Dissipation of Planetary Atmospheres

Dissipation of Planetary Atmospheres 

the diffusion of planetary atmospheres owing to the escape of the gases that make up the atmospheres into space. The random thermal motion of the gas particles means that some of them, located in the uppermost layers of the atmosphere, acquire a velocity that exceeds the critical velocity of escape at which a body overcomes the force of gravity and is able to go beyond the limits of the planet’s gravitational field. Thus, dissipation depends on the force of the planet’s gravity; on the temperature of its exosphere, which determines the kinetic energy of the molecules; and on the molecular weight of the particles, on which, according to the kinetic theory of gases, their velocity depends. At each temperature there is an average velocity for molecules of a specified type, from which there is a significant departure for some of the molecules (according to Maxwell’s equation). Consequently, an atmosphere with molecules whose average velocity does not exceed 0.2 of the critical velocity is stable for astronomically long periods of time. When the average thermal velocity is equal to 0.25 of the critical velocity, the atmosphere dissipates within 50,000 years, whereas at a velocity of 0.33 of the critical velocity, it dissipates within a few weeks.

Table 1. Average thermal velocities of molecules
Gas	Molecular weight	Mean square molecular velocity at 0°C (km/sec)
Hydrogen...............	2	1.84
Helium...............	4	1.31
Water vapor...............	18	0.62
Nitrogen...............	28	0.49
Oxygen...............	32	0.46
Carbon dioxide...............	44	0.39

The relation between the average thermal velocities of molecules at 0°C (Table 1) and the critical velocities of escape (Table 2) can be seen by comparing Tables 1 and 2. There-fore, the moon and Mercury cannot have stable atmospheres, on Mars only the heavy gases are stable, only hydrogen and helium escape from earth-type planets, and asteroids and most satellites are totally devoid of atmospheres. The actual state of planetary atmospheres depends on the relation between the processes of atmosphere formation and destruction.

Table 2. Critical velocities of escape
Planet...............	Velocity of escape (km/sec)
Moon...............	2.4
Mercury...............	3.8
Mars...............	5.1
Venus...............	10.4
Earth...............	11.2
Saturn...............	36.7
Jupiter...............	61.0

REFERENCES

Moroz, V. I. Fizika planet. Moscow, 1967.
Atmosfera Zemli i planet. Moscow, 1951. (Collection of articles; translated from English.)
Vvedenie v fiziku Luny. Moscow, 1969.

K. P. FLORENSKII