Albedo of water. Albedo effect and global warming

The total radiation that has reached the earth's surface is partially absorbed by soil and water bodies and converted into heat; it is spent on the oceans and seas for evaporation, and is partially reflected into the atmosphere (reflected radiation). The ratio of absorbed and reflected radiant energy depends on the nature of the land, on the angle of incidence of the rays on the water surface. Since it is practically impossible to measure the absorbed energy, the value of the reflected energy is determined.

The reflectivity of land and water surfaces is called their albedo. It is calculated as a percentage of the reflected radiation from the incident on a given surface, along with the angle (more precisely, the sine of the angle) of incidence of the rays and the amount of optical masses of the atmosphere they pass through, is one of the most important planetary factors of climate formation.

On land, albedo is determined by the color of natural surfaces. All radiation is able to assimilate a completely black body. The mirror surface reflects 100% of the rays and is not able to heat up. Of real surfaces, pure snow has the highest albedo. Below are the albedo of land surfaces by natural zones.

The climate-forming value of the reflectivity of different surfaces is extremely high. In ice zones at high latitudes, solar radiation, already weakened by the passage of a large number of optical masses of the atmosphere and falling on the surface at an acute angle, is reflected by eternal snow.

The albedo of a water surface for direct radiation depends on the angle at which the sun's rays fall on it. Vertical rays penetrate deep into the water, and it assimilates their heat. Inclined rays from the water are reflected, as from a mirror, and it is not heated: the albedo of the water surface at a Sun height of 90 "is 2%, at a Sun height of 20 ° - 78%.

Surface views and zonal landscapes Albedo

Fresh dry snow…………………………………………… 80-95

Wet snow………………………………………………….. 60-70

Sea ice…………………………………………………….. 30-40

Tundra without snow cover………………………….. 18

Stable snow cover in temperate latitudes 70

The same unstable……………………………………….. 38

Coniferous forest in summer…………………………………………. 10-15

The same, with stable snow cover……….. 45

Deciduous forest in summer……………………………………. 15-20

The same, with yellow leaves in autumn……………….. 30-40

Meadow…………………………………………………………………… 15-25

Steppe in summer…………………………………………………….. 18

Sand of different colors…………………………………….. 25-35

Desert………………………………………………………….. 28

Savannah in dry season……………………………………… 24

The same, in the rainy season………………………………………. eighteen

The entire troposphere………………………………………………… 33

Earth as a whole (planet)…………………………………….. 45

For scattered radiation, the albedo is somewhat less.
Since 2/3 of the earth's area is occupied by the ocean, the assimilation of solar energy by the water surface acts as an important climate-forming factor.

Oceans in subpolar latitudes assimilate only a small fraction of the heat of the Sun that reaches them. Tropical seas, on the contrary, absorb almost all solar energy. The albedo of the water surface, like the snow cover of the polar countries, deepens the zonal differentiation of climates.

In the temperate zone, the reflectivity of surfaces enhances the difference between the seasons of the year. In September and March, the Sun is at the same height above the horizon, but March is colder than September, as the sun's rays are reflected from the snow cover. The appearance of first yellow leaves in autumn, and then hoarfrost and temporary snow increases the albedo and reduces the air temperature. The stable snow cover caused by low temperatures accelerates the cooling and further reduction of winter temperatures.

The long-term albedo trend is directed towards cooling. In recent years, satellite measurements show a slight trend.

Changing the Earth's albedo is potentially a powerful impact on climate. As albedo, or reflectivity, increases, more sunlight is reflected back into space. This has a cooling effect on global temperatures. On the contrary, a decrease in albedo heats up the planet. A change in albedo of only 1% gives a radiative effect of 3.4 W/m2, comparable to the effect of CO2 doubling. How has albedo affected global temperatures in recent decades?

