# 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 "outside, external, beyond", Ancient Greek: σφαῖρα sphaĩra "sphere") is the uppermost layer of Earth's atmosphere. In the exosphere the density is so low that particles collide only rarely. That makes it possible for energetic particles to escape Earth's gravity altogether.

## Earth's exosphere

The main gases within the Earth's atmosphere are the lightest atmospheric gases, mainly hydrogen, with some helium, carbon dioxide, and atomic oxygen near the exobase. 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 lower boundary of the exosphere is known as exobase; it is also called the thermopause as in Earth's atmosphere the atmospheric temperature becomes nearly a constant above this altitude. Before the term exobase was established this boundary was also called the critical level where barometric law no longer applies.[1] The altitude of the exobase ranges from about 500 to 1,000 kilometres (310 to 620 mi) depending on solar activity.[citation needed]

The exobase can 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:

$l = \frac{R T} {m_{A}g}$

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

1. ^ Bauer & Lammer, Planetary Aeronomy: Atmosphere Environments in Planetary Systems, Springer, 2004.
• Gerd W. Prolss: Physics of the Earth's Space Environment: An Introduction. ISBN 3-540-21426-7