The Terrestrial Atmosphere

1
The Terrestrial Atmosphere
Queste dispense sono utili sia per Astronomia I
Laurea Triennale in Astronomia che per Elementi
di Astronomia e Astrofisica per il Corso di
Ingegneria Aerospaziale (sia triennale che
specialistica)
2
The terrestrial atmosphere - 1
This chapter is devoted to the examination of the
influence of the Earths atmosphere on the
apparent coordinates of the stars and on the
shape of their images the discussion will be
limited essentially to the visual band. The
discussion of the effects of the atmosphere on
photometry and spectrophotometry are deferred to
a later chapter.
The figure gives a schematic representation of
the vertical structure of the atmosphere the
visual band is mostly affected by what happens in
the troposphere, namely in the first 15 km or so
of height, where some 90 of the total mass of
the atmosphere is contained.
3
The terrestrial atmosphere -2
Na Layer
4
The terrestrial atmosphere - 3
The temperature profile in the troposphere is
actually more complicated than shown in the
Figure. The height of the tropopause (a layer of
almost constant temperature) from the ground
ranges from 8 km at high latitudes to 18 km above
the equator it is also highest in summer and
lowest in winter. The average temperature
gradient is approximately 6 C/km, but often,
above a critical layer situated in the first few
km, the temperature gradient is inverted, with
beneficial effects on astronomical observations,
thanks to the intrinsic stability of all layers
with temperature inversion (such as the
stratosphere and the thermosphere), essentially
because convection cannot develop. This is the
case for instance of the Observatory of the Roque
de los Muchachos (Canary Islands, height 2400 m
a.s.l.), where the inversion layer is usually few
hundred meters below the telescopes at the top of
the mountain.
5
Chemical composition and structure -1
The chemical composition of the troposphere is
mostly molecular Nitrogen N2 and molecular Oxygen
O2 (approximately 34 and 14 respectively), with
traces of the noble gas Argon and of water vapor
(the water vapor concentration may be as high as
3 at the equator, and decreases toward the
poles). See next slide. Above the tropopause, at
higher heights in the stratosphere, the
temperature raises considerably thanks to the
solar UV absorption by the Ozone (O3) molecule
with the process UV photon O3 O2Oheat.
The mesosphere ranges from 50 to 80 km in this
region, concentrations of O3 and H2O vapor are
negligible, hence the temperature is lower than
in the stratosphere. The chemical composition of
the air becomes strongly height-dependent, with
heavier gases stratified in the lower layers. In
this region, meteors and spacecraft entering the
atmosphere start to warm up.
6
Chemical composition and structure - 2
Standard composition of air Nitrogen
78.084 Oxygen 20.946 Argon 0.934 Carbon
dioxide 0.038 Water vapor 1 Other
0.002 Nitrogen is normally inert except upon
electrolysis by lightning and in certain
biochemical processes of nitrogen fixation).
7
The ozone O3
O3 is a molecule containing 3 O atoms. It is blue
in color and has a strong odor. Normal molecular
O2, has 2 oxygen atoms and is colorless and
odorless. Ozone is much less common than normal
oxygen. Out of each 10 million air molecules,
about 2 million are normal oxygen, but only 3 are
ozone.
Most atmospheric ozone is concentrated in a layer
in the stratosphere, about 15-30 kilometers above
the Earth's surface. Even this small amount of
ozone plays a key role in the atmosphere,
absorbing the UVB portion of the radiation from
the sun, preventing it from reaching the planet's
surface.
8
Water vapor nomenclature - 1
Water vapor is water in the gaseous phase. The
actual amount is the concentration of water vapor
in the air, the relative concentration is the
ratio between the actual amount to the amount
that would saturate the air. Air is said to be
saturated when it contains the maximum possible
amount of water vapor without bringing on
condensation. At that point, the rate at which
water molecules enter the air by evaporation
exactly balances the rate at which they leave by
condensation. The partial pressure of a given
sample of moist air that is attributable to the
water vapor is called the vapor pressure. The
vapor pressure necessary to saturate the air is
the saturation vapor pressure. Its value depends
only on the temperature of the air. The
Clausius-Clapeyron equation gives the saturation
vapor pressure over a flat surface of pure water
as a function of temperature. Saturation vapor
pressure increases rapidly with temperature the
value at 32C is about double the value at 21C.
The saturation vapor pressure over a curved
surface, such as a cloud droplet, is greater than
that over a flat surface, and the saturation
vapor pressure over pure water is greater than
that over water with a dissolved solute.
9
Water vapor nomenclature - 2
Relative humidity is the ratio of the actual
vapor pressure to the saturation vapor pressure
at the air temperature, expressed as a
percentage. Because of the temperature dependence
of the saturation vapor pressure, for a given
value of relative humidity, warm air has more
water vapor than cooler air. The dew point
temperature is the temperature the air would have
if it were cooled, at constant pressure and water
vapor content, until saturation (or condensation)
occurred. The difference between the actual
temperature and the dew point is called the dew
point depression. The wet-bulb temperature is
the temperature an air parcel would have if it
were cooled to saturation at constant pressure by
evaporating water into the parcel. (The term
comes from the operation of a psychrometer, a
widely used instrument for measuring humidity, in
which a pair of thermometers, one of which has a
wetted piece of cotton on the bulb, is
ventilated. The difference between the
temperatures of the two thermometers is a measure
of the humidity.) The wet-bulb temperature is the
lowest air temperature that can be achieved by
evaporation. At saturation, the wet-bulb, dew
