About the color of the sky
In connection with the well-known events, namely, the beginning of the work of the Curiosity rover on the red planet, the conspiracy moods on the Internet, as well as among the inhabitants of the Habr, have again become aggravated.
Somewhere here it was mentioned about a certain, according to commentators, “yellowish” article, with an explanation that the sky on any planet cannot be constantly reddish. Specifically, the article did not see, so if it is on the habre - then in advance sorry for the potential for duplication.
And now - more to the point. Just briefly talk about the phenomenon of scattering of electromagnetic waves. Do as much as possible without formulas.
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In 1871, John William Strett, better known as Lord Rayleigh (although he was not yet that year), offered a description of scattering based on the classical electrodynamic theory, which subsequently perfectly explained the blue color of the sky during the day and red at sunset.
The process itself occurs when an electromagnetic wave propagates in an environment filled with some small particles. In the case of the Rayleigh model, it works if the size of these particles is much smaller than the wavelength. As applied to visible light, those are the size of the gas molecules that make up the planet’s atmosphere, which determines the observed characteristics of the phenomenon.
So, the wavelength is much larger than the particle size. For this reason, it can be assumed that the particle is in a uniform field, changing in time with the frequency of oscillation of the wave, and as a result of this, the particle, like any material object placed in the field, acquires an electric P and a magnetic M moment. I mean, it becomes a dipole, creating its own electric and magnetic field. The magnitude of the moments, of course, depends on time - they oscillate with the same frequency as the wave.
And the oscillating dipole is obviously an emitter (a significant part of the transmitter antennas works on this principle), and re-radiates the energy incident on it - this is the scattering mechanism in the Rayleigh model. The amplitude of the scattered wave at large (much longer wavelength) distances is proportional to the square of the frequency:
It is also determined by the direction n , in which re-radiation occurs, and by the distance to the dipole R , but at the moment we are not interested.
The intensity is equal to the square of the amplitude, and therefore proportional to the fourth power of the frequency (the formula for the radiation intensity at an infinitely small solid angle):
Thus, the scattering increases sharply with increasing wave frequency (shift to the violet region of the spectrum). The blue and blue colors of the sky (and not purple) are already due to the effects of enhanced absorption at high frequency. At low frequencies, absorption is proportional to the cube of the frequency, and at large frequencies, the fifth power becomes the dominant process (between times, it is precisely because of this that the planet with the atmosphere is effectively protected from external X-ray and gamma radiation of not too high energy).
Both scattering and absorption of electromagnetic waves in the atmosphere sharply increase with decreasing wavelength. Thus, the color of the sky, ceteris paribus, is completely determined by the ratio of these two factors, and nothing else.
On Earth, the atmosphere is quite dense, and therefore the absorption in it is quite strong. Therefore, during the day, when the sun is high, its rays travel a relatively short path in the atmosphere, so that the shortwave part of the spectrum is not strongly absorbed. As it dissipates more strongly, it is the predominant one - the sky becomes blue. And at sunrise and sunset, the light from the sun goes essentially parallel to the local part of the planet’s surface, and its path is many times longer - as a result, not only blue and blue hues are filtered out by absorption, but also green and yellow.
In addition, the dawn light enters the atmosphere at a very acute angle, which determines some role of refraction and dispersion (decomposition occurs into the spectrum) - the red part of the spectrum refracts less and goes a longer way along the surface.
With a relatively low atmospheric density, like on Mars, one should expect, first of all, a noticeable decrease in the intensity of the scattering process. However, the sky from this only becomes darker, but does not blush.
The Rayleigh model, as one would expect, can be obtained from the general theory in the approximation of small sizes of scattering particles. The scattering of an electromagnetic wave on spheres (in the original paper, 1908) of arbitrary size is described in the Mie theory (however, it is often mentioned only in the context of the situation of large particles).
