Calculation of light refraction in Venus atmosphere from Venera 4 satellite dat

Skotnikov, M. M.

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National Aeronautics and Space Administration
Uoddard Space Flight Center
Contract No.NAS-5-12487
ST —PA —OA —10855
ON LIGHT REFRACTION IN THE ATMOSPHERE OF VENUS
by
M. M. Skotnikov
(USSR)
N69-32162
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1 7 JULY 1967
ST — PA — OA — 10855
ON LIGHT REFRACTION IN THE ATMOSPHERE OF VENUS
Kosmicheskiye Issledovaniya
	
by M. M. Skotnikov
Tom 7, vyp. 3, 436 - 440,
Izdatel'stvo "NAUKA", 1969
SUMMARY
Calculation of light refraction is conducted on the
basis of data on direct investigations of Venus' atmosphere
with the aid of Soviet AS "VENERA -411.
It is established that at an altitude of 8.3 km from
the assumed surface, horizontal rays by-pass the planet over
a circumference. Trajectories of light rays, originating
from the assumed surface of the planet at various angles,
are computed. It is shown that the rays returning to the sur-
face are those emitted at angles to horizon not exceeding 2°.
*
* *
As a . result of the successful flight of AS "VENERA-4" fundamental physico-
chemical data have been obtained on the lower atmosphere of planet Venus.
The information on the composition and density of Venus' atmosphere allows us
to conduct calculations of light refraction so as to obtain a representation
on optical phenomena taking place near its surface. As a result, profiles
were obtained of the index of refraction and its gradient in the atmosphere of
Venus. The position was defined of the critical sphere containing the rays of
light propagating around the planet along closed circumferences and the calcu-
lation has been conducted of light ray trajectories, propagating in the vici-
nity of planet's surface.
i
(*) 0 REFRAKTSII SVETA V ATMOSFERE VENERY
P$^' ^—
A
$d lY	 ^i
d^Js^	
f a^
WI
2
INDEX OF REFRACTION IN VENUS' ATMOSPHERE AND ITS GRADIENT. Profiles
of density and of its gradient in the atmosphere of Venus about 25 km thick,
traversed by AIS "VENERA-4", borrowed from [1], are represented in Figure 1.
Calculations of the index of refraction
and of its gradient were conducted
with the use of Fig.l data according
to the well known formula
n-1
k.	 (1)
P
Here n is the index of refraction,
p is the density and k is the Gladstone-
Dale constant determined by the compo-
sition of the atmosphere. According
Fig.1
lations were conducted
According to literature
0.227 — 0.22 cm 3 /g [2 -
to data obtained from VENERA-4, the
atmosphere of the planet contains
about 90% CO 2 ; this is why all calcu-
for an atmosphere consisting entirely of carbon dioxide.
data the value of k for CO 2 varies within the limits
- 4].
The obtained dependence of the refraction index of Venus' atmosphere on
the altitude h for both values of k is plotted in Figure 2 (next page). The
divergence between the two curves is less than three percent (3%). Shown in
k	 the same figure is the course of the gradient of the refraction index (k = 0.227
cm 3 /g). This graph is fundamental for the subsequent calculations of refraction.
The results, borrowed from the work [ 5], are also shown in Fig . 2 by a dashed
line. One may notice that the results of measurements in the upper part of the
atmosphere [ 5] "butt in" with the data obtained here. The tying of coordinates
was done in correspondence with [1]. It is also interesting to note that the
points, obtained during direct determination of (n — 1) (dashed line) in Fig.2
with the curve for k = 0.227, passes in the lower layers of the atmosphere