point, and air temperatures are all equal
otherwise the dew point temperature is less than
the wet-bulb temperature, which is less than the
air temperature.
10
Water Vapor Mixing ratio
Specific humidity is the ratio of the mass of
water vapor in a sample to the total mass,
including both the dry air and the water vapor.
The mixing ratio is the ratio of the mass of
water vapor to the mass of only the dry air in
the sample. As ratios of masses, both specific
humidity and mixing ratio are dimensionless
numbers. However, because atmospheric
concentrations of water vapor tend to be at most
only a few percent of the amount of air (and
usually much lower), they are both often
expressed in units of grams of water vapor per
kilogram of (moist or dry) air. Absolute humidity
is the same as the water vapor density, defined
as the mass of water vapor divided by the volume
of associated moist air and generally expressed
in grams per cubic meter. The term is not much in
use now.
11
Water reservoir
Water vapor is constantly cycling through the
atmosphere, evaporating from the surface,
condensing to form clouds blown by the winds, and
subsequently returning to the Earth as
precipitation.
Heat from the Sun is used to evaporate water, and
this heat is put into the air when the water
condenses into clouds and precipitates. This
evaporation - condensation cycle is an important
mechanism for transferring heat energy from the
Earth's surface to its atmosphere and in moving
heat around the Earth.
12
Greenhouse effect due to water vapor
Water vapor (not CO2 as commonly believed!) is
the most abundant of the greenhouse gases in the
atmosphere, and the most important in
establishing the Earth's climate. Greenhouse
gases allow much of the Sun's shortwave radiation
to pass through them but absorb the infrared
radiation emitted by the Earth's surface.
Without water vapor and other greenhouse gases
in the air, surface air temperatures would be
well below freezing.
13
Aerospace devices
A multitude of systems exist for observing water
vapor on a global scale and at high altitudes,
supplementing the instruments on the ground, that
measure in special sites and at ground level.
Each has different characteristics and
advantages. To date, most large-scale water vapor
climatological studies have relied on analysis
of radiosonde data, which have good resolution in
the lower troposphere in populated regions but
are of limited value at high altitude and are
lacking over remote oceanic regions.
14
The Water Vapor content in 1992
NASA Water Vapor Project (NVAP) Total Column
Water Vapor 1992 The mean distribution of
precipitable water, or total atmospheric water
vapor above the Earth's surface, for 1992. This
depiction includes data from both satellite and
radiosonde observations.
15
Cloud effects on Earth Radiation
16
The outer layers
Following the smooth decrease in the mesosphere,
the temperature raises again in the thermosphere,
because the solar UV and X-rays, and the
energetic electrons from the magnetosphere can
partly ionize the very thin gases of the
thermosphere. The weakly ionized region which
conducts electricity, and reflects radio
frequencies below about 30 MHz is called
ionosphere it is divided into the regions D
(60-90 km), E (90-140 km), and F (140-1000 km),
based on features in the electron density
profile. Finally, above 1000 km, the gas
composition is dominated by atomic Hydrogen
escaping the Earths gravity, which is seen by
satellites as a bright geocorona in the resonance
line Ly-? at ? 1216 Å.
17
Refraction Index
As is well known, the light propagates in a
straight line in any medium of constant
refraction index n, with a phase velocity v given
by
where ? is the dielectric constant and ? the
magnetic permeability of the medium. All these
quantities are wavelength dependent. The group
velocity u is instead
At the separation surface between two media of
different refraction index (say vacuum/air), the
ray changes direction, so that the observer
immersed in the second medium sees the light
coming from an apparent direction different from
the true one (see Figure)
18
The atmospheric refraction - 1
Suppose that the atmosphere can be treated as a
succession of parallel planes (hypothesis of
plane-parallel stratification), by virtue of its
small vertical extension with respect to the
Earths radius. According to Snells laws, when
the ray coming from the region of index of
refraction n0 encounters the separation surface
with a medium of refraction index n1gt n0, part of
the energy will be reflected to the left, on the
same hemi-space with the same angle r0 with
respect to the normal. This part will not be
considered here, it only implies a dimming of the
source. The remaining fraction will be refracted,
in the same plane as the incident ray, to an
angle r1 lt r0. Indeed, in a clear atmosphere
without clouds, no sharp air-vacuum separation
surface exists, the refraction index gradually
increases from 1 to a final value nf near the
ground, with typical scale lengths much greater
than the wavelength of light (as already said, we
limit our considerations to the visual band), so
that the continuously varying direction can be
considered as a series of finite steps in the
plane passing through the vertical and the
direction to the star.
19
The atmospheric refraction - 2
By following each refraction in cascade we have
where ni1gt ni, and ri1lt ri. By equating each
term
Therefore in a plane-parallel atmosphere the
total angular deviation only depends on the
refraction index close to the ground, independent
of the exact law with which it varies along the
path.
20
The atmospheric refraction - 3
The net effect is as shown in the figure the
star is seen in direction z smaller than the
true direction z, namely closer to the local
Zenith, by an amount R which is the atmospheric
refraction z z R
By virtue of
, and for small Rs (in practice, if z lt 45)
and finally
21
Density - temperature relationship
The refraction index n depends from the density ?
according to Gladstone-Dales law
and with the hypothesis of a perfect gas of
pressure P, temperature T and molecular weight ?

