the planets, but we consider the above as the key points for developing an understanding of the atmospheric evolution of the Terrrestrial planets.

ORIGIN OF THE ATMOSPHERES

After their formation, the Terrestrial planets essentially had no atmospheres (if they had captured some hydrogen and helium from the Solar Nebula, it was rapidly lost to space). Whatever atmospheres the Terrestrial planets have today was captured or was generated after the planets formed; the Terrestrial planets have secondary atmospheres.

There are two modes for the generation of secondary atmospheres:

• Since the planets formed from the accretion of solid rock particles, volatile elements were trapped inside of them. Later, as the interiors of the planetary bodies heated and melted, the volatiles were released through volcanic eruptions, outgassing.

• The atmospheres were added to the planets after they were formed. This could occur either as a slow capture from the Solar Nebula directly (not likely), from material brought in by the intense Solar Wind from the young Sun, or by comets.

It is not clear which of the above theories are correct.

OUTGASSING

Current studies of Terrestrial volcanoes show that they do emit large amounts of volatile materials such as water, carbon dioxide, nitrogen, and sulfur dioxide, however, it is not clear if enough volatile material can be trapped during the formation of the planets.

For example, consider water. On the Earth, there is enough water to cover the planet to a depth of around 3 kilometers. How much water is this? Well the mass of water on the Earth is

mass of water = x volume

mass of water = 1 gm per cc x 4 R**2 x depth of the oceans

mass of water ~ 1.5x10**24 grams

The current rate of outgassing of water from volcanoes is

Rate = 10**14 grams per year

If this rate is typical, it would have taken roughly 15 billion years to make the oceans via outgassing. If the rate were higher in the past (as it surely must have been), then we could produce the oceans in 4.6 billion years (the age of the Solar System).

"COMETS"

A typical comet might be half water ice. The mass of a 1 km x 1 km x 1 km comet is roughly

comet = 2 grams per cc x (4/3) x 10**15 cc 8x10**15 grams

If half of the comet is water, then we would need roughly 400 million cometary impacts to bring in the water. There are many hundreds of billions of comets in the Oort cloud and so, there is an ample supply of comets, but is the rate of cometary impacts sufficiently large to warrant considering this as a viable model. Based on recent cratering history, the rate of crater formation by 1 km objects is roughly one every few tens of thousands of years. At the current rate, deposition of water by comets would take tens of trillions of years. So, unless the rate was significantly higher in the past (as it probably was) or there is a class of small comets which completely dominates the mass of the typical comet, this scenario has problems.

ATMOSPHERIC RETENTION

Why don't Mercury and the Moon have atmospheres?

There are two competing effects which determine whether a planet retains an atmosphere:

• the strength of the gravitational field at the surface of the planet (as measured by the escape speed of the planet)

• the speed with which the gas particles move around (as determined by the temperature and masses of the particles which make up the atmosphere); The temperature is a measure the average energy of the particles in a gas.
  • For say, a gas of nitrogen molecules, the higher the temperature the faster the molecules move.

  • For a gas of a given temperature less massive particles move faster than more massive particles.

  So, we note that there are two important properties to consider:

  • the mass of the planet is crucial since the escape velocity depends strongly on the mass of the planet (via the gravitational force); the more massive the planet the higher the escape speed

  • the distance of the planet from the Sun since the temperature of the gas depends strongly upon how much energy it absorbs from the Sun; the closer to the Sun the hotter the planet's surface is likely to be (What about Venus? We return to this point later).

  Comment

  An important point to bring up is that the temperature of a gas measures the average energy of the gas particles. That is, some particles have less energy and some particles have more energy than the value given by the temperature. Around 0.1 % of the particles will have energies greater than 10 times the average energy. What this means is that even if the average speed of the gas particles seems too low for atmospheric evaporatation, a non-negligible fraction of the particles will be moving fast enough to escape. It turns out that if

  v/v > 1/6

  then gas particles can escape from the planet in a reasonable amount of time. What is a reasonable amount of time?

  Let us define R = v/v. For the Earth and a 1,000 K gas:

  R-values for Various Gases

  

  So, H and He escape, but the heavier compounds are retained.

  Timescales for Atmospheric Escape

  

EQUILIBRIUM SURFACE TEMPERATURES AND THE GREENHOUSE EFFECT

Let us estimate the surface temperature for the planets. We will define what is known as the Equilibrium Temperature

Assumptions:

• the planet absorbs heat from the Sun at a certain rate and then re-radiates this energy at precisely the same rate (hence, the use of the word equilibrium).

• the planet radiates like an idealized creature which is defined to be a perfect emitter and absorber of radiation)--a blackbody radiator.

For an atmosphereless (and cloudless) planet have,

Temperature a

For a planet with an atmosphere, we need to modify the argument. Due to the presence of the atmosphere not all of the solar radiation strikes the planet. Some of it is reflected by the cloud layer and returns to space. We measure this effect by defining the Albedo for the planet. The

Albedo, A, is the fraction of the solar radiation which is reflected to space. This means that a fraction (1-A) of the radiation reaches the Earth.

Atmospheric Temperatures

For Mars, the two temperatures are roughly the same while for Venus and Earth the temperatures differ significantly. Why? Well, the reason is is that Venus and Earth both exhibit Greenhouse Effects. The Earth has a much milder Greenhouse effect than does Venus, but it still has one. The mild Greenhouse effect is important because it is what makes the planet comfortable.