How to adjust the albedo of the active surface. Total radiation, reflection of solar radiation, absorbed radiation, headlights, earth albedo. See what "Albedo" is in other dictionaries

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

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 heat balance Earth. 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 the 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 across the entire climate system indicates that observed climate changes are caused primarily by increases in atmospheric concentrations of greenhouse gases due to economic activity person.

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 average speed 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 in the event that 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 the globe(together with the atmosphere) back to the 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 the reflection from earth's surface, scattering of direct radiation by the atmosphere into world space (backscattering) and reflections from the upper surface of 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%. (four)

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. On the border 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.

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 - do not worsen physical characteristics asphalt concrete and be as cheap and easy to synthesize as possible.

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.

Surface	Characteristic	Albedo, %
Soils
black soil	dry, level ground freshly plowed, damp
loamy	dry wet
sandy	yellowish whitish river sand	34 – 40
Vegetation cover
rye, wheat in the period of full ripeness	22 – 25
floodplain meadow with lush green grass	21 – 25
dry grass
forest	spruce	9 – 12
pine	13 – 15
birch	14 – 17
Snow cover
snow	dry freshly fallen moist clean fine-grained moist soaked in water, gray	85 – 95 55 – 63 40 – 60 29 – 48
ice	river bluish green	35 – 40
marine milky blue
water surface
at solar altitude 0.1° 0.5° 10° 20° 30° 40° 50° 60-90°	89,6 58,6 35,0 13,6 6,2 3,5 2,5 2,2 – 2,1

The predominant part of the direct radiation reflected by the earth's surface and the upper surface of the clouds goes beyond the atmosphere into the world space. About one third of the scattered radiation also goes into the world space. The ratio of all reflected and scattered solar radiation to total solar radiation entering the atmosphere is called Earth's planetary albedo. The planetary albedo of the Earth is estimated at 35 - 40%. The main part of it is the reflection of solar radiation by clouds.

Table 2.6

Magnitude dependency To n from the latitude of the place and time of year

Latitude	Months
III	IV	V	VI	VII	VIII	IX	X
	0.77	0.76	0.75	0.75	0.75	0.76	0.76	0.78
	0.77	0.76	0.76	0.75	0.75	0.76	0.76	0.78
	0.77	0.76	0.76	0.75	0.75	0.76	0.77	0.79
	0.78	0.76	0.76	0.76	0.76	0.76	0.77	0.79
	0.78	0.76	0.76	0.76	0.76	0.76	0.77	0.79
	0.78	0.77	0.76	0.76	0.76	0.77	0.78	0.80
	0.79	0.77	0.76	0.76	0.76	0.77	0.78	0.80
	0.79	0.77	0.77	0.76	0.76	0.77	0.78	0.81
	0.80	0.77	0.77	0.76	0.76	0.77	0.79	0.82
	0.80	0.78	0.77	0.77	0.77	0.78	0.79	0.83
	0.81	0.78	0.77	0.77	0.77	0.78	0.80	0.83
	0.82	0.78	0.78	0.77	0.77	0.78	0.80	0.84
	0.82	0.79	0.78	0.77	0.77	0.78	0.81	0.85
	0.83	0.79	0.78	0.77	0.77	0.79	0.82	0.86

Table 2.7

Magnitude dependency To in + from the latitude of the place and time of year

(according to A.P. Braslavsky and Z.A. Vikulina)