(where R is now the gas universal constant)
,
22
The atmospheric refraction in the visible
In the visual band (? ? 550 nm), for standard
values of temperature and pressure (T 273 K, P
760 mm Hg), the value of the refraction index
is nf ? 1.00029, so that in round
numbers R(15) ? 16, R(45) ? 60 Already
for Zenith distances as small as 20, the
refraction is larger than the annual aberration,
and of most of the effects discussed in previous
chapters which alter the apparent direction of a
star. Introducing the dependence from temperature
and pressure
(P in mm Hg, T in K)
23
Cauchys formula for the refraction index
The relationships n(?) can be expressed by the
so-called Cauchys formula
In standard conditions of temperature and
pressure
(? in micrometers), corresponding to a variation
of about 2 over the visible range, namely to
about 1.2 at 45.
24
The chromatism of the refraction
The refraction index n depends from the
wavelength, diminishing from the blue to the red,
and the same will be true for the refraction
angle R the image on the ground of the star is
therefore a succession of monochromatic points
aligned along the vertical circle the blue ray
will be below the red one, and thus the blue star
will appear to the eye above the red one
The atmosphere behaves therefore like a prism
producing a short spectrum in the vertical plane,
whose length increases with the zenith distance,
reaching several arc seconds at low elevations.
25
The atmospheric refraction at large Zenith
distances
For zenith distances larger than 45, the path of
the ray inside the atmosphere is so long that the
curvature of the Earth cannot be ignored. The
mathematical treatment becomes more intricate,
even if restricting it to successive refractions
in the same plane with n decreasing outwards with
continuity. With these simplifying assumptions,
the refraction is expressed by following
integral
After several steps, the integral can be solved
as
where l is a typical length, l ? 8 km.
26
Effect of the refraction on the astronomical
coordinates
The main effect of refraction is to move the
star closer to the Zenith in the vertical plane,
thus raising its elevation h but leaving
essentially unchanged its azimuth A. XX R
?h PXX PXZ q ZX z, ZX z PX
90-? XU ??
For an object in meridian, the refraction is all
in declination, and in particular this is true
for the Sun at true noon.
27
Approximate formulae for refraction
For Zenith distance not greater than
approximately 45, after several passages we
finally get
by means of which formulae we can derive the true
(or the apparent, according to the sign)
topocentric positions. Obviously no such
correction is necessary for a telescope in outer
Space.
28
Vertical gradients of temperature
Calling H the height over the ground, we have
The variation of pressure with the height is
equal to the weight of the air in the elementary
volume having unitary base and height dH,
so that
where the constant g/R equals approximately 3.4
K/km, and is called adiabatic lapse. Hence the
conclusion that the variations of the refraction
index depend from the vertical gradients of the
temperature. A practical consequence is that all
effort must be made to control and minimize those
gradients over the accessible volume of the
telescope enclosure.
29
Turbulence, Scintillation, Seeing