Albedo trends up to 2000

The Earth's albedo is determined by several factors. Snow and ice reflect light well, so when they melt, the albedo goes down. Forests have a lower albedo than open spaces, so deforestation increases albedo (let's say that deforestation will not stop global warming). Aerosols have a direct and indirect effect on albedo. The direct influence is the reflection of sunlight into space. An indirect effect is the action of aerosol particles as centers of moisture condensation, which affects the formation and lifetime of clouds. Clouds, in turn, affect global temperatures in several ways. They cool the climate by reflecting sunlight, but can also have a heating effect by retaining outgoing infrared radiation.

All these factors should be taken into account when summing up the various radiative forcings that determine the climate. Land-use change is calculated from historical reconstructions of changes in cropland and pasture composition. Observations from satellites and from the ground make it possible to determine trends in the level of aerosols and cloud albedo. It can be seen that cloud albedo is the strongest factor of the various types of albedo. The long-term trend is towards cooling, the impact is -0.7 W/m2 from 1850 to 2000.

Fig.1 Average annual total radiative forcing(Chapter 2 of the IPCC AR4).

Albedo trends since 2000.

One way to measure the Earth's albedo is by the Moon's ashen light. This is sunlight, first reflected by the Earth and then reflected back to Earth by the Moon at night. The Moon's ash light has been measured by the Big Bear Solar Observatory since November 1998 (a number of measurements were also made in 1994 and 1995). Fig. 2 shows albedo changes from satellite data reconstruction (black line) and from lunar ash light measurements (blue line) (Palle 2004).

Fig.2 Changes in albedo reconstructed from ISCCP satellite data (black line) and changes in the moon's ash light (black line). The right vertical scale shows the negative radiative forcing (ie cooling) (Palle 2004).

The data in Figure 2 is problematic. Black line, ISCCP satellite data reconstruction" is a purely statistical parameter and has little physical meaning because it does not take into account the non-linear relationships between cloud and surface properties and planetary albedo, nor does it include aerosol albedo changes, such as those associated with Mount Pinatubo or anthropogenic sulfate emissions(Real Climate).

Even more problematic is the albedo peak around 2003, visible in the moon's blue ashen light line. It strongly contradicts the satellite data showing a slight trend at this time. For comparison, we can recall the Pinatubo eruption in 1991, which filled the atmosphere with aerosols. These aerosols reflected sunlight, creating a negative radiative forcing of 2.5 W/m2. This has drastically lowered the global temperature. The ash light data then showed an exposure of almost -6 W/m2, which should have meant an even greater drop in temperature. No similar events occurred in 2003. (Wielicki 2007).

In 2008, the reason for the discrepancy was discovered. The Big Bear Observatory installed a new telescope to measure lunar ashlight in 2004. With the new improved data, they recalibrated their old data and revised their albedo estimates (Palle 2008). Rice. 3 shows the old (black line) and updated (blue line) albedo values. The anomalous peak of 2003 has disappeared. However, the trend of increasing albedo from 1999 to 2003 has been preserved.

Rice. 3 Change in the Earth's albedo according to measurements of the moon's ashy light. The black line is the albedo changes from a 2004 publication (Palle 2004). Blue line - updated albedo changes after improved data analysis procedure, also includes data over a longer period of time (Palle 2008).

How accurately is the albedo determined from the moon's ashen light? The method is not global in scope. It affects about a third of the Earth in each observation, some areas always remain "invisible" from the observation site. In addition, measurements are infrequent and are made in a narrow wavelength range of 0.4-0.7 µm (Bender 2006).

In contrast, satellite data such as CERES is a global measurement of Earth's shortwave radiation, including all effects of surface and atmospheric properties. Compared to ash light measurements, they cover a wider range (0.3-5.0 µm). An analysis of the CERES data shows no long-term albedo trend from March 2000 to June 2005. Comparison with three independent datasets (MODIS, MISR and SeaWiFS) shows a "remarkable fit" for all 4 results (Loeb 2007a).

Rice. 4 Monthly changes in mean CERES SW TOA flux and MODIS cloud fraction ().

Albedo has been affecting global temperatures - mostly in the direction of cooling in a long-term trend. In terms of recent trends, the ashlight data shows an increase in albedo from 1999 to 2003 with little change after 2003. Satellites show little change since 2000. The radiative forcing from albedo changes has been minimal in recent years.