So, if the particles are much larger than the wavelength, the reverse of the Mie theory is inversely applied to Rayleigh. The cause of the scattering is the same - re-radiation of the incident wave energy by oscillating dipoles. Its detailed description is very difficult to do, since for this it is necessary to completely solve the system of Maxwell's equations for a wave in space filled with such scattering objects. Therefore, often, when telling about a given theory, they limit themselves only to listing its features in comparison with the Rayleigh problem. We will use the beaten track and indicate the most characteristic points:
So, the second feature is the most significant. It explains the white and gray color of clouds, fog, dust, the change in the color of the sky from the zenith to the horizon.
On this basis, the sky on Mars should be gray-blue. Blue due to Rayleigh scattering, and gray due to dust constantly hanging in the atmosphere. The latter is due to low gravity and dryness of the rock combined with strong winds.
And the orange and red tint of the sky can only be observed during storms. As, however, and on the Earth occurs (on a picture from Wikipedia - a sand storm in Sydney).
During dust storms, fairly small particles of dust in high concentrations, especially if they are raised several kilometers above the surface, dramatically increase the absorption of the shortwave part of the spectrum, and the red tint becomes predominant. A similar phenomenon can be observed during powerful volcanic eruptions. A vivid historical example is the unusually intense shades of dawns described during the Krakatau eruption (1883).
upd: article in UFN with a detailed review of scattering .
upd 1: When looking at the formula describing absorption, the cube was attributed to the wrong symbol. In fact, the intensity of absorption is proportional at a low frequency - the first degree, at large - the third (and not the third and fifth). The dielectric constant can play a significant role, since it itself is also a function of frequency.
reply
upd 2: As always happens, it was not necessary to think long with numerical estimates. It suffices to compare atmospheric pressures, and see that on Mars the intensity of Rayleigh scattering will be 2-3 orders of magnitude lower than on Earth. Which excludes the visible bluish color of the sky. Is it possible to reveal it in the spectra, for example, by diurnal change. But there is no need, it seems. As a result, the color is almost completely determined by the dust hanging in the atmosphere. And here, due to scattering on large particles, we obtain a uniform effect for any wavelength, which is equivalent to overcast gray color. With amendments to the features of reflection and absorption of the particles themselves.
Somewhere here it was mentioned about a certain, according to commentators, “yellowish” article, with an explanation that the sky on any planet cannot be constantly reddish. Specifically, the article did not see, so if it is on the habre - then in advance sorry for the potential for duplication.
And now - more to the point. Just briefly talk about the phenomenon of scattering of electromagnetic waves. Do as much as possible without formulas.
')
Rayleigh Scattering
In 1871, John William Strett, better known as Lord Rayleigh (although he was not yet that year), offered a description of scattering based on the classical electrodynamic theory, which subsequently perfectly explained the blue color of the sky during the day and red at sunset.
The process itself occurs when an electromagnetic wave propagates in an environment filled with some small particles. In the case of the Rayleigh model, it works if the size of these particles is much smaller than the wavelength. As applied to visible light, those are the size of the gas molecules that make up the planet’s atmosphere, which determines the observed characteristics of the phenomenon.
So, the wavelength is much larger than the particle size. For this reason, it can be assumed that the particle is in a uniform field, changing in time with the frequency of oscillation of the wave, and as a result of this, the particle, like any material object placed in the field, acquires an electric P and a magnetic M moment. I mean, it becomes a dipole, creating its own electric and magnetic field. The magnitude of the moments, of course, depends on time - they oscillate with the same frequency as the wave.
And the oscillating dipole is obviously an emitter (a significant part of the transmitter antennas works on this principle), and re-radiates the energy incident on it - this is the scattering mechanism in the Rayleigh model. The amplitude of the scattered wave at large (much longer wavelength) distances is proportional to the square of the frequency:
It is also determined by the direction n , in which re-radiation occurs, and by the distance to the dipole R , but at the moment we are not interested.
The intensity is equal to the square of the amplitude, and therefore proportional to the fourth power of the frequency (the formula for the radiation intensity at an infinitely small solid angle):
Thus, the scattering increases sharply with increasing wave frequency (shift to the violet region of the spectrum). The blue and blue colors of the sky (and not purple) are already due to the effects of enhanced absorption at high frequency. At low frequencies, absorption is proportional to the cube of the frequency, and at large frequencies, the fifth power becomes the dominant process (between times, it is precisely because of this that the planet with the atmosphere is effectively protected from external X-ray and gamma radiation of not too high energy).