• The Earth's atmosphere is turbulent, and
  variations of the index of refraction cause the
  plane wavefront from distant objects to be
  distorted. This distortion introduces amplitude
  variations, positional shifts and image
  degradation, causing two astronomical effects
• scintillation, namely an intensity variation
  which typically varies over linear scales of few
  cm. Therefore for large aperture telescopes it is
  a small effect.
• seeing positional changes and image quality
  changes. The effect of seeing depends on aperture
  size for small apertures, one sees a diffraction
  pattern moving around, while for large apertures,
  one sees a set of diffraction patterns (speckles)
  moving around on scale of 1 arcsec.
• These observations imply
• wavefronts are flat on scales of small apertures
• instantaneous slopes vary by 1 arcsec.
• The typical time scales are from few milliseconds
  up to dozens of seconds.
• The effect of seeing can be derived from theories
  of atmospheric turbulence, worked out originally
  by Kolmogorov, Tatarski, Fried.

30
Structure function
The structure of the refraction index n in a
turbulent field can be described statistically by
a structure function
where x is separation of points, r is position.
Kolmogorovs theory of turbulence gives
where Cn is the refractive index structure
constant. From this, one can derive the phase
structure function at the telescope aperture
where the coherence length r0 (also known as the
Fried parameter) is
(z zenith angle, ? wavelength). Finally, the
function D? can be converted into an image shape
on the focal plane of the telescope.
31
The Fried parameter - 1
Notice that r0 increases with ??6/5 ??1. 2.
Physically, the image size d from seeing is
(roughly) inversely proportional to r0
a larger r0 means better seeing.
As is well known, the image size from a
diffraction-limited telescope of aperture D is
Therefore, seeing dominates when r0 lt D. Seeing
is more important than diffraction at shorter
wavelengths, diffraction is more important at
longer wavelengths diffraction and seeing cross
over in the IR (at ? 5 microns for a 4m
telescope). The crossover moves to shorter
wavelengths for smaller telescopes or better
seeing.
32
The Frieds parameter - 2
Frieds parameter r0 varies from site to site
and also with time in each site. A typical site
has r0 ? 10 cm at 5000Å , namely a seeing of
1". On rare occasions, in the best sites, the
seeing can be as low as 0".3. Most sites can be
characterized by three regimes called surface
layer (wind-surface interactions and man-made
seeing), planetary boundary layer ( influenced
by diurnal heating), free atmosphere (in the
tropopause around 10 km, high wind shears)
33
An example of Cn2
34
The isoplanatic angle
In addition to Frieds parameter, one has to
consider the angular coherence of the turbulence
pattern over the sky, defining the isoplanatic
angle

• where H is the average distance of the seeing
  layer
• for r0 ? 10 cm, H 5 km , ? ? 1.3 arcsec. In
  the infrared r0 ? 70 cm, H 5 km , ? ? 9 arcsec.
  
• A more favourable parameter is the isoplanatic
  angle for image motion (not wavefront
  distortion), defined as
• ?kin ? 0.3D/H.
• For D 4m, H 5 km, ?kin ? 50 arcsec.
• Another useful parameter is the correlation time
  ?0, which is approximately the dimension of the
  typical air bubble divided by the velocity of the
  wind. As r0, also ?0 increases with ?6/5.

35
The seeing
To resume the previous considerations bubbles of
air having slightly different temperatures, and
therefore slightly different refractive indexes,
are carried by the wind across the aperture of
the telescope. The Fried parameter r0 can be used
to simplify the description of a very complex
rapidly varying medium, namely the typical size
of the bubble. Values vary from few centimeters
(a poor site) to some 30 cm (a very good site).
r0 can be understood also as the effective
diameter of the diffraction limited telescope in
that site (with respect to the angular
resolution). Another useful parameter is the
maximum angle over which fluctuations are
coherent (isoplanatic angle). Both Frieds
parameter and isoplanatic angle improve with
increasing wavelength, the correction is better
in the IR than in the Visible.
36
Representation of the seeing

• In this model by Ragazzoni et al., there are two
  main components of the seeing
• one coming from high altitudes (choice of site)
• one due to ground layers (it can be actively
  controlled by shape of dome and proper
  thermalisation of structure)
• The spectral power of the air turbulence is
  appreciable over a large interval of frequencies
  f, say 1 to 1000 Hz, with a 1/f distribution.