gradually to the curve for k = 0.22; it is possible that this is linked with
the dependence of CO2 refraction on temperature [4].
I,/Y
!/D
A, X*
i/11 di
10
l^IS
	 Ja
lass
	 a
3
A-/
Fig.2	
elf
PROPAGATION OF LIGHT AROUND THE PLANET
It is well known that the curvature radius of a light ray propagating in
an isotropic medium is inversely proportional to the gradient of the index of
refraction. On the basis of this, for a ray of light, propagating around the
planet along a concentric circumference, one may write the following equation:
( 31c ••11' _ i_ _ _1 _
Here R* is the radius of the critical sphere; Ro is the radius of the
planet, h is the height of the critical sphere above the planet surface and
On / 8r) *
 is the critical value of the refractive index' gradient.
4In the first approximation we shall take for the quantity R* the radius
Ro * , responding to the point h — 0 in Fig.l;. in [1] this level was assumed
for the position of planet's surface. Assuming in accord with [6] and Fig.2,
Ro *
 -° 6076 km, we shall obtain
0,164-I"cw-i.
The corresponding value of density gradient is 0.723 . 10-6 g/cm". In Fig.l
and 2 to these values of gradients responds the height h*
 — 8.3 km. Consequent-
ly, the critical surface is located at an altitude of - 8.3 km from a surface
responding to Ro * a
 6076 km, up to which data on Venus' atmosphere are available.
Inasmuch as h* << Ro * , further refinements of (8n / 8r) */sfiouN yield no sub-
stantial correction in correspondence with formula (2); it constitutes in all
- 0.14%. Taking into account that all initial values are well known with no-
ticeably great errors, the obtained correction may not be introduced into the
value of (8n / 8r) *
 sought for. At k — 0.22,h* z 8.0 km. With an error of no
more than 0.5%, to the found value of the critical gradient could satisfy a
region of the atmosphere in the neihborhood of Ro* — 6076 km, 30 km thick.
If in accord with [7], we should assume for the radius of the planet Ro — 6056 km,
the altitude of the critical surface from the planet surface would constitute
h o *
 = 28.3 km. Subsequert refinements of data on Venus' atmosphere will allow
us to introduce into the values and results obtained here the corresponding
corrections; they will also apparently provide the possibility of penetrating
into deeper layers of the planetary atmosphere. However, one may hope that the
position of the critical sphere in the field of the gradient of the refractive
index and the position relative to this surface of the light ray paths obtained
below near it, will not change substantially.
PROPAGATION OF LIGHT RAYS NEAR THE SURFACE OF THE PLANET
Taking into account the linear character of the dependence of the light
ray deflection angle on the value of the gradient of the index of refraction,
the aggregate deflection cE may be broken into two parts: er — f + C. One of
the parts, f = e* is conditioned by the constant component of the gradient
(8n /8h) * , appearing to be the cause of ray motion around the planet along the
5surface. The variable part of E, inducing the displacement of the ray relative
to the planet ' s surface, is due to the influence of the residual part of the
index of refraction gradient an / ah. Then, considering only the motion of the
ray relative to planet ' s surface and approximating at the same time the variable
part of an / ah over separate portions of the graph of Fig.2 in the form of a
straight line an / ah = a - ah, we may obtain the differential equation of mo-
tion of the ray in the following form:
tPh
	