To understand the processes that affect the climate of our planet, let's recall some terms.

the greenhouse effect- this is the increase in the temperature of the lower layers of the atmosphere compared to the temperature of the thermal radiation of the planet. The essence of the phenomenon lies in the fact that the surface of the planet absorbs solar radiation, mainly in the visible range and, heating up, radiates it back into space, but already in the infrared range. A significant part of the Earth's infrared radiation is absorbed by the atmosphere and partly re-radiated to the Earth. This effect of mutual radiant heat transfer in the lower layers of the atmosphere is called the greenhouse effect. The greenhouse effect is a natural element of the Earth's heat balance. Without the greenhouse effect, the average surface temperature of the planet would be -19°C instead of the real +14°C. Over the past few decades, various national and international organizations have been defending the hypothesis that human activity leads to an increase in the greenhouse effect, and, therefore, to additional heating of the atmosphere. At the same time, there are alternative points of view, for example, linking temperature changes in the Earth's atmosphere with natural cycles of solar activity.(1)

The fifth assessment report of the Intergovernmental Panel on Climate Change (2013-2014) states that, with a probability of more than 95%, human influence has been the dominant cause of warming observed since the mid-20th century. The consistency of observed and calculated changes throughout the climate system indicates that observed climate changes are caused primarily by increases in atmospheric concentrations of greenhouse gases due to human activities.

The current climate change in Russia as a whole should be characterized as continuing warming at a rate more than two and a half times the average rate of global warming.(2)

diffuse reflection- this is a reflection of the light flux incident on the surface, in which the reflection occurs at an angle different from the incident. Diffuse reflection becomes if the surface irregularities are of the order of the wavelength (or exceed it) and are arranged randomly. (3)

Earth Albedo(A.Z.) - The percentage of solar radiation given off by the globe (together with the atmosphere) back into world space, to the solar radiation that arrived at the boundary of the atmosphere. The return of solar radiation by the Earth is composed of reflection from the earth's surface, scattering of direct radiation by the atmosphere into the world space (backscattering) and reflection from the upper surface of the clouds. A. 3. in the visible part of the spectrum (visual) - about 40%. For the integral flux of solar radiation, the integral (energy) A. 3. is about 35%. In the absence of clouds, visual A. 3. would be about 15%. (4)

Spectral range of the electromagnetic radiation of the Sun- extends from radio waves to X-rays. However, the maximum of its intensity falls on the visible (yellow-green) part of the spectrum. At the boundary of the earth's atmosphere, the ultraviolet part of the solar spectrum is 5%, the visible part is 52% and the infrared part is 43%, at the Earth's surface the ultraviolet part is 1%, the visible part is 40% and the infrared part of the solar spectrum is 59%. (5)

solar constant- the total power of solar radiation passing through a single area, oriented perpendicular to the flow, at a distance of one astronomical unit from the Sun outside the earth's atmosphere. According to extra-atmospheric measurements, the solar constant is 1367 W/m².(3)

Earth surface area– 510,072,000 km2.

1. Main part.

Changes in the current climate (in the direction of warming) are called global warming.

The simplest mechanism of global warming is as follows.

Solar radiation, entering the atmosphere of our planet, on average, is reflected by 35%, which is the integral albedo of the Earth. Most of the remainder is absorbed by the surface, which heats up. The rest is taken up by plants through photosynthesis.

The heated surface of the Earth begins to radiate in the infrared range, but this radiation does not escape into space, but is delayed by greenhouse gases. We will not consider types of greenhouse gases. The more greenhouse gases, the more heat they radiate back to the Earth, and the higher, accordingly, the average temperature of the Earth's surface becomes.

The Paris Agreement, an agreement under the United Nations Framework Convention on Climate Change, addresses the need to "keep global mean temperature rises 'well below' 2°C and 'make efforts' to limit temperature increases to 1.5°C". But in it, apart from reducing greenhouse gas emissions, there is no algorithm for solving this problem.