The angles are exaggerated, actually AdOpt
correction can be made over small fields of view.
37
A first remedy Speckle Interferometry

• a very large number of short duration exposures
  (? 1 ms) are taken with very long focal length (?
  100m) and narrow bandwidth (? 1 nm) in each
  exposure the seeing is frozen, each speckle
  represents the diffraction figure of the aperture
• Fourier Transform allows the reconstruction of
  the true image
• The technique works well for simple structures
  (e.g. double or multiple stars, disks). The
  figures shows the reconstruction of a triple star.

38
A better remedy Adaptive Optics

• The fairly complex techniques that are nowadays
  implemented on the largest telescopes to contrast
  the seeing are known collectively as Adaptive
  Optics devices.
• A suitable reference wavefront is also
  necessary. Suitably bright stars are rare.
• An artificial laser star is a possible solution.

39
The artificial laser star
40
Before and after AdOpt
If one freezes the image with short exposure
times (say less than 0.01 sec) and a narrow
filter, the seeing image breaks up in large
number of speckles, each having dimension of
the order of the diffraction figure of the
telescope. The number of speckles is of the order
of (seeing diameter/diffraction figure)2
41
The Galactic Center with the Keck AdOpt
Without AdOpt
With AdOpt
42
Quality of the image -1
The quality of an image can be described in many
different ways. The overall shape of the
distribution of light from a point source is
specified by the point spread function (PSF).
Diffraction gives a basic limit to the quality of
the PSF, but any aberrations or image motion add
to structure/broadening of the PSF. Another way
of describing the quality of an image is to
specify it's modulation transfer function (MTF).
The MTF and PSF are a Fourier transform pair.
Turbulence theory gives
where ? is the spatial frequency. Note that a
Gaussian goes as ? 2, so this MTF is close to a
Gaussian. The shape of seeing-limited images is
roughly Gaussian in core but has more extended
wings. This is relevant because the seeing is
often described by fitting a Gaussian to a
stellar profile.
A potentially better empirical fitting function
is a Moffat function
43
Quality of the image -2
Probably the most common way of describing the
seeing is by specifying the full-width-half-maximu
m (FWHM) of the image, which may be estimated
either by direct inspection or by fitting a
function (usually a Gaussian) note the
correspondence of FWHM to ? of a Gaussian FWHM
2.355? . The FWHM doesn't fully specify a
PSF, and one should always consider how
applicable the quantity is. Another way of
characterizing the PSF is by giving the encircled
energy as a function of radius, or at some
specified radius. A final way of characterizing
the image quality, more commonly used in adaptive
optics applications, is the Strehl ratio SR. The
Strehl ratio is the ratio between the peak
amplitude of the PSF and the peak amplitude
expected in the presence of diffraction only. In
practice, in the visible region it is already
very good reaching SR 0.1 .
44
The EE of the Rosetta WAC
The WAC is in space, so there is no seeing to
worry about, only the vibrations of the
spacecraft or thermal distortions of the jitter
of the attitude.
45
Extinction and spontaneous emission by the
atmosphere
In addition to chaotic refraction effects, the
atmosphere absorbs a fraction of the incident
light, both in the continuum and inside atomic
and molecular lines and bands. Furthermore, the
atmosphere spontaneously emits in particular
atomic and molecular bands (this is in addition
to scattering of artificial lights, see later).
The molecular oxygen O2 in particular is so
effective at blocking radiation around 6800A and
7600A that Fraunhofer could detect by eye two
dark absorption bands in the far red of the solar
spectrum, bands he called respectively B and A
(he examined the spectra from red to blue, the
current astronomical practice is from blue to
red).
46
Extinction
Let us consider the absorption due to a thin
layer of atmosphere at height between h and hdh
in the usual simple model of a plane-parallel
atmosphere. The light beam from the star makes an
angle z with the Zenith, so that the traversed
path is dh/cosz secz?dh. If I?(h) is the
intensity at the top of the layer, at the exit it
will be reduced by the quantity
In total, if I?(?) is the intensity outside the
atmosphere, at the elevation h0 of the
Observatory the intensity will be reduced to
47
Optical Depth
where we have introduced the a-dimensional
quantity ?? called optical depth
The variable k? (dimensionally, cm-1) represents
the absorption per unit length of the atmosphere
at that wavelength. Astronomers use a particular
measure of the apparent intensity, namely the
