Exosphere

Earth atmosphere diagram showing the exosphere and other layers. The layers are to scale. From Earth's surface to the top of the stratosphere (50km) is just under 1% of Earth's radius.

The exosphere (Ancient Greek: ἔξω [éxō] Error: {{Lang}}: text has italic markup (help) "outside, external, beyond", Ancient Greek: σφαῖρα [sphaĩra] Error: {{Lang}}: text has italic markup (help) "sphere") is the uppermost layer of Earth's atmosphere. An upward traveling molecule moving through the exosphere fast enough to attain escape velocity can escape to space with a low chance of collisions; if it is moving below escape velocity it will be prevented from escaping from the celestial body by gravity. In either case, such a molecule is unlikely to collide with another molecule due to the exosphere's low density.

The term is also used for extremely thin atmospheres such as those of Saturn's moons Rhea and Dione. These kind of atmospheres can be called surface-bounded exospheres.

Earth's exosphere

The main gases within the Earth's exosphere are the lightest gases, mainly hydrogen, with some helium, carbon dioxide, and atomic oxygen near the exobase. The exosphere is the last layer before outer space. Since there is no clear boundary between outer space and the exosphere, the exosphere is sometimes considered a part of outer space.

Lower boundary

The altitude of its lower boundary, known as the thermopause and exobase, ranges from about 250 to 500 kilometres (160 to 310 mi) depending on solar activity. Its lower boundary at the edge of the thermosphere has sometimes been estimated to be 500 to 1,000 km (310 to 620 mi) above the Earth's surface. The exobase is also called the critical level, the lowest altitude of the exosphere, and is typically defined in one of two ways:

1. The height above which there are negligible atomic collisions between the particles (free molecular flow) and
2. The height above which constituent atoms are on purely ballistic trajectories.

If we define the exobase as the height at which upward traveling molecules experience one collision on average, then at this position the mean free path of a molecule is equal to one pressure scale height. This is shown in the following. Consider a volume of air, with horizontal area $A$ and height equal to the mean free path $l$, at pressure $p$ and temperature $T$. For an ideal gas, the number of molecules contained in it is:

$n={\frac {pAl}{RT}}$

where $R$ is the universal gas constant. From the requirement that each molecule traveling upward undergoes on average one collision, the pressure is:

$p={\frac {m_{A}ng}{A}}$

where $m_{A}$ is the mean molecular mass of the gas. Solving these two equations gives:

$l={\frac {RT}{m_{A}g}}$

which is the equation for the pressure scale height. As the pressure scale height is almost equal to the density scale height of the primary constituent, and since the Knudsen number is the ratio of mean free path and typical density fluctuation scale, this means that the exobase lies in the region where $\mathrm {Kn} (h_{EB})\simeq 1$.

The fluctuation in the height of the exobase is important because this provides atmospheric drag on satellites, eventually causing them to fall from orbit if no action is taken to maintain the orbit.

Upper boundary

In principle, the exosphere covers all distances where particles are still gravitationally bound to Earth, i.e. particles still have ballistic orbits that will take them back towards Earth. Theoretically, the upper boundary of the exosphere can be defined as the distance at which the influence of solar radiation pressure on atomic hydrogen exceeds that of the Earth’s gravitational pull. This happens at half the distance to the Moon (190,000 kilometres (120,000 mi)). The exosphere observable from space as the geocorona is seen to extend to at least 100,000 kilometres (62,000 mi) from the surface of the Earth. The exosphere is a transitional zone between Earth’s atmosphere and interplanetary space.

References

• Gerd W. Prolss: Physics of the Earth's Space Environment: An Introduction. ISBN 3-540-21426-7