Given that the United States withdrew from this agreement on June 01, 2017, a new international project is needed. And Russia can offer it.

The main advantage of the new agreement should be a clear and effective mechanism for mitigating the impact of greenhouse gases on the Earth's climate.

The most interesting way to reduce the impact of greenhouse gases on the climate may be to increase the average albedo of the Earth.

Let's take a closer look at it.

In Russia, there are about 625,000 km of roads covered with asphalt, in China and the USA - an order of magnitude more in total.

Even if we assume that all roads in Russia are single-lane and category 4 (which is absurd in itself), then the minimum width will be 3m (according to SNiP 2.07.01-89). The road area will be 1875 km2. Or 1,875,000,000 m2.

The solar constant outside the atmosphere, as we remember, is 1.37 kW/m2.

To simplify, let's take the middle band, where the solar energy at the earth's surface (an average value for the year) will be approximately equal to 0.5 kW/m2.

We get that the power of solar radiation falls on the roads of the Russian Federation 937,500,000 watts.

Now we divide this number by 2. The earth is spinning. It turns out 468,750,000 watts.

The average integral albedo of asphalt is 20%.

By adding pigment or broken glass, the visible albedo of asphalt can be increased up to 40%. The pigment must spectrally match the radiation range of our star. Those. have yellow-green colors. But, at the same time - not to worsen the physical characteristics of asphalt concrete and to be as cheap and easy as possible in synthesis.

With the gradual replacement of old asphalt concrete with a new one, in the process of natural wear of the first one, the total increase in the reflected radiation power will be 469 MW x 0.4 (visible part of the solar spectrum) x0.2 (difference between the old and new albedo) 37.5 MW.

We do not take into account the infrared component of the spectrum, because it will be absorbed by greenhouse gases.

In the whole world, this value will be more than 500 MW. This is 0.00039% of the total incoming radiation power to the Earth. And to eliminate the greenhouse effect, it is necessary to reflect the power by 3 orders of magnitude more.

The situation on the planet will worsen and the melting of glaciers, because. their albedo is very high.

The total radiation reaching the earth's surface is not completely absorbed by it, but is partially reflected from the earth. Therefore, when calculating the arrival of solar energy for a place, it is necessary to take into account the reflectivity of the earth's surface. Reflection of radiation also occurs from the surface of clouds. The ratio of the entire flux of short-wave radiation Rk reflected by a given surface in all directions to the radiation flux Q incident on this surface is called albedo(A) given surface. This value

shows how much of the radiant energy incident on the surface is reflected from it. Albedo is often expressed as a percentage. Then

(1.3)

In table. No. 1.5 gives the albedo values ​​for various types of the earth's surface. From the data in Table. 1.5 shows that freshly fallen snow has the highest reflectivity. In some cases, a snow albedo of up to 87% was observed, and in the conditions of the Arctic and Antarctic, even up to 95%. Packed, melted and even more polluted snow reflects much less. Albedo of various soils and vegetation, as follows from Table. 4, differ relatively slightly. Numerous studies have shown that the albedo often changes during the day.

The highest albedo values ​​are observed in the morning and evening. This is explained by the fact that the reflectivity of rough surfaces depends on the angle of incidence of sunlight. With a vertical fall, the sun's rays penetrate deeper into the vegetation cover and are absorbed there. At a low height of the sun, the rays penetrate less into the vegetation and are reflected to a greater extent from its surface. The albedo of water surfaces is, on average, less than the albedo of the land surface. This is explained by the fact that the sun's rays (the short-wave green-blue part of the solar spectrum) penetrate to a large extent into the upper layers of water that are transparent to them, where they are scattered and absorbed. In this regard, the degree of its turbidity affects the reflectivity of water.

Table No. 1.5

For polluted and turbid water, the albedo increases noticeably. For scattered radiation, the albedo of water is on average about 8-10%. For direct solar radiation, the albedo of the water surface depends on the height of the sun: with a decrease in the height of the sun, the albedo value increases. So, with a sheer incidence of rays, only about 2-5% is reflected. When the sun is low above the horizon, 30-70% is reflected. The reflectivity of the clouds is very high. The average cloud albedo is about 80%. Knowing the value of the surface albedo and the value of the total radiation, it is possible to determine the amount of radiation absorbed by a given surface. If A is the albedo, then the value a \u003d (1-A) is the absorption coefficient of a given surface, showing what part of the radiation incident on this surface is absorbed by it.

For example, if a total radiation flux Q = 1.2 cal / cm 2 min falls on the surface of green grass (A \u003d 26%), then the percentage of absorbed radiation will be

Q \u003d 1 - A \u003d 1 - 0.26 \u003d 0.74, or a \u003d 74%,

and the amount of absorbed radiation

B absorb \u003d Q (1 - A) \u003d 1.2 0.74 \u003d 0.89 cal / cm2 min.

The albedo of the surface of water is highly dependent on the angle of incidence of the sun's rays, since pure water reflects light according to Fresnel's law.

where Z P – zenith angle of the sun Z 0 is the angle of refraction of the sun's rays.

At the position of the Sun at the zenith, the albedo of the surface of a calm sea is 0.02. With an increase in the zenith angle of the Sun Z P albedo increases and reaches 0.35 at Z P\u003d 85. The excitement of the sea leads to a change Z P , and significantly reduces the range of albedo values, since it increases at large Z n due to an increase in the probability of rays hitting an inclined wave surface. Excitement affects the reflectivity not only due to the inclination of the wave surface relative to the sun's rays, but also due to the formation of air bubbles in the water. These bubbles scatter light to a large extent, increasing the diffuse radiation coming out of the sea. Therefore, during high sea waves, when foam and lambs appear, the albedo increases under the influence of both factors. Scattered radiation enters the water surface at different angles. cloudless sky. It also depends on the distribution of clouds in the sky. Therefore, the sea surface albedo for diffuse radiation is not constant. But the boundaries of its fluctuations are narrower 1 from 0.05 to 0.11. Consequently, the albedo of the water surface for total radiation varies depending on the height of the Sun, the ratio between direct and scattered radiation, sea surface waves. It should be borne in mind that the northern parts oceans are heavily covered with sea ice. In this case, the albedo of ice must also be taken into account. As you know, significant areas of the earth's surface, especially in middle and high latitudes, are covered with clouds that reflect solar radiation very much. Therefore, knowledge of the cloud albedo is of great interest. Special measurements of cloud albedo were carried out with the help of airplanes and balloons. They showed that the albedo of clouds depends on their shape and thickness. The albedo of altocumulus and stratocumulus clouds has the highest values. clouds Cu - Sc - about 50%.

The most complete data on cloud albedo obtained in Ukraine. The dependence of the albedo and the transmission function p on the thickness of the clouds, which is the result of the systematization of the measurement data, is given in Table. 1.6. As can be seen, an increase in cloud thickness leads to an increase in albedo and a decrease in the transmission function.

Average albedo for clouds St with an average thickness of 430 m is 73%, for clouds Swith at an average thickness of 350 m - 66%, and the transmission functions for these clouds are 21 and 26%, respectively.

The albedo of clouds depends on the albedo of the earth's surface. r 3 over which the cloud is located. From a physical point of view, it is clear that the more r 3 , the greater the flux of reflected radiation passing upward through the upper boundary of the cloud. Since albedo is the ratio of this flow to the incoming one, an increase in the albedo of the earth's surface leads to an increase in the albedo of clouds. The study of the properties of clouds to reflect solar radiation was carried out using artificial Earth satellites by measuring the brightness of clouds. The average cloud albedo values ​​obtained from these data are given in table 1.7.

Table 1.7 - Average albedo values ​​of clouds of different forms

According to these data, cloud albedo ranges from 29 to 86%. Noteworthy is the fact that cirrus clouds have a small albedo compared to other cloud forms (with the exception of cumulus). Only cirrostratus clouds, which are thicker, largely reflect solar radiation (r= 74%).