Both scattering and absorption of electromagnetic waves in the atmosphere sharply increase with decreasing wavelength. Thus, the color of the sky, ceteris paribus, is completely determined by the ratio of these two factors, and nothing else.
On Earth, the atmosphere is quite dense, and therefore the absorption in it is quite strong. Therefore, during the day, when the sun is high, its rays travel a relatively short path in the atmosphere, so that the shortwave part of the spectrum is not strongly absorbed. As it dissipates more strongly, it is the predominant one - the sky becomes blue. And at sunrise and sunset, the light from the sun goes essentially parallel to the local part of the planet’s surface, and its path is many times longer - as a result, not only blue and blue hues are filtered out by absorption, but also green and yellow.
In addition, the dawn light enters the atmosphere at a very acute angle, which determines some role of refraction and dispersion (decomposition occurs into the spectrum) - the red part of the spectrum refracts less and goes a longer way along the surface.
With a relatively low atmospheric density, like on Mars, one should expect, first of all, a noticeable decrease in the intensity of the scattering process. However, the sky from this only becomes darker, but does not blush.
Scattering mi
The Rayleigh model, as one would expect, can be obtained from the general theory in the approximation of small sizes of scattering particles. The scattering of an electromagnetic wave on spheres (in the original paper, 1908) of arbitrary size is described in the Mie theory (however, it is often mentioned only in the context of the situation of large particles).
So, if the particles are much larger than the wavelength, the reverse of the Mie theory is inversely applied to Rayleigh. The cause of the scattering is the same - re-radiation of the incident wave energy by oscillating dipoles. Its detailed description is very difficult to do, since for this it is necessary to completely solve the system of Maxwell's equations for a wave in space filled with such scattering objects. Therefore, often, when telling about a given theory, they limit themselves only to listing its features in comparison with the Rayleigh problem. We will use the beaten track and indicate the most characteristic points:
- The complexity of the description is due to the fact that for large particle sizes the approximation of a uniform field becomes unacceptable.
- For large particle sizes, the scattering intensity is almost independent of the wavelength.
So, the second feature is the most significant. It explains the white and gray color of clouds, fog, dust, the change in the color of the sky from the zenith to the horizon.
On this basis, the sky on Mars should be gray-blue. Blue due to Rayleigh scattering, and gray due to dust constantly hanging in the atmosphere. The latter is due to low gravity and dryness of the rock combined with strong winds.
And the orange and red tint of the sky can only be observed during storms. As, however, and on the Earth occurs (on a picture from Wikipedia - a sand storm in Sydney).
During dust storms, fairly small particles of dust in high concentrations, especially if they are raised several kilometers above the surface, dramatically increase the absorption of the shortwave part of the spectrum, and the red tint becomes predominant. A similar phenomenon can be observed during powerful volcanic eruptions. A vivid historical example is the unusually intense shades of dawns described during the Krakatau eruption (1883).
upd: article in UFN with a detailed review of scattering .
upd 1: When looking at the formula describing absorption, the cube was attributed to the wrong symbol. In fact, the intensity of absorption is proportional at a low frequency - the first degree, at large - the third (and not the third and fifth). The dielectric constant can play a significant role, since it itself is also a function of frequency.
reply
upd 2: As always happens, it was not necessary to think long with numerical estimates. It suffices to compare atmospheric pressures, and see that on Mars the intensity of Rayleigh scattering will be 2-3 orders of magnitude lower than on Earth. Which excludes the visible bluish color of the sky. Is it possible to reveal it in the spectra, for example, by diurnal change. But there is no need, it seems. As a result, the color is almost completely determined by the dust hanging in the atmosphere. And here, due to scattering on large particles, we obtain a uniform effect for any wavelength, which is equivalent to overcast gray color. With amendments to the features of reflection and absorption of the particles themselves.
Source: https://habr.com/ru/post/149860/
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