magnitude, defined by m m0 -2.5logI (see in a
later lecture), so that
D? is called the optical density of the
atmosphere, while the variable X(z) secz is
called air-mass. The minimum value of the airmass
is 1 at the Zenith, and 2 at z 60 (the limit
of validity of the present approximate
discussion).
48
The Bouguer line
Suppose we start observing the star at its upper
transit, and then keep observing it while its
Hour Angle (and therefore also its Zenith
distance) increases we would notice a linear
increase of its magnitude in agreement with the
previous equation, namely a straight line with
slope 2.5D? in a graph (m, secz). It is common
practice to plot the m-axis pointing down. This
straight line is known as Bouguer line, from the
name of the XVIII century French astronomer who
introduced it. The extrapolation of this line to
X 0 (a mathematical absurdity) gives the
so-called loss of magnitude at the Zenith, or
else the magnitude outside atmosphere. According
to the formulae for coordinate transformations,
we have
where ? is the latitude of the site, ? and HA the
coordinates of the star.
49
Continuous extinction at Mauna Kea
The Table shows the continuous extinction of the
atmosphere above Mauna Kea, whose elevation above
sea level (4300 m) is higher than that of most
observatories so that the transparency of the sky
is at its best, in the extended visible region.
50
Figures of the extinction from the visible to the
near IR
The figure on the left gives the optical depth,
the one on the right the transmission (one is the
reverse of the other). In the violet region, the
transparency quickly goes to zero, essentially
because of the ozone O3 molecular absorption at
the other end of the spectrum the transparency is
reasonably good until about 2.4 micrometers, when
the H2O and CO2 molecules heavily absorb the
light. The astronomical photometric wide bands
(U,B,V, R, I, J, H, ) are indicated.
51
Spontaneous and artificial emissions
To complete these considerations about the
influence of the atmosphere on the photometry
(and also on the spectroscopy) of the celestial
bodies, we must add that the atmosphere
contributes radiation, by spontaneous emission
and by scattering of natural and artificial
lights. If the Observatory is close to populated
areas, bright emission lines of Mercury and
Sodium from street lamps are observed Hg at ??
4046.6, 4358.3, 5461.0, 5769.5, 5790.7 Na at
5683.5, 5890/96 (the yellow D-doublet), 6154.6
Ne at 6506, and so on. Natural lines come from
the atomic Oxygen in forbidden transitions
(designated with OI) at ?? 5577.4, 6300 and
6367, and especially from the molecular radical
OH who provides a wealth of spectral lines and
bands filling the near-IR region above 6800A. The
OH comes from the dissociation of the water vapor
molecule under the action of the solar UV
radiation. Therefore, the atmosphere is a
diffuse source of radiation, whose intensity
strongly depends on the Observatory site. To set
an indicative value in the visual band, a
luminosity equivalent to one star of 20th mag per
square arcsec at the Zenith can be assumed.
52
The VIS-NIR spectrum of the night sky
The night sky is calibrated (see ordinate) in
surface brightness, given as mag/(arcsec)2. Mt.
Boyun is in Korea.
53
The Near-IR sky emission
A very detailed section of the near-IR night sky
OH-emission obtained at ESO Paranal with UVES.
http//www.eso.org/observing/dfo/quality/UVES/uves
sky/sky_8600U_1.html
54
A second limit of the terrestrial atmosphere the
artificial lights
The full Moon has difficulties in competing with
the spectrum of artificial lights.
55
The situation in Italy
If the extrapolation is correct, in 2025 no
Italian will be able to see the Milky Way
56
Planetary light pollution
From a paper by Cinzano, Falchi e Elvidge (2001)
57
Effects of the atmosphere at radiofrequencies - 1
The ionosphere will introduce a delay on the
arrival time of the wave, given by
(seconds), being I the path along the line of
sight and Ne the electron density (cm-3). This
density varies with the night and day cycle, with
the season and also with the solar cycle.
The variable ionospheric delay is one of the main
causes of error in the time signals broadcasted
by satellites such as GPS and GLONASS.
58
Effects of the atmosphere at radiofrequencies -2
The troposphere also introduces a delay, which
can be resolved in two components, a dry one and
a wet one. The dry component amounts to about 7
ns at the Zenith, and varies with the modified
cosec z we have discussed for the optical
observations
The wet component depends on the amount of water
vapor, and amounts to about 10 of the dry one,
but it varies rapidly and in unpredictable
way.   Finally, two other mediums affect the
propagation of the radio waves, namely the solar
corona and the ionized interstellar medium.