The problem of asteroid-comet hazard, i.e., the threat of a collision between the Earth and small bodies of the solar system, is recognized today as a complex global problem facing humanity. This collective monograph summarizes data on all aspects of the problem for the first time. Modern ideas about the properties of small bodies of the Solar System and the evolution of their ensemble, the problems of detection and monitoring of small bodies are considered. The issues of assessing the level of threat and the possible consequences of falling bodies to Earth, ways of protecting and reducing damage, as well as ways to develop domestic and international cooperation on this global problem are discussed.

The book is intended for a wide range of readers. Scientists, teachers, graduate students and students of various specialties, including, first of all, astronomy, physics, earth sciences, space technicians and, of course, readers interested in science, will find a lot of interesting things for themselves.

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Asteroids, like all bodies of the solar system except the central body, shine by the reflected light of the Sun. When observing, the eye registers the light flux scattered by the asteroid towards the Earth and passing through the pupil. A characteristic of the subjective sensation of a light flux of varying intensity coming from asteroids is their brilliance. It is this term (rather than brightness) that is recommended for use in the scientific literature. In fact, the eye reacts to the illumination of the retina, i.e., to the luminous flux per unit area of ​​the area perpendicular to the line of sight, at a distance of the Earth. Illumination is inversely proportional to the square of the asteroid's distance from Earth. Considering that the flux scattered by an asteroid is inversely proportional to the square of its distance from the Sun, it can be concluded that the illumination on Earth is inversely proportional to the square of the distance from the asteroid to the Sun and to the Earth. Thus, if we denote the illumination created by an asteroid located at a distance r from the Sun and? from the Earth, through E, and through E 1 - the illumination created by the same body, but located at a unit distance from the Sun and from the Earth, then

E \u003d E 1 r -2? -2 . (3.2)

In astronomy, illumination is usually expressed in stellar magnitudes. An illumination interval of one magnitude is the ratio of illuminations created by two sources, in which the illumination from one of them is 2.512 times greater than the illumination created by the other. In a more general case, the Pogson formula holds:

E m1 /E m2 = 2.512 (m2-m1) , (3.3)

where E m1 - illumination from a source with magnitude m 1, E m2 - illumination from a source with magnitude m 2 (the smaller the illumination, the greater the magnitude). From these formulas follows the dependence of the brightness of the asteroid m, expressed in magnitudes, on the distance r from the Sun and? from the earth:

m = m 0 + 5 lg(r?), (3.4)

where m 0 is the so-called absolute magnitude of the asteroid, numerically equal to the magnitude that the asteroid would have, being at a distance of 1 AU. from the Sun and the Earth and at a zero phase angle (recall that the phase angle is the angle at the asteroid between the directions to the Earth and to the Sun). Obviously, such a configuration of three bodies cannot be realized in nature.

Formula (3.4) does not fully describe the change in the brightness of an asteroid during its orbital motion. In fact, the brightness of an asteroid depends not only on its distance from the Sun and Earth, but also on the phase angle. This dependence is associated, on the one hand, with the presence of damage (the part of the asteroid not illuminated by the Sun) when observed from the Earth at a non-zero phase angle, and, on the other hand, with the micro- and macrostructure of the surface.

It must be borne in mind that the asteroids of the Main Belt can only be observed at relatively small phase angles, up to about 30°.

Until the 80s. 20th century It was believed that adding a term proportional to the phase angle to formula (3.4) makes it possible to fairly well take into account the change in brightness depending on the phase angle:

m = m0 + 5 lg(r?) + k?, (3.5)

where? - phase angle. The proportionality coefficient k, although different for different asteroids, varies mainly within the range of 0.01–0.05 m/°.

According to formula (3.5), the increase in magnitude m with increasing phase angle is linear, m0 is the ordinate of the point of intersection of the phase curve (actually straight) with the vertical at r = ? = 1 and? = 0°.

More recent studies have shown that the phase curve of asteroids is complex. A linear decrease in brightness (an increase in the magnitude of the object) with increasing phase angle takes place only in the range from approximately 7° to 40°, after which a nonlinear decrease begins. On the other hand, at phase angles less than 7°, the so-called opposition effect takes place - a nonlinear increase in brightness with a decrease in the phase angle (Fig. 3.15).