It --	 u - uh.
,
Here a and a are constants, determined by the Fig.2. Eq.(3) is written
in a curvilinear system of coordinates (sOh), in which the axis Os is directed
parallelwise to planet's surface at the level R * = 6076 km (h - 0), and the
axis Oh coincides everywhere with the direction of the radius. Resolving (3)
at boundary conditions s = 0, h = ho, dh / ds - 6 0 for the trajectories of
rays proceeding near the planet ' s surface, we shall obtain
1	 n --• ult
X, : _- _-.ArClr_...._
fa
The trajectory of rays initially proceeding parallelwise to the surface
of the planet is obtained from (4) at 6 0 = 0
nu	 ^1„	 —	 60h -	 }- h,,---	 -	 _ (ar((uS)-;-'^- c	 (5)
u	 u ^'a	 rot
Here ho is the maximum value of h;in (5) h = ho at s t i = 0. The index 1/2
•'l
signifies that this equation describes only one half of the trajectory determi-
ned by Eq.(4). The second half of the trajectory is symmetrical to it on the
strength of light ray reversibility. For the inclination angle of the ray of
light to planet's surface, from ( 5) we may obtain the following expression:
	
ds	 )'u
When computing the trajectories of rays lying below the critical altitude
h* 8.3 km, the values of parameters were as follows: a = 0.119 . 10
-e
 cm-t,
a	 0.144'10-4 CM-2.
(3)
(4)
6In the curvilinear system of coordinates the rays, proceeding at the
altitude of 8.3 km, are not deflected, which is visible from relations (5)
and (6); at aho	a, the latter vanishes (t ee - 0), while the first becomes
infinite. At h o = h", function (5) undergoes a discontinuity; the light ray
then propagates parallelwise to the surface of the planet.
Fig .3(*)
The incidence angles of light rays on the planet ' s surface were computed
by formula (6) (co). The results of calculation as a function of hoare plotted
in Fig.4. It is fairly easy to see that as
h o increases (and consequently 812max also),	 b o	 e	 f ^..«
' Vfthe angles of incidence of rays do not rise 	 a
r 
unboundedly. For ho > 7 km, the angle c o	 -rx,
-apt	 ---- -	 J - -- - -----_...--
already varies unnoticeably and approaches 	 rAr
the limit E omax	 'r= '"a^+ which constitu-	 rx
tea for the assumed values of a and a the
value of 0.0321, or in degrees: 1 * 50^.	 Fig.4
Therefore, the angle Eomax a domax = 1 0 50	 (*)
is a threshold for the rays returning to
the planet. The rays outgoing at angles greater than 1°50' do not return to
the planet. The trajectories of rays outgoing from the planet at different
angles d o and, at the same time rising to a different altitude, are plotted
in Figure 3 above. Here dots denote the centers of trajectories, where the
rays become parallel to the surface of the planet. As may be see from Fig.3,
distances smax increase rapidly with the rise of do and ho, this rise being
particularly noticeable at rapprochement to h * 8 . 3 km, where discontinuity
of function (5) takes place. But this phenomenon is observed only in a very
narrow region directly adjacent to h * °- 8 . 3 km, which is clearly seen from
(*) [for practical purposes Figs.3 and 4 of the n::ginal version have
been interverted].
7the data compiled in Table 1 below. Here Ah o is the distance of the rays from
the "critical" surface, assuming h *
 = 8.3 km.
T e n t v t
Alto. is
	 70	 7	 7.10- -4 	7,10-+
-Tmex. KA 2MR0 !i%)	 101-10
	 12&x!
It may be seen from Table 1 that greater distances are covered by rays
proceeding in a very narrow region of space. The distances exceeding 12,000 km
are covered by rays passing in a channel with width of the order of 0.007 mm.
Consequently, part of the light from the sunlit side of the planet may also
penetrate in its night part to fairly great distances. But only a small amount
of energy will then be transferred in that very narrow light channel. To an
observer located on an even or smooth surface, a faraway horizon will appear,
outgoing to numerous thousand kilometers with art insignificant rise of the
locality, constituting less than 2°.
CONCLUSION. We should note that all the conclusions and calculations
conducted here are valid only for a quiet atmosphere with spherical symmetry.
The analysis of refraction conducted here is based upon the results of the first
direct investigation of Venus' atmosphere parameters. The refinement of the
obtained results may be conducted alongside with su sequent study of planet's
parameters and its geometric characteristics.
*** T H E E N D ***
Received on 28 June 1968.
REFERENCES
1. V. S. AVDUYEVSKIY, N. F. BORODIN, V.A. KUZNETSOF... ET AL. DAN, 199, 2, 1968.
2. HANDBOOK OF CHEMISTRY AND PHYSICS. Ed.37, USA.
3. M. P. VULAKOVICH, V. V. ALTUNIN. Teplofizicheskiye svouystva dvuokisi ugle-
roda (Thermophysical properties of CO2 ). Atom-
4. A. MUCHELS, J. HAMERS. Physics, 4, 995, 1937.	 izdat, 1965.
5. MARINER STANFORD GROUP SCIENCE, 158, 1678, 19 7.
6. V. S. AVDUYEVSKIY, M. YA. MAROV, M. K. ROZHDESTVENSKIY. Kosm. Issledov.
7, No.2, 233, 1969.
7. M. E. ASH, I. I. SHAPIRO, W. B. SMITH. Astronom. J. 72, 338, 1967.
CONTRACT No.NAS-5-.2487 	 Translated by ANDRE L. BRICHANT
VOLT INFORMATION SCIENCES INC.
on 16 July 19691145 - 19th St.NW, D.C. 20036. Tel: 223-6700. 
.


On light refraction in the atmosphere of Venus

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