WORKS OF THE CENTRAL SCIENTIFIC RESEARCH INSTITUTE OF GEODESY, AERIAL SURVEYING AND CARTOGRAPHY

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP81-01043R002200130008-1
• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 121
• Document Creation Date: December 23, 2016
• Document Release Date: August 2, 2013
• Sequence Number: 8
• Publication Date: May 9, 1958
• Content Type: REPORT

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9 111p3r 1958
ORKS OF THE CENTRAL SCIENTIFIC RESEARCH INSTITUE OF
GEODESY AERIAL SURVEYING AND CARTOGRAPHY
U. S. JOINT PU6LICATIONS
RESEARCH SERVICE
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-t
CS0-1578
Wt F.KL-, OF TT.2'.: j7FMAL, SCIEbTIF C HESEARGH ITSTITUTE OF
I.A.,'OEST3 A T.".7A1., biVYU1G Al ZAFTOGRA. HY
Truay Tsentral 'nog? auonno-
ssledov atel ' skc.ro nsti tuta
Jeoctesiyal Aeros"emki t ar-
tografii, 34o. 1211 ()scow,
1957, pp. 1-112.
TABLE LI? CU, Twrs
Page
V.F. Yeremeyev. Tab.es for the Caiclo. a ticn
of Deviations of Vertical_ Lines on the
Physical Surcace of the Earth arc of Ele-
vations of the Quasi-Geoid 1
V.F. Yeremeyev and Is. Yurkina. Allowinp
for the Fffect, of Distant Zone::, on the
Klevation of 1,3',e. Quasi-Geoid and tne De-
viation of the Vertica.
16
Yurkina. p.S. Folorienskiy1 s .1, lip ti cal
Gr i for the Calculation of %,.evations of
of the ?uas,.- 24
M.I. Yurkina. The Solution of the Integra,.
Equation Descrbini the t-oni of tile -artn 41
Yeremeyev. Determination of a dna for
the Computation of aevations of the
Quasi-70eoia an. oeviations of the Vertica,_
from the r'orir.u.,_as of Stokes anc Wening-
l'eines 44
? Yeremeyev. Formulas an,. Tr,ole !or re
;:a,..,..:ulation of Creodetic Coorhates cy t t-
Po.Lodenskiy iethoo 77
? Yerelheyev'. A Method i'or the Solution of
the Reverse Geonetic i-roblem for reat Dis-
tares thruigh the Ca-culation ji COOrd)!-
ates f P "Xeniano Pc:Int of a Geodetic
105
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CSO-1578
TABLES FOR THE CALCULATION OF DEVIATIONS OF VERTICAL LINES
ON THE PHYSICAL SURFACE OF THE EARTH AND OF ETY,VATIONS OF
OF THE ,.kPASI-GEOID
Works of the Central Scientific V.F. Yeremeyev
Re-:eanh Institute of Geodesy,
Aerial Surveying and Cartography,
pp 3-16
M. S. Melodenskiy obtains, in his article L71_7; formulas
for the elevation of the quasitgeoid and for the deviations
and 17 of the ver ical on the physical surface of the Earth:
c=7: dS1 S (P0, t1)) da + -1- f (1)
- 1 nyo f [g---F-2-2,,-;0
o yo ro
r
S
1
= + 4 ilr,o f [g y + 3 r5cpd51 as (pa, 4)2Po J ro 1 Po atli cos A da -
O S
? ? ?4) cos A f!S+ ?2n 5;00 cos (n, x)
Yor02
1 i 5
lo
+
4nyo
1 f [g y+ 3 8cP dsi as (P0, 4))
2 po ro po aqi sn i A da ?
a
I f 8T sin A dS .40 cos (n,
s To2 lo
27c4==kgd-fiTpbcpda,
hgr ( Y) (g?i) o do.
, (2)
(3)
(4)
The symbols used here correspond, i ths-, main, to those
aaopted in the previously cited paper (1)_1( see drawing).
S ( p 0, 4, ) is the generalized Stokes function;
/s the 'radius vector .originating at the center of the
refeince patio and leading to a variable point S of the
surface, of the Earth, whose position is approximated by.
plotting only the normal elevations of points on the surface
of the Earth from the reference purta6 .c-
r
o represents an identical radius vectorAa point S of the
surface, corresponding to the point -under study of the
!Jhysical surface;
1,0 is the aistance between the points of i:ntersection of
radii-vectors p and 1)0 with the reference surface;
r is the alstanA betieen the point under i estigation
situated on the surface S an.i the intersection of radius
ve ctor p of the variable point with the reference surfaceg
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?
h is the normal elevation of the point unuer study;
R is the radius of the reference surface;
wis the angular distance from the point under study;
fif;is theamient of the reference surface;
A is the azimuth of element d(r;
dS 1.E:the element of surface 3; .
n is the orientation of an exterAor perpendicular to
the surface of the Earth at the .point under study;
x and y are the orientations used in calculating deviations
tand 1 ; x and y pass through the point under study uarallel
it the i,eference surface;
g is the measured value for the force of gravity; ?
:If is the normal value for the ,force of gravity, corresponding
to the measured value; it is calculated for the latitude and
normal elevation of the point;
tilo is the residual density of the surface layer; M, S.
Moloddnskiy L 1.1 designates this density as S7riol;
0 is the value of af at the point under htudy;
4
0
s (po, tI) =
,
2 3r 1 5R
---+? ? ?; cos 4i-3--cosR, 1
4)-i-
r Po2 PoP0 Po 2p,2
po - R cos .1)), (5) .
as (Po, ___ 2 r? cos 4' 3r0 cos
? 5 R sin
No+r3 2 rp02
Po"
+ 3 ? sin f4) In 1 (r + p0? R cos .) ?
P08 2po
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?
3R rR sin 4) + poro cos ?-j-
- ?cos +
Pos r (r po ? R cos 1))
(6)
Let
Let us point out that the expression for 2-S-Lea.41-
Po
in C
3_7 contains a typographical error. Neverthlsatiltesgs,
forrLula (6) in its correct form is used for calculations
in papers njand L74_/. Table 1 is intended for the
calculation of
F(pc,,+) = ? S (po, 4)) sin 4),
2
while Table makes it possible to obtain
Q (P0,1)) = R2 x" aS (Po, 4,)
2To Po ag'
(7)
(8)
It has been posited, in compiling the tables (?xxxithriz
h is to be expressed in kilometers), that:
f (Po, qi) = F (R, 4)) AF (P0,0 = F +
+ ?F (P?' 4')
1
I apo . p0=R 2 402 11,0= R,
4_ h2 )1
[ a2F (Po,
Q (Po, = Q (R, AC2 (Po, Q(R, 4))
+ h raQ (Po, 01 + h2 A 2
I [ (32Q (Po' 4))
L apo p0= R 2 ("Po- p0 = R,
F (R, I)) = ? 6 sin-- + 1 ? 5 cos ?
? 3 cos 4) In (sin-LP+ s1n2-1,
2 2
Q (RA)) = cog -i[csc_1? + 12 sin -? ? 32 sin2i +
2 2 2 2
+ ? 4, 12 sin2-? ln (sin I + sin2i)].
2 2
3
1 + :in T
For the function
Lambert Z. 5.2*.
Since the relation eio
corrections AF(po,y) R
in comparison a ith (Ry 4/ )
(f) is stfficiently largai.,
(9)
(10)
, tables have been compiled by
approaches
and 4Q(
and Q (R,
Values fo
?3?
unity (ifle