Rice. 3.15. Magnitude versus phase angle for asteroid (1862) Apollo

Since 1986, to calculate the apparent magnitude of asteroids in the V rays (the visual band of the spectrum of the photometric system UBV) a more complex semi-empirical formula is used, which makes it possible to more accurately describe the change in brightness in the range of phase angles from 0° to 120° . The formula looks like

V = H + 5 lg(r?) - 2.5 lg[(1 - G)? 1+G? 2]. (3.6)

Here H is the absolute magnitude of the asteroid in the V beams, G is the so-called tilt parameter, ? 1 and? 2 - phase angle functions defined by the following expressions:

I = exp ( - A i B i ), i = 1, 2,

A 1 = 3.33, A 2 = 1.87, B 1 = 0.63, B 2 = 1.22.

After the elements of the orbit are determined and, therefore, r, ? and? can be calculated, formula (3.6) makes it possible to find the absolute stellar magnitude if there are observations of the apparent stellar magnitude. To determine the G parameter, observations of the apparent magnitude at various phase angles are required. At present, the value of parameter G has been determined from observations for only 114 asteroids, including several NEAs. The found values ​​of G vary from –0.12 to 0.60. For other asteroids, the G value is assumed to be 0.15.

The flux of solar radiant energy in the visible wavelength range incident on the surface of an asteroid is inversely proportional to the square of its distance from the Sun and depends on the size of the asteroid. This flow is partially absorbed by the surface of the asteroid, heating it, and partially scattered in all directions. The ratio of the flux scattered in all directions to the incident flux is called the spherical albedo A. It characterizes the reflectivity of the asteroid's surface.

Spherical albedo is usually represented as a product of two factors:

The first factor p, called the geometric albedo, is the ratio of the brightness of a real celestial body at zero phase angle to the brightness of an absolutely white disk of the same radius as the celestial body, located perpendicular to the sun's rays at the same distance from the Sun and Earth as the celestial body itself. body. The second factor q, called the phase integral, depends on the shape of the surface.

In contradiction with its name, the geometric albedo determines the dependence of the scattering of the incident flow not on the geometry of the body, but on the physical properties of the surface. It is the geometric albedo values ​​that are given in tables and are meant when talking about the reflectivity of asteroid surfaces.

Albedo does not depend on body size. It is closely related to the mineralogical composition and microstructure of the surface layers of an asteroid and can be used to classify asteroids and determine their sizes. For different asteroids, the albedo varies from 0.02 (very dark objects that reflect only 2% of the incident light from the Sun) to 0.5 or more (very bright ones).

For what follows, it is important to establish a relationship between the radius of an asteroid, its albedo, and absolute magnitude. Obviously, the greater the radius of the asteroid and the greater its albedo, the greater the luminous flux it reflects in a given direction, all other things being equal. The illumination that an asteroid creates on Earth also depends on its distance from the Sun and Earth and the flux of the Sun's radiant energy, which can be expressed in terms of the Sun's magnitude.

If we designate the illumination created by the Sun on Earth as E ? , the illumination created by the asteroid - as E, the distances from the asteroid to the Sun and the Earth - as r and?, and the radius of the asteroid (in AU) - as?, then the following expression can be used to calculate the geometric albedo p:

If we take the logarithm of this ratio and replace the logarithm of the ratio E/E ? by the Pogson formula (3.3), we find

lg p \u003d 0.4 (m ? - m) + 2 (lg r + lg ? - lg ?),

where m? is the apparent magnitude of the Sun. We now replace m by formula (3.4), then

lg p \u003d 0.4 (m ? - m 0) - 2 lg ?,

or, expressing the diameter D in kilometers and assuming the apparent stellar magnitude of the Sun in rays V equal to –26.77 [Gerels, 1974], we get

log D \u003d 3.122 - 0.5 log p - 0.2H, (3.7)

where H is the absolute magnitude of the asteroid in V rays.

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