Latitude	Months
III	IV	V	VI	VII	VIII	IX	X
	0.46	0.42	0.38	0.37	0.38	0.40	0.44	0.49
	0.47	0.42	0.39	0.38	0.39	0.41	0.45	0.50
	0.48	0.43	0.40	0.39	0.40	0.42	0.46	0.51
	0.49	0.44	0.41	0.39	0.40	0.43	0.47	0.52
	0.50	0.45	0.41	0.40	0.41	0.43	0.48	0.53
	0.51	0.46	0.42	0.41	0.42	0.44	0.49	0.54
	0.52	0.47	0.43	0.42	0.43	0.45	0.50	0.54
	0.52	0.47	0.44	0.43	0.43	0.46	0.51	0.55
	0.53	0.48	0.45	0.44	0.44	0.47	0.51	0.56
	0.54	0.49	0.46	0.45	0.45	0.48	0.52	0.57
	0.55	0.50	0.47	0.46	0.46	0.48	0.53	0.58
	0.56	0.51	0.48	0.46	0.47	0.49	0.54	0.59
	0.57	0.52	0.48	0.47	0.47	0.50	0.55	0.60
	0.58	0.53	0.49	0.48	0.48	0.51	0.56	0.60

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.

Wherein highest values albedo is recorded 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 reaches 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%).

Page 17 of 81

Total radiation, reflected solar radiation, absorbed radiation, PAR, Earth's albedo

All solar radiation coming to the earth's surface - direct and scattered - is called total radiation. Thus, the total radiation

Q = S? sin h + D,

where S– energy illumination by direct radiation,

D– energy illumination by scattered radiation,

h- the height of the sun.

With a cloudless sky, the total radiation has a daily variation with a maximum around noon and an annual variation with a maximum in summer. Partial cloudiness that does not cover the solar disk increases the total radiation compared to a cloudless sky; full cloudiness, on the contrary, reduces it. On average, cloudiness reduces the total radiation. Therefore, in summer, the arrival of total radiation in the pre-noon hours is on average greater than in the afternoon.
For the same reason, it is larger in the first half of the year than in the second.

S.P. Khromov and A.M. Petrosyants give midday values of total radiation in the summer months near Moscow with a cloudless sky: an average of 0.78 kW / m 2, with the Sun and clouds - 0.80, with continuous clouds - 0.26 kW / m 2.

Falling on the earth's surface, the total radiation is mostly absorbed in the upper thin layer of soil or in a thicker layer of water and turns into heat, and is partially reflected. The amount of reflection of solar radiation by the earth's surface depends on the nature of this surface. The ratio of the amount of reflected radiation to the total amount of radiation incident on a given surface is called the surface albedo. This ratio is expressed as a percentage.

So, from the total flux of total radiation ( S sin h + D) part of it is reflected from the earth's surface ( S sin h + D)And where BUT is the surface albedo. The rest of the total radiation
(S sin h + D) (1 – BUT) is absorbed by the earth's surface and goes to heat the upper layers of soil and water. This part is called absorbed radiation.

The albedo of the soil surface varies within 10–30%; in wet chernozem, it decreases to 5%, and in dry light sand it can rise to 40%. As soil moisture increases, the albedo decreases. The albedo of vegetation cover - forests, meadows, fields - is 10–25%. The albedo of the surface of freshly fallen snow is 80–90%, while that of long-standing snow is about 50% and lower. The albedo of a smooth water surface for direct radiation varies from a few percent (if the Sun is high) to 70% (if low); it also depends on excitement. For scattered radiation, the albedo of water surfaces is 5–10%. On average, the albedo of the surface of the World Ocean is 5–20%. The albedo of the upper surface of the clouds varies from a few percent to 70–80%, depending on the type and thickness of the cloud cover, on average 50–60% (S.P. Khromov, M.A. Petrosyants, 2004).

The above figures refer to the reflection of solar radiation, not only visible, but also in its entire spectrum. Photometric means measure the albedo only for visible radiation, which, of course, may differ somewhat from the albedo for the entire radiation flux.

The predominant part of the radiation reflected by the earth's surface and the upper surface of the clouds goes beyond the atmosphere into the world space. A part (about one-third) of the scattered radiation also goes into the world space.

The ratio of reflected and scattered solar radiation leaving space to the total amount of solar radiation entering the atmosphere is called the planetary albedo of the Earth, or simply Earth's albedo.

In general, the planetary albedo of the Earth is estimated at 31%. The main part of the planetary albedo of the Earth is the reflection of solar radiation by clouds.

