MORE PRECISELY 8-1 Why Air Sticks Around
Some planets and moons in the solar system—for example, Venus and Titan (the largest moon of Saturn)—have atmospheres thicker than Earth's. Other objects—such as Mars—have thinner atmospheres. Still others—the Moon and Mercury, for example—have virtually no atmospheres at all. The jovian planets have atmospheres rich in hydrogen, while gaseous hydrogen is rare on the terrestrial worlds.

Why do some planets and moons have atmospheres, while others do not, and what determines the composition of the atmosphere if one exists? Why does a layer of air, made up mostly of nitrogen and oxygen, lie just above Earth's surface? After all, experience shows that most gas naturally expands to fill all the volume available. Perfume in a room, fumes from a poorly running engine, and steam from a tea kettle all rapidly disperse until we can hardly sense them. Why doesn't our planet's atmosphere similarly disperse by floating away into space?

The answer is that gravity holds it down. Earth's gravitational field exerts a pull on all the atoms and molecules in our atmosphere, preventing them from escaping. However, gravity is not the only influence acting, for if it were, all of Earth's air would have fallen to the surface long ago. Heat competes with gravity to keep the atmosphere buoyant. All gas molecules are in constant random motion. The temperature of the gas is a direct measure of this motion—the hotter the gas, the faster the molecules are moving (see More Precisely 3-1). The Sun continuously supplies heat to our planet's atmosphere, and the resulting rapid movement of heated molecules produces pressure. This pressure tends to oppose the force of gravity, exerting a net upward force and preventing our atmosphere from collapsing under its own weight. Let's explore this competition between gravity and heat in a little more detail.

An important measure of the strength of a body's gravity is its escape speed—the speed needed for any object to escape forever from its surface. (Sec. 2.7) This speed increases with increased mass or decreased radius of the parent body (often a moon or a planet). Mathematically, it can be expressed as follows:

Thus, if the mass of the parent were to quadruple, the escape speed would double. If the parent's radius were to quadruple, then the escape speed would be halved, and so on.

To determine whether a planet will retain an atmosphere, we must compare the planet's escape speed with the molecular speed, which is the average speed of the gas particles making up the atmosphere. This speed actually depends not only on the temperature of the gas but also on the mass of the individual molecules—the hotter the gas or the smaller the molecular mass, the higher the average speed of the molecules:

Thus, increasing the temperature of a sample of gas by a factor of 4—for example, from 100 K to 400 K—doubles the average speed of its constituent molecules; at a given temperature, molecules of hydrogen (molecular mass 2) in air move, on average, 4 times faster than molecules of oxygen (molecular mass 32), which are 16 times heavier.

For nitrogen (molecular mass 28) and oxygen in Earth's atmosphere, where the temperature near the surface is nearly 300 K, the typical molecular speed is about 0.5 km/s (actually, 0.52 km/s), far smaller than the 11.2 km/s needed for a molecule to escape into space (see the Earth Data Box). As a result, Earth is able to retain its nitrogen—oxygen atmosphere. On the whole, our planet's gravity simply has more influence than the heat of our atmosphere.

In reality the situation is a little more complicated than this simple comparison of speeds. Atmospheric molecules can gain or lose speed by bumping into one another or by colliding with objects near the ground. Thus, although we can characterize a gas by its average molecular speed, the molecules do not all move at the same speed, as illustrated in the accompanying figure. A tiny fraction of the molecules in any gas have speeds much greater than average—one molecule in 2 million has a speed more than three times the average, and one in 1016 exceeds the average by more than a factor of 5. This means that at any instant, some molecules are moving fast enough to escape, even when the average molecular speed is much less than the escape speed. The result is that all planetary atmospheres slowly leak away into space.

Don't be alarmed—the leakage is usually very gradual! As a rule of thumb, if the escape speed from a planet exceeds the average speed of a given type of molecule by a factor of 6 or more, then molecules of that type will not have escaped from the planet's atmosphere in significant quantities in the 4.6 billion years since the solar system formed. Conversely, if the escape speed is less than six times the average speed of molecules of a given type, then most of them will have escaped by now, and we should not expect to find them in the atmosphere.

For air on Earth, the mean molecular speeds of oxygen and nitrogen are comfortably below one-sixth of the escape speed. However, if the Moon originally had an Earth-like atmosphere, that lunar atmosphere would have been heated by the Sun to much the same temperature as Earth's air today, so the average molecular speed would have been about 0.5 km/s. Because the Moon's escape speed is only 2.4 km/s, any original lunar atmosphere long ago dispersed into interplanetary space. Similarly, Mercury's escape speed is 4.2 km/s. Its peak surface temperature is around 700 K, corresponding to an average molecular speed for nitrogen or oxygen of about 0.8 km/s, more than one-sixth of the escape speed, so there has been ample time for those gases to escape.

We can also use these arguments to understand some aspects of atmospheric composition. For example, hydrogen molecules move, on average, at about 2 km/s in Earth's atmosphere at sea level, so they have had plenty of time to escape since our planet formed (6 2 km/s = 12 km/s, which is greater than Earth's 11.2 km/s escape speed). Consequently, we find very little hydrogen in Earth's atmosphere today. However, on the planet Jupiter, with a lower temperature (about 100 K), the speed of hydrogen molecules is correspondingly lower—about 1.1 km/s. At the same time, Jupiter's escape speed is 60 km/s, over five times higher than on Earth. For those reasons, Jupiter has retained its hydrogen—in fact, hydrogen is the dominant ingredient of Jupiter's atmosphere.