Part of the direct and reflected radiation is involved in the process of plant photosynthesis, so it is called photosynthetically active radiation(FAR). FAR - the part of short-wave radiation (from 380 to 710 nm), which is the most active in relation to photosynthesis and the production process of plants, is represented by both direct and diffuse radiation.

Plants are able to consume direct solar radiation and reflected from celestial and terrestrial objects in the wavelength range from 380 to 710 nm. The flux of photosynthetically active radiation is about half solar flow, i.e. half of the total radiation, and practically regardless of weather conditions and location. Although, if for the conditions of Europe the value of 0.5 is typical, then for the conditions of Israel it is somewhat higher (about 0.52). However, it cannot be said that plants use PAR in the same way throughout their life and in various conditions. The efficiency of PAR use is different, therefore, the indicators "PAR use factor" were proposed, which reflects the efficiency of PAR use and the "Efficiency of phytocenoses". The efficiency of phytocenoses characterizes the photosynthetic activity of the vegetation cover. This parameter has found the widest application among foresters for assessing forest phytocenoses.

It should be emphasized that plants themselves are able to form PAR in the vegetation cover. This is achieved due to the arrangement of the leaves towards the sun's rays, the rotation of the leaves, the distribution of leaves of different sizes and angles on different levels phytocenoses, i.e. through the so-called canopy architecture. In the vegetation cover, the sun's rays are repeatedly refracted, reflected from the leaf surface, thereby forming their own internal radiation regime.

The radiation scattered within the vegetation cover has the same photosynthetic value as the direct and diffuse radiation entering the surface of the vegetation cover.

Table of contents
Climatology and meteorology
DIDACTIC PLAN
Meteorology and climatology
Atmosphere, weather, climate
Meteorological observations
Application of cards
Meteorological Service and World Meteorological Organization (WMO)
Climate-forming processes
Astronomical factors
Geophysical factors
Meteorological factors
About solar radiation
Thermal and radiative equilibrium of the Earth
direct solar radiation
Changes in solar radiation in the atmosphere and on the earth's surface
Radiation Scattering Phenomena
Total radiation, reflected solar radiation, absorbed radiation, PAR, Earth's albedo
Radiation of the earth's surface
Counter-radiation or counter-radiation
Radiation balance of the earth's surface
Geographic distribution of the radiation balance
Atmospheric pressure and baric field
pressure systems
pressure fluctuations
Air acceleration due to baric gradient
The deflecting force of the Earth's rotation
Geostrophic and gradient wind
baric wind law
Fronts in the atmosphere
Thermal regime of the atmosphere
Thermal balance of the earth's surface
Daily and annual variation of temperature on the soil surface
Air mass temperatures
Annual amplitude of air temperature
Continental climate
Cloud cover and precipitation
Evaporation and saturation
Humidity
Geographic distribution of air humidity
atmospheric condensation
Clouds
International cloud classification
Cloudiness, its daily and annual variation
Precipitation from clouds (precipitation classification)
Characteristics of the precipitation regime
The annual course of precipitation
Climatic significance of snow cover
Atmospheric chemistry
The chemical composition of the Earth's atmosphere
Chemical composition of clouds
Chemical composition of precipitation
Precipitation acidity
General circulation of the atmosphere

The problem of asteroid-comet hazard, i.e., the threat of a collision of the Earth with small bodies solar system, is recognized today as a complex global problem facing humanity. In this collective monograph for the first time data on all aspects of the problem were summarized. 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. Issues of assessing the level of threat and possible consequences bodies falling to the Earth, ways to protect and reduce damage, as well as ways to develop domestic and international cooperation on this global problem.

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 in the solar system except 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 to be used in 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 from 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 parameter G, 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.

Flux of radiant energy of the Sun in the wavelength range visible light, falling on the surface of the 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 heavenly body, located perpendicular to the sun's rays at the same distance from the Sun and Earth as the celestial body itself. 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 physical properties surfaces. 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: