JPRS ID: 8453 TRANSLATIONS ON EASTERN EUROPE SCIENTIFIC AFFAIRS

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1.1 May ~.9 79
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TRANSLAT;ONS ON EASTERN EUROPE
$CItNTIFIC AFFAIRS
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CONTENTS PAG~
CZ~CNOSLOVAKIA
Modern Methods and Experiments in Dynamic Satellite Ceodesy
(Jaroslev Klokocnik; CEODETICKY A KARTOGRt1FICKY
OB20R, No 10, 11, 19?8)...........~ 1
Steam Generator Calculations for Bohunice V-1 Reactor
(Josef Zadrazil, Vincent Polak; JADERNA ENERGIE,
No 1, 1979) 24
- a - [III - EE - 65 FOUO]
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CZECHOSLOVAKIA
UDC 528,2;62g,783
HODERN htETHODS AND EXPERII~NTS IN DYNAMIC SATELLITE GEODFSY
Pra~ue GEODETICKY A KARTOGRAFICKY OBZOR in Czech No 10�and 11~ 1478
~~p 245-249, 275-283
(Article t+y Engineer Jaroslav Klokocnik, Institute of Astronorqy, Czechoslovak
Academy ~f Sciences, Ondre,~ov)
[No l0, pp 245-2491
[Textj 1, F~rposes and Meth~ds of Dynamic Satellite Geodesy
1.1 Introduction
Satellite p,eodesy is concernE~d With determining the shape of the earth from
satellite observations. There are two main approaches to satellite geodesy:
p,eometric and dynamic.
In the former, the satellite is merely an ob,~ective, like a geodetic point on
the earth's surface or a balloon in balloon ~eodesy. At least tWO ground sta-
tions from which t2:e satellite is visible at one time take simultaneous sight-
ings on it. From the measured directions to the sAtellite, the direction be-
tween the qround stations is determined. From several neusurements ta;cen ~
simultnneously from several stations, a trian~ulation network can be set up.
Its proportions may be taken frcm traditionRl nonsatellite measurements~
Satellite triangulation can span the oceans And thti~ can create a worldwid~
reference system.
The other method requires knowledge of the satellite's orbit, i.e. the speci-
fic p~ramaters which at a~iven r,ar,ent uniquely define the position and speed
~f the sntellite in space. Obse:vations are used to determine a sateilite's
orbit nnd changes in it, and to seek the causes of such clianges. The range
~f critical tasks in satellite geodesy is extensive and reaches beyond the _
confines of geodesy~ involving for example geophysics, global geology and the
theor;f of relativity.
The mnin ourpose of dynEUnic satellite geodesy is to determine the grav~tationc~l
constant, to make the determination more precise (as well as providing an
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independent control method~ and to determine the ~eocenti�ic coordin~~tes ot'
ground observation stations in a single worldwide coordinate syatem. The con-
nection between observations and these results is the satellite orbit, We may
say that the more precisely the orbit is determined, the more precisely the
p,r~vit~,tionc~l field is determined and the greater the quality and quantity of
the parameters ugefl to describe it, But the accuracy with wh3ch the orbit is
determined depends on knowledge of orbital changea,,and the increasing re-
quii�ements for accuracy are greatly complicating the task.
In p~rt, ttie orbit too is an ob~ective, or is used in predicting the futui~e
motion oi' the satellite (calculation of an ephemeris), wh3ch will be tracked
for a wide variety of purposes and used in satellite maneuvers snd linkups
of space vehicles. Tracking of satellites, determination of orbits and their
chan~es, and determination !ff the gravitational constant and station coor-
dinates may be treated as an iterative cycle.
The "primary aims" mentioned above are closely connected with determination
01' fluctuations in the earth's fields and variatians in rotation; here the
methods of satellite Reodesy are gradually replacing astronomical'methods.
'"he main stages in the dynamic method of satellite geoclesy can be classified
as follows:
measurements and their reduction;
determination of satellite orbits;
calculc~tion of the gravitational constant and other unknowns. We will discuss
these individual points briefly.
_ 1.2 Measurement
By "measurement" we mean observation of a satellite froM the earth's surface
or from snother satellite or observation of the earth's surface or the oceans
from a satellite, or specific measurements made on board the satellite and
transmitted to the ground~ The measurement results are primarily data which
~re used to determine the satellite's orbit. "Reduction" of the observations
is the procedure by which the raw measurements are filtered and corrected for
various perturbing factors using various methods, so as to bring them into
standard form for flirther use.
1.21 Mensurements From the Rsrth
In observing satellites from the earth, the folloWing types of ineasurement in
the o~~tic~l or radio parts of the spectrum are most important:
i~hoto.c,rnphy witY, special satellite cameras. The satellite photograph is used
to determine the d3rection to the satellite or certain topocentric coordinates
~f the satellit~, e.g. riR.ht ascension oc and declina.tion d. Reduction in
thi~ cnse entails transformation of the measured photographic coordinates of
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the ~atellite observed a~rainst t,he str~rs into celestial coordinates a- ~,nd
~ in ~he ca.talog epoch. We emphasize that photographic obnerv~tions can be
used t~ determin~ only the direction to the satellite, i,e, the direction
~ of the topocentric �vector Pp (Fi~. 1), but not the vector's magnitude IP~ ,
Tracking with laser ranging instruments. The ti~;~e between th~ pmisaion of a
laser pulse and its retu2�n frotn the target is measured (the satell.:t~ must be
prnvided with a meta]. reflector), The topocentric distance to ttie eatellite
IPI , i.e, the magnitude of the vector P but not its direction, can be cal-
culateci from the transit time, The laser system must be calibrated by meas-
ui�ements with a ground-based tttrget, and the c~lculated distance mu~t be cor-
i�ected for scatterinq of the signal by the atmosphere, for the fact that the
distance is not mensured from the center of the satellite but from its re-
flectin~ surf~ce, ai:d so on~ -
4~eus~irement of the doppler shift of a signal transtt;itted by the satellite,
This mer~suren;ents qives the topocentric velocity . The direction and dis- ~
tr.~nce ~~an bc~ deter^ained by radar, but gec:erally with low accuracy. The
d~ppler measurements must be corrected for the influence of the ionosphere and
tr~rosphere and other minor effects.
Rcic~io measurements can determine ~ and oossibly the mngnitude IPI. Rudio
measurements are less accurate than ce.mera and laser measurements, and for
a nwnber of reasons are unsuit~ed to dynumic satellite ~eodesy.
Interferometric measurements. 'Ibro ang~:lar values ~re measured with a method
~imilar to the photog:a.phic method, Reduction entails elimination of the
effect of signal scattering by the atmosphere, secondary reflections near the
~ntenna, diffraction and equipment errors.
Toduy, laser and doppler measurements are the most accurate~ Top performance
~ives errors in the tenths of ineters for the topocentric vector and in the
tens of ineters for the s~tellite's position in its orbit and for the geocentric
coordinates of ground stntions. The interferometric mei:hod which is currently
bein~ introduced into astronomy, ~eodesy and geo~ynamir.s ha~ qreat promise c~s
re~lyds accuracy.
1.22 Other Methods of Meas;;rement
7n observing one satellite froM an~�.!:~r, :he variation of ttie relative velo-
rit,y i:, cietermined, e.g. fron r.he doppl~~r shi:t of transmitted si~nals or
interferometricRlly. One o: ~he satelii'�,s collects the measurements and
trnnsmits them to the eqrLh.
The usua] "earth-to-sntelli~e" method o.^ m~=~suring is inverted in satellite
~Lltimetry r~nd laser Lrackin~- of Proun9-based reflectors fror~ the satellite.
A rndnr or laser altireLPr :.ieasures the vertic~l distance from the satellite
to the nadir. From the r~easured transit *ir~e, the altitude can be calculated,
anci f'rom this and orbital the profile of ~he ocean ~eoid can be determined.
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Th~ "1as~r scanning" pro,~ect, in which e~ satelli~e~borne laser radar (range
finder) scans the earth's surface at various an~les and records the laser
signals reflected from ground~based reflectors, 3s very much a new departure.
Instead of a number of expensive ground~�pased laaer ranging instruments, ~
single laser on the satellit~ does the measuring; with only "read:tng stations"
required on the earth.
Finally, by "onboaz~d measurements transmitted to es~rth" we mean gravitational .
Pradiometry and microaccelerometry. Most of these approache~ will be discuse~
in more 3etail in Part 2 of tYiis article.
~~ch type of ineasurement requires timi:~p, commensurate with the measurement
~ccurary. Fnr example, the transit ti~e in laser measurements of topocer,tric
dist~?r~r.es with an accuracy nf tl meter must generally be found with an accu-
racy tn nanosecond~ (by computer), clocked to UTC world time or some other
standnrd within a feW ten-thou4andths of a second,
_ 1.3 ~ntellite Orbits
1.3.1 Orbital Parbmeters
Now, to the notion of "satellite orbit". The motion of the satellite in a
~iven reference coordinatE system is described by equations of motion, which
are second-order differential equations. Their solution gives six constants:
the orbital parameters. These can be the~ rectangul~r geocentric coordinates
x, y and z and their first derivatives with respect to time, i.e~ the veloci-
ties x, jr and z, More informative, and extremely widely usca, are the so-
c~.lled "elliptical orbital paremeters" (Fig~ 2[not reproduced]), These are:
~the ma~or semiaxis a of the orbital pllipse; the eccentricity e oP the orbit;
the right ascension of the ascending node i.e. the angular dist�ance Jt of
the ascending node of the orbit from the vernal equinox; the argument of
the perigee w, i~e. the distance P of the perigee from the ascending node;
the inclination i of the orbit to the equator; and the time at which the
satellite reaches perigee, from which the right anomaly v in Fig. 2 can be
calculated.
1.3.2 Perturbation of the Orbit _
If the earth were a homo~ene~us sphere and there were no atmosphere, sun, moon
or planets, once a satellite was placed in a given orbit around the earth it
would remain there indefinitely. In fact, however, the orbit is sub,ject to
various perturoations, secular (long-term) and periodic (short- and long-
periodic). Tt~e causes (mechani3ms) of these perturbations can be classifs�d
as gravitAtional, nongravitational and apparent. The effect of these per�
turbations is to make the orbital parameters functions of ti~ce.
GravitntionQl perturbations of the orbit result primarily from the deviation
of the earth's shape from sphericity and the nonuniform distributfon of matter
wit}lin the earth. The most marked secular perturbation of the orbit is
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th~ effect of the enrth'~ polc~r flutttnin~; un ~ and w, Thi~ leads to t~
r~tntian nf the inter:ections J~,'U and P~,
P' (fi~3, 2) amounting to 360� per
month. In nddition, the moon and sun produce so.-cttlled "luni3olar" perturba-
tion of' the orbit, It is well known tr.at tt~e ~ttractivE forces of the sun and
moon produre tides in the oceRnS nn~l the l~nd, 4nd hence elastic deformationg
o� the earth; these ici turn produce other, secondary, lunisolar--t3da1--
perturbatians of the satellite orbit.
For r.lose-in satellites, the primt~ry perturb~,tion results from ntmospheric
drag, Atmospheric resist~nce has the sectit~r effect of decren:~in~ the ma,jor
seminxis and eccet~tricity of the orbit, ;,o ttu~,t the s~.telliL-e comes closer to
the enrth's sttrface; the process of orbital contraction accelerates until
the satellite unavoidably enters the denser la,yers of the ntmosphere.
.
Ttie nonPravitational forces include, in addition to atmospheric drag, the
pressiire of solar radiation, both direct and reflected from the e~,rth. Both
effects are bein~{ intensivel,y studied, Apparent forces result from the
chaice of the coordin~te system.
l.l~ The Gr~svitationr~l Potentisl
1.~~.1 I~;xprLnsion as a Series of 5pherical ~'unctions
We now introduce one go~sible mathematic~l formulation of the grt~vitational
potentinl itinci outline the procedure of using satellite observations to deter-
mine the constants Z~ and S~ of the ~ravitational field along with station
coorclinates.
We can write the gravitatione.l poLential V in ttie form of a series expansion
, in sphericnl fLnctionst
~ ~
v arf ~ 1~ t r` 1 M(~
~"m cos m7.
�_o M-o
-f- S~,� sin �~,~ll'ti~.~ ~ein q~)~ ~ ~l)
1
where GM is th~ ~eocec~*.ric ~rt~vitatic~n~.i constant,
r, c~ nnd ~ are respectively the magnitude of the ~eocentric vector of the
::rlLeltite (FiP. lj and its ~eo~eritric l~titude and longitude,
il i;; t.hc length factor (mr~,Jor semiax.is of the reference ellipsoid), in the
:~iunE ~lnit~ ris r,
n r~nri m are inte~ers designet,in~ the de~3ree and order of the flzncti~ns and
coeCficients given below (with n~ n)~
cos ~
I' � m n are spherical (Lapalace) hnrmonic functions of degree n,
nm i n
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1'~~~ ?~rr ~cmn1 ephc~ricrLl (r,onnl harmonic) functions or Leaendre polynamialn
(f'~u~cL.lc~n~s) of degree n,
P~ are tesseral spherical (tesseral harmonic) funetions or associ~,ted
Leget~dre funetions of degree n and order m(sometimes called sectorial
funetions for n= m), and
Ct~ and S~ arE the usual designations of the dynamic (Stokes) constants or
harmonic coefficients. In equation (1) they are dimensionless. For m= 0
they are called zonRl, for m~ 0 they are called tesseral and for n= m thE~y
~re called sectorial constants, analogou~ly to the functions wi~;h which they
are associated.
The bar indicates that these are values which have been normalized in some
manner, according to international practice. The harmonic coefficient,s char-
Eicterize the dynamic properties of the body (which could be dctermined numer-
iciilly if we knew the distribution of matter in the body) and its external
qruvit;titional field.
Wc t~rive already mentioned the secular perturbations of the node and perige~:
of ttie orbit re~ulting from the pola:^ flattening of the earth. These are,
with some simplification, characteri;:f~d by the magnitude of coefficients
C2~~. A non~ero coefficient�C3 ~0 indocates a tendency of the body to a"pear"
shape, while non2ero individual zonal coefficients indicate an asymmetry in
the northern and southern hemispheres. The tesseral and sectorial harmonics
define the structure of the gravitational field as a functian of the geogrr~ph-
ical latitude and longitude simultaneously. Fig. 3 gives an approximate geo-
metric interpretation [not reproduced~ of the significance of the harmonic
coefficients. .
1.42 Determination of the Gravitational Constant and Station Coordinates
From Perturbution of the Satellite Orbit
Assume that from satellite observations we have determined instantaneous (os-
culaLing) elliptic~l orbitnl parameters. If we ignore the effect of the
earth's ~;rfivita'tionul field, we ce.n write these parameters as polynomial
function, of time t~nd nn average t~ for the epoch o� all the observations
in ttie form
F%t = F.a -}~d1;t F%~i~~ - lo) -I- Eis~t - to)~ , ~2)
where i and ~ are indices with ranges i= 1,...,6 and ,j = 0, l, 2,.... Ei~
desi~,r~utes each of the orbital param~ters (section 1.31) in succession;
~i0 designntes the parameters at t0.
* Ttie parameters may be expressed in various coordinate systems; but since
their ciefinitions and transformations are outside the scope of a general ar-
ticlc~, we state only that they are given in a system defined by the earth's
equat~r, the pole of rotution and the vernal equinox. This is usually called
the "celestial" system; it is not inertial, but is sub,ject to precessien and
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IC we u1r~o take into account the perturbation p~rt of the potential Vgr in
c~auut,i~n (1), i.~:,
Var ~ v (Q~1l~r) r ~3~
tF?er~~~crturbutions ~gr reaulting from this perturbation potential wi11 be
r~dded to the right side of equation (2). In the interval t- t0, we have
1~'~, = f E dt. (4)
We seek ~n analytical expression for the perturbation E. Thia requires use
of the Lc~grange planetary equations, which express the relationship between
the perturbation potential and changes in orbital parfuneters. Froin (3) and
(4), rih:i , 4
~l~ ~~.4 ~ L(a, e, I). V,r ~ ~5)
wtiere Ei is again the i-th element and L1 is a linear differential operator.
The reader wi11 find specific equations in the literature cited.
E;qu~tion (5) provide~ c~ method of calculating the perturbation Ei resulting
from the set of harmonic coefficients C~ And S~ included in the perturba-
tion potential (3) and de�ined by expansion (1). In r~ddition, for the par~-
meters in (2) we may now write symbolically
E~~ = E~(E',~, E~,, E,,, C~~~ S~~) 7~ 1, 2,
i _ 1 6. (a)
Since the relation betweer, the rectangular Cartesian coordinates x3, ys and
z5 of the satellite in the cel.estial system and the elliptical orbital
~~artuneters is
x, cua (o W) cosS2-sin cu) siii S? cosl
= r cos (v tu) 3iii S? sin (v cu) cos S2 cosl
z, sin (u cu) sin I
r~:a(1-e~)!(1-}-eoosu),
we m~y write the relationships between the satellite coordinates and the
harmonic coefficients C~ and syr.ibolicully as fallows:
. x~ x~~l'''io~ ~:~t, ~':1:, . . . ~'nm~ ~~n~n~ ~8~
and ~imilarly for ys and zs.
r~utntion. Accordingly in eqtiation (2) there arise apparent orbital perturba-
~ions symbolized by the term DEi. The r_oordinates of the ground-based obser-
vc~tion st~tions (almost exclusively ~iven in a system connected with the
" r�t.~~~,in~; ~r;Lrth, which is clearly the mcst natural) must be converted into
the celestial system (mover~ent of the poi~.~,celestial time of observation).
7'hese measurements are ~enerally given in a different coordinat~e system, e.g.
ri~?ht riscension and declination oc, , a in the star catalog epoch. Here too
~e need a trar~sfor~ation, at least for precession and nutation Erom the catalog
epoch to time t~.
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Now we should have to write equations to transform the measurements (from
various satel.lite observations) and the geocentric coordinates X, Y, Z of the
observ~tion stations into the coordinate system in which the position of the
satel~ite xs, yg, z9 is expressed (i.e. into the celestial system). After
line~rizing these relationships we would obtain correc~ion equations for _
ad,~ustment by least squares. Here we cannot give a deta3led analysis bec~use
we do not know the definitions and transformations of the coordine,te systems.
We simply write
f�,a,
v = -l bE~
t-o
^mCaa
Sn
L ~knm ~'nin'+' Znm "sn~n~ ~sd~ k~d I' ~jd~~
w~! m~0
where 1 is an absolute term,
S Ei ure carrections to parameters Ei in series (2), i= 1,...,6, 0, 1,
2, ,.,,,~m~, ki, k~, k~, kX, ky, and kZ are �symbolic representations of ~
the coefficients of the unknowns and
C~, S~, ~ X, ~Y and 0 Z(together with sEi ) are the unknowns sought in
the least-squares ad,~ustment, i.e. the harmonic coefficients and co2�rections
to the geographic coordinates X, Y and Z of the observation stations.
Equation (9) shows that it is correct to determine the gravitational constants
and station co~rdinates simultanecusly. In practice this is not always pos-
sible owing to the considerable correlation between the tesseral harmonic
coefficients and the station coordinates. Accardingly, the ad,justment is
divided up; th~: satellite orbital parameters and a limited set of geopoten-
tial coefficients can be~ determined for approximate coordinates, after which
the coordinates of sele~ted stations are made more precise and the hr~rmonic
n n
coefficients again refined. These iteration cycles are repeated using ad-
ditional obs.:rvational data so as to refine all the unknowns and to expand
the ~et of harmonic coefficients and designated stations.
The upper llmit nmgX of the degree of the harmonic coefficients in equr.tion
(9) is determined experimentally with reference to the quantity and quality
of the initial de;,a. With presen~-day satellite measurements (cameras,
lasei�s, doppler apparatus), the set of harmonic coefficients can be deter-
minc.d only up to nmax - m= 10 or 12, or higher in some cases (with orbital -
resonance: see Part 2). The finer structure of the gravitational field
c~nnot be recorded from satellite orbits determined with an accuracy on the
order of tens of ineters by today's methods. To determine ihe coefficients
of hi~;her levels and orders, gravitational measurements on the land and
th~ c~r~:an r3.re being taken for ad,justment purposes, but this problem too is
not completely solved. Tt~e most up-to-date ~olution of equation (1), obtained
by combining satellite and gravitational methods, extends to approximately
n= m= 30. This determines the shaF~e of the geoid surface with an accuracy on
the order of 1 meter and the geocentric station coordinates to approximately
+10 meters.
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~�5 C~nclueion
We have given a brief and partial discussion of the purposes and "sta.ndnrd"
methods of dynamic satellite geodesy in i'indin~ the parameters of the earth'~
~ravit~tional field and other unknowns. In Part 2, we will examine satellite
altimetry, gradientometry, satellite-to-satellite tracking, subsatellite pra-
,~ects and other modern methods impinging upon dynamic s~tellite ~{eodesy with
the common goal of gradually refining descriptions of the earth's gravitatiunal
field, aiming at an accuracy on the order of centimeters in determin3ng geo- -
centrir. coordinates. This accuracy will malce it possible, for example,,to
follow tnover~ents of the earth's crust and to predict et~rthquakes in danger
are~s, to refine geopk~ysical models of the internal structure�of the earth,
to conduct various oceanographic studie~, to study the earth-moon tid~,l system
in det~ail, to test the theory of relativity and so on.
BIBLIOGRAPHY FOR PART 1
V. Abfilnkin; and G. Balmino. La Ceodynamique Spatiale. Notes de Cours
[Cou~�se Notes on Spatial Geodesy], Lannion, 1y74. CNES publication, 1976.
K. Ar�nold. VEF~FF. ZIPE, 7, 1972�
D. Bi�cuwer; and G. M. Clemence. htethods of Celestiul Mechanics. New ~ark,
Academic Press, 1961.
M. Murshc~. Osnovy kosmicheskoy geodezii[Introduction to Space Geodesy]. II.
Mosco~+, 1975 [in Russian].
M. G~.poschkin. SAO SPEC. REP. 353, 1973.
W. M. Kaula. Theory of Satelli~e Geodesy. Waltham, Mass., Blaisciell, 1966.
D. G. King-Hele. "The Bakerian Lecture, 1971i: A View of Earth and Air,"
PROC. ROY. SOC. A., 178, ;975. pp 67-109.
. C. A. Lundquist; and G. Veis. SAO SPEC. REP. 200, Vol. 1. 1966.
U. Veis. ~AO CONTRIB. ASTROPHYS. 3, No 9(dissertation, Ohio State Univ.),
W~shing'on, D. C., 1960.
H. G. W~]ter; and M. Wales. "Tt~e Differential Correction of Close Ear.~~h
Sntellite Orbits," Yart 1, Sci. Rep. ESRO SR-7, ESD AC, 1.967.
9
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H'~ft dl~'~ICtAL U5~ dNLY
(No 11, pp ~75-~831
(m~Xti~ Madern Methods and ~xper3ments
~,1 Introduction
- tn I'~rt 1 W~ ggw tYat the mc?in pur~~c~$e t~f dynamic satell.ite g~nciesy in to
- determfne th~ earth's gr~vit~tional constnnt and th~ geocpntric roorflinateg
_ of ~~b~ervntion gt~tion~. We kndw t h~ m~in points of th~ appro~eh te deter-
minutinn of thene quantitie~. NoW we wi11 acqunint durselves with resultg
achi~ved to dgte~, after which we wi1~ turn our attention to the mddern
methr~dn nnd experiments themselvea.
2.2 Mod~ls o� the Earth'g Gravitatidnal F'ield
7'he set of harmoniC ~oefficien:e and station c~ordinates fnrm~ the so-cc~lled
"p,rr~vitational field model"; frequently an overall or glnb~l solution for
t.hc p,r.opot~ntia:l ia dincues~d; among methods of antellite geodesy w~ Wi11
diacus:~ n"peometric" or "dynamic" solu*�ion on the basis of the data, or a
"satellite," "gravimetric (terreatrial)" or "combineci" solutidn (where sgtel-
lite measurements are combinc~ with gravitationul anomaly and othAr duta. _
'I'he most important solutions tt,us far obtained are as folloWS:
Stnndard Earth I(1966), II (1969), III (1973) and V(1976) (14, 16, 17, 35);
Lhe Goddard Space Flight Center Models of the ~arth, 1-10 (1g6~-1977), e.g
(33, 50); .
.^,fiItd 1 and 2(1975), 19j6) (5, 6~, and the Dimitri,jevich (13~ and ~tapp (e.g.
(39~) Krnvimetric models.
'I't,e first-mentioned solution, Standard Garth I(35~~ is Lhe aork of the
Smithsor,ian A~trophysical Instit~te (Cambridge, USA). Photographic observa-
tions t'rom a network of 16 Baker-Nunn ce.mer~s were used to determine the
coml~lete harmonic coefficients to n= m= 8(and zonsl to n= 12) and some
other coefficients. ihe accuraey of deterr~ination of Lhe geocentric coordin-
ates xas nbovt �20 meters. One of the most up-Lo-date geopotential ;c>>itions,
S~ V(l~j, uses laser measurer~ents and open-air magnetic anomaly maasurem~~nts
(1 x 1� ) frc~: 86~ of the entire earLh's surface, and is co~?plete t~ n= m= 2u
(plus several "resonance terms" to n= 37); in addition, more than 100 sta-
tion locntions have been determined with an accuracy o2' �3-5 meters, and a
geoid surface to With:n �1 meter.
hnot}~r~r soluLion is being derived by Lhe Goddard Sp~ce ~'light Center. 4ne
~f thc neWest, combined, solutions, GEM 6(50~, contains the co~plete har-
m~nir cocfficients to n= m= 25 and Lhe coordinF.tes of 369 atations. Some
1;~+,000 photographic, 76,000 laser and 332,000 radar and doppler measurements
arre uaed. The French-German GRIM 2(6j model is a combined solution from
F~hotc~graphic and laser measure~~nLs, res~lts from orbital resonances for at
1~
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, le~~t m= 1~-15, ~nd ~~~,000 1 x 1� gr~vit~tional r3n~m~.lie~. Th~ t~~g~r~l terms
are wnrked out tc (3n, 30), nnd the n~cur~~y di' th~ g~~~~ntric caordinateg ig
�5-10 metera, whi.le that of the geoid i~ ~3 met~rn,
Using the get df hurmonic cc~efficienta C~ and 8~ from the ind3vidual oolu-
tion~, it ig eagy to depict the "~h~p~" ~f th~ egrth by m~pping th~ congtt~nt
, potentinl gurfaces defined by ~quation (1) on a epec3fic, si~;~l~ mg~h~m ti-
rz~lly fl~ffn~d ~urfare~ F'ig. 4(not r~produced) shoWa ~ c~ntour ro~p of th~
~t~npe di the geoid With respect to th~ rotatian~.l. ~llip~oid Wh3ch mngt
closrly npproximatea the enrth. mh~ examplc is tnken :'rom reference [47~ and
reprer~ent~ a combin~tian of the (}~1 6(~3) combin~d golution With 1 x 1�
prnvit~tional anom~.ties.
'The hnrnonic cneffici~nts o� higher degrees ~nd ordere h~ve not yet bcen de-
Lermined With aufficient reliability and EiCCU2`LtCyl ~5, 6, 1~, 20, 25~ to muke
pc~gsible n determination of the ahape of the geoid xnd Lhe coordinatec o~'
abservatinn st~tiong With the centimeter accurncs which is required �nr vari~-
~us upplicntions (see coriclusion of
p~rt 1). A number of the coefficienta
ure :~trongly correl~ted With e$ch other (19~. 'Phe ~restest correlr~tions ure
beLaeen the tesseral coefficients und station eoordinates. Accordin~;ly vnri-
ous ulternntive methods for in~ependent control determinntion~ and methbds
capat,le ~f determining th~ harmonic coefficients of highcr degrees nnd order~
are being sought. Belox We Will discuss ~atellite altimetry (2.3), 'renonant- _
rl~ i ~ ~:~Lc11 ite:, ( 2. 4), geodynFUnic satellites and "drag-free" systems ( 2. 5),
l;~ser "scrsnning" from satellite~ in orbit (2.6), satellite-to-satellite
- trnc'r,ing (2.7), gravitational gradiento~etry (2.8) and radiointerferomctry
~ V ~ ~ ~ ~
2.3 Satellite Illtimetry -
The principle o2' this metrod is simple (see Part 1). A~i altimeter, i.e. u
verLic�.1)y-oriented radar or laser ranging instrument, is insta].led on board
the sut.ellite. Let us assume that measurements are being made over the ocean.
It~ ,tc~,f,1, i.~ ti re:~~i]t nf the effect of tiden, Wind, Waves und other minor
inf:itence~ on the geoid surface.~ l:ccordingly, the shape of the oceun pc~rt
of the ge~id can be determined f'rom altimetric measurement~ if the satellite
urbi! is knos+n (2, 11, 36, 38, 52j� i'he meusurement process consints of
sending ~~ignal to the surfrice and determfnfng the height of the satellite
t~bove Lhe measur�_:: location from the transiL Lime (Fig. 5[not reproduced~).
The ?~1Litude is cleurly insuft'icient Lo determine the shape of the geoid; it~
is nece~sary at the samc time to Lrack the orbiL, i.e. to determine the orbitul
p~r�r~rneters (using ground-tased laser ranging instruments or doppler unit~, for
exnmp.lc) nnd Lo determine the instnntaneaus geocentric vecLor of the
~.ztellitc.*+~ [footnote on following page)
~ ~!~ir ::L:~L~_mc�nt ubc,ut, t,he s i t'feret;cc bcLueen thc ~eoid and ~he de~th ot' tt~c
~i i ri'rr~ ~rom Lh~~ textbook concept of the geoid. I3ut is i~ required for
Lhe :>ake of grenLer ncruracy. '1'hese defia~ions are properly the ~ub~ect of
F;eodyntmic and oceanagrrsphic studie~.
11
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~I'he clc~ur~ey o� m~aaur~m~nt d~pet~ds primarily ~n the accuracy of the itiltimeter~
c~ravit~ttion~l stabilix~tion of the a~tel].tte is r~quir~d in order ~o guarantee
v~rtic~~ orientation. ~h~ effect of in~caur~cieg in flet~rmin~tion nf the orbit
c~n be p~rtly compena~ted by a suit~~b1~ computiei� method (7, 11J~
~xr~npl~s are given in F'ig. 6[not reprdduced]~ Here th~ gh~p~ of ~ g~~tion di'
th~ ~ec~id ~urface in th~ C~ribbean 5ea based on altim~tric meagurem~nts from
Skylnb ig compered with the GEM 6 model (33, 5~~~ ~hi~ is ~ tiyp3cc~1 ~xample,
und the follnwing conclugion may be dr~wn: beyond gystem~tic differ~nc~s
b~tw~en altimetry and overall solutiong ( mostly 1.en~ than t20 met~ra) and
between indiv3dual soluti~ns, identical �rends in the ghap~ of the geoid are
appar~nt; the nver~ll solution for the geoid surfuce is smoother, whi1~ ~zl-
timetry givea more de`Qi1, e.g, unders~s Lrencr?es, ridg~s, rifts ~nd so on.
The xccuracy of Lhe Skylab altimetric mea~urements was about tl meter, and
the et�ror in orbit determinQtion 5 meters. The altimeter o� G~05 3 ggv~ re-~
3ults accurate to Within t0.6 metera (and after filtering to within 0.~ meters~;
the orbit was tr~cked by a network of doppler atations (constantly 20-40
~tatians worldwide), and wan determined with about a 3-meter radial error.
In additinn to Skylab measurements (52~, a number of au+hors (1~, 37� 38] h~ve
used a nwnber of GEOS 3 overflights with multiple measurements on the locutions
to create ocean geoids for aceas of Austrnlia and North Americu.
Yrepurations are being made Lo launch the oceanographic satellites S~ASAT-A
(May 1978) and S~ASAT-:3 (1980) with laser reflectors on board so as to deter-
mine Lhe ocean geoid with an accuracy of t10 em and to conduct oceanographic
reseF.rch. The orb~=t is to be determined 'by ground-based l~sers and doppler
instruments and by trecking from other satellites (see below).
2,4 Orbital Resonance
Orbital resonance of satellites has already been used successfLlly for seven
years as an independent control determination of selected harmonic ceeffici-
enta, and at the same time for determination of high-level and high-order
coeffici~nts whose values in comprehensive solutiens are unreliable or e~~en
incorrect. ~
[from preceding page~ The current conceptian of satellite altimetry is
about 1~~ yersrs old (32, 34~. The first attempta to reflect a satellite sig-
nc~l from the surface of the earth wer~ carried out with the Canadian iono-
spheric 3c~tellite 1962~9a. (3~+~. For com~unication purposes, a laser trans-
mittcr wns used in the flight of Gemini 7~34~; radar eltimetry was used in
Lhe fpollo prograrc; Lhe first geodesic experimen~ Was made from the manned
Skyir~b ~tntion (1973) (52J ~see Fig. 6[no~ reproduced)); and today the re-
sults :'rom G'~;OS 3~2, 11, 38j have been made public by the US NASA organiza-
tion nnrt of the American progro~ on Earth and Ocean Dynamics.
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Sr~t~llit~ r~son~nc~ ig the gituution in whiCh u~~te~.lite mak~~ an 3nt~grul
numb~r p of orbitg in rxn integr~l numb~r ot of
gideri~l de~y~~ For clarity,
let ug asgum~ a g~t~llite in a polnr orbit m~lcing 1~ orbits a duy, go thxt
C~i / a = 15/1. The g~ographic~l lrcagitud~ of th~ int~rg~ction nt' the nrbit~nl
plan~ wt~h the e~rth'~ ~qu~tc~r wi11 ~ht~nge by 24� with each pASg, go that
nfter 1S orbitg the gnt~111te w311 be buck over th~ geme pc~intg on the ~~rth.
Thig proc~gs wi11 be rep~Eted w~til perturbing fdree~ (th~ ~ffect of C~ p,
atmog~heric drag and ~n or.) chgnge the drbit.~ ~inc~ thig r~gonance Conc~ition
cdntinu~s for a rel~tively ldng time, r~p~at~d fli~ht ov~r the s~me pgrta af
~ ttip ~ravitational field l~ads to u long-periddic perturbgtidn nf
the drbit
inste~d of progreggive ~hort-perlodic perturbations: i.e. in the t~n~eral.
terms with m= 15 in equation (1). Perturbations in the other tesnernl h~r-
monic Coefficientg average out over time, but long-periodic p~rturbations in-
~rec?~e unc. take on the character of seculur pertucb~tiong, r~ccumul~ting sn
that by u~ing method analogous to the ordinnry methnd fbr determining the
~ravitational constant (Part 1) a lineur admbination of ha~cnonic coefficients
nf order m=/~~ ~ 1, 2,...) is determined. These noefficients ure ~~etermined
:;epnrately from the others, xithout large mutual Cor.relations, and moz�e rexl--
i~Licc~.l.ly than in comprehensive geopotential solutions, pnrticulnrly for higti
valiie~ of n xnd m. Herein, nccordingly, lie the clenr c~dvantage~ ~nd disc~d-
vuntAges of the method. ~he independent determintttion ~nd the hi~h urders nrf~
~dv~ntages. A disadvantage is ~he small set of constant3 determined; more-
over it is neceasary to wait until resonant orbit ig reached. '.he uriques-
'..:oned advnntage of Lhe method is the fact that no purticular ad,~usti.ng up-
pnrat~is i.~ required either on the ground or on the ~atellite (quite ttie op-
posite of ctill other methods).
In Lhe lnst fex yearg, the orbits o: about 30 sutellites have been un~lyzed,
purticulurly in resonance periods of 13/1, 14/1, 15/1, 29/2 and 31/2. Mo3t
of Lhis work has been foreign: see referet~ces 18, 19, 20, 40, 41, 48, 49, 51;
other studies have come from Czechoslovakia: see references 21, 22, 23, 24,
25, 1+~~, among others.
%�5 Ceociynamic Satellites and "Drag-Free" Systems
2�51 Introduction
Part 1 provided n notion of orbitnl perturbation~, und We saW Lhat the cul-
~~ulnt,ion of harmonic coefficients and coordinates of points on the earth'~
::urfnce depends to n considerable extent on the accuracy of their detEarminu-
Lion. Gruvitational perturbutions are We11 1%noxn up to the rather smc~11 ef-
t'ect:: of high-order and higt~-degree Lerms (other tl~rsn resonanc~j, and the
rrror in the orbit from incor~plete knoal~dge of tt.ese is today on the order
nt' trns ot' me*ers for the geocentric posir,ion of the st~tellite. Non~ravita-
Lionrsl perturbations such es the effect the ataosphere and the pressure of
>olnr radiation have been l~ss Well modei~iter iter~tti~tt method aith provision for specifying the level of pre-
cisian; the c~~lculr~tion proceeded sect~r by sector along the length of the
tubes in each bundle. In view of the relatively small temperature difference,
the ~vergge temperature of e? given sector was used in calculating the thermo-
~~hys{cr?1 properties of the coolant and trgnsf~r surfac~ material in the trans-
fer r~uations. The temperature of the primary coolant at the outlet collector
of the steam generator Was determined from the temperatures on exiting from
the individual bundles of tubes. From the computation formulas used it is
clenr that at a constant operating pressure in the drum, the other operating
E~~rarr.eters of the secondary circuit do not influence the heat transfer
vr~1 u~~, sc~ th~.t it m1y be usrd in deterainin~ the characteristics of the
E~rimnry and secondary circuits during co~~utation of the characteristics of
the poaer station block as a s+hole (6, 7].
28
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~n~ o~~~ictnt. us~ ornY
In the pre~~ding paragraph r+~ ~t~0aribpd th~ ~~ur~~ ~f ~al~ulatt~n nf the
~h~rmnl f1ux~~ q~ giv~n up ta th~ c~ol~nt in th~ ~~~ondary ~ircuit in th~
individual ~~~tnr~. Th~n~ fiux~g pradue~ in ~e~tian~ ~..1 bnd ~.1 h~~ting di'
the fe~c~W~t~r ta th~ ~~tur~tion temper~ture cnrr~~pdnc~ing td th~ pr~~~ur~ in
th~ drum, ~nd in a11 ~~~tic~ng gt~~n i~ pr~du~~~; ~th~ c~u~ntity i~ gav~~n~d by
the dryn~~g c~lculat~d aft~r its eep~r~tic~n in th~ ~te~m vdlum~, by
thr amdun~ oi' blaudatim dr dr~?in~~ (ahieh for gimplieity r~~g ~s~um~d ta b~ in
pr~p~rtien ta th~ ~mount e~' ~t~sm pradu~ed), ~nr1 fin~lly by th~ m~g~itur~~ ~f
tt?~ t~~nt inss~8 eround the generetor ~h~il (rlc~~unted t'ar i n th~ cr~1~ul~ti~~~
by thr t,hcrmnl ~f~'i~iency ~oeffi~i~nt p~ at' ~h~ gen~r~tor)~ Th~ ~quatfnn
c~p p~ u~a s~t up ~or e~eh ~eCtic~n g@CtlPd~fl~ tti thi~ pr~~~dur~; eqti~tion
( 6) r~~$ nui~ably ad,~ugt~d ~nd th~ pr~~ent equ~tidn ~olved by it~rt~tidn e~e~ the
comput~r. Th~ re~ulting ~t~~mm p~r~neters fnr th~ ~~candgry ~ircuit Were deter-
min~d by guceming ~nd bal~n~in~ the h~~t in ~,11 C~mput~ti~n s~cti~ng.
f~v u~ing thi~ metho~, th~ valu~s ni' th~ det~rYninin~ i'~ctorg can b~ ~eleGt~d
und the ~rendx of the th~rm~pt~ysic~l op~rbting ch~rg~teri~tica Within th~ ~
~tefun p,ener~tor ~~1GUl~t~d fcr individugl. ~e~tinng; th~ opernting pgrr~met~rs
nC the anrking ~ubst~c~~ ~r~ ~1sc~ ~glculated ~t the ~xitg from th~ ~rim~ry
~nd 3eCnndnry cireuits. The det~rmining fectnrs in the development ~nd uge
~,i' thi~ method fgll into thr~~ groups:
a?. ,?.I,~u:;tubl~ ve?lues of nperating pgr~meter~ whi~ch are aggocinted with pro-
duction regimes of thp prim~ry eu~d ~econdary cireuit~ bnd ahich inrlude tem-
perature, pr~~sure and mn~~ flox of th~ primary ceolgnt at th~ gt~gm g~nerator
iniet, nnd the entl.alpy and tpmper~ture of the secondsry-circuSt feedw~ter;
b. the ~teum generator parameterg Lhemgelves, Whirt~ mu~t be bMSed ~n meunured
v~~l.~~c:; in 3imu2ation calculations; Lhey include the thermnl efficiency of the
~team ~enerator, g correctian fnetor for the preaence of oxidi2ed (dirty)
ti~~nsfer surfaces, Lh~ Wat~r level in th~ steaz~ ~ener~tor drum, Lhc m~ss f16W
in bloudown or drgin~g~, gnd the ~Me~sure in the drum;
c. computational and geometric ccnstants vhich depend on the calculation pro-
cedure and the design of the 3team genernLor.
u. Cor~putation Results nnd biscussion
Our meth~d Wnn used to develop the SC}iPGVi cor~puter program in ~OFiTRAN IV;
cnnpuLntion wqs carried out on a Tesla 270 computer.
't'tie i.r�~�r~~i:; of Lhe thermop?~ysic~l parameters inside Lhe drumtrere calculated for
l~ di::tinct cnlculation sector~. ~Phe number of such areas rould be incrensed
�~inp, our method so u~ to obtain a better calculation of heat tranafer nver
the full length of Lh~ tubes, bu~ Lhi~ would aeaken our as~umption thut there
i~ no heat trr~nsfer ar flux in the horiz~ntul direction betxeen individual ser-
tior~s~ nnd aould also require a taore detailed Lreatment of the local che.nges
in ench sector resulting fro~a bloxdoxn or drainage, introduction of feedsrater
r~nd removnl of steam, as Well as from loce~l heat losses.
29
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tn t,h~~ r.~~m~rut~tidn, thc ~;c~~mctrie ~~h~~~nt~ ~r~d ba~i~ d~~ip,~ p~,rnm~trr~ v~r~
t~~kr.r~ t`ram r~f~rpn~~n 2] ~nd t,h~ ma~nitud~g of
tih~ Critic~~. f~~tz~r~ t~e~t`e
cha~~n wi~hin the r~n~~ ai' r~comm~~A~d v~lu~~ faliaaing ~n ~n~1y~i~ af ~omputt~-
tiion~l re$u~t~a by th~ m~tt.~c~ c~~~erib~~ be1oW~
l~dr numb~r df re~~dnr, th~ comput~d therm~i ~ffici~ney ~ p~} v~r~~d b~tWeen
' d,978 ~~id 0~9~~; but it i~ cle~r th~t the pre~i~i~t~ rritt: Whieh thi~ r?~lu~ i~
rho~en a~~~at~a on~y th~ eom~u~~d qu~?ntity ~e~am pro~uce~. Td mak~ ~h~ ~~m-
putati~ne more pr~c~~e, iL ai11 be n~c~as~ry ~o m~1c~ us~ ~f m~~~ured v~~u~~
for h~~t loss in the st~am ~en~r~~or during op~r~tinn, Whil~ for in~ivi~u~1
~amput~tion e~ctor~ it vil~, b~ n~c~s~gr~ ta tr~gt h~~t lo~ge~ in t~rm~ ~f the
eorr~~pdnc~ing dt~~m surface eletn~rit8. .
mo eaieul~te the b~gic oppr~tin~ eh~r~eteristic~, rre ~nnly~ed the ~ffect df
~cir~~~inn o~ thermal resi$tanee cerr+ection coefficientg on the r~gult. mhi~
analysis enablee us to state th~t ~~l~ctior? of t,".~ eaeffici~nt k h~8 no �
fund~m~ntal effect on the r~sulta Within th~ rang~ of recommen~~~ valu~~~ ~'he
~~cur~~y of d~t~rmination ef therm~l resist~nc~ k t5), ~a ia ~hown in ~'ig.
has n cnnsidernbl~ ~ffeet on the temp~r~tur~ of t~~ prim~ry cooi~nt t1~ ~t the
vutl~t ~nd on at~e.m produetion mp. Thu~ for the pi~nned ap~rating p~r~.m~ters
We found k2 �(2�0 - 2.5)~8.59845~10-3 m2-deg C/kW. ~1e may r~commend that the
r~c~igtnnce k~ be apecified for ~ given valu~ of t1~ ~nd the heat trang~'~r
equations be corrected for the epecific aitu~tion~ 3inc~ in prgetice the
vulue nf k~ dependg on the heat conductivity and thic;cnesg of th~ depo~it~d
lnyer, if we know the age of the layer we can determine the degree nf "aging"
of the tranFf~er surface und thue determine ita effecL on Lhe steam gen~rator
psrsrneters in the interval beLaeen cleanings. A moxe profaund analysia nf
heat transfer tirould require correction of the equation~ used for the gpecific
lnyout and geometr~ of the transfer surfaceg within the boiling water ~nd an
un~er~ttu~c~ing of the ~ffect of a nonuniform heat ?onding nf Lrie transfer sur-
fa~es c~n creation of a heat-resistant 1~yer in L1~e individual sectorg.
Another important quantity in calculating the operating characteriatics is the
c~ccurnry of determine.tion of generator drum pressure. The dependence of the
main operating chare.cteristics on this pregsure (pB) is ahown in Fip,. 3 for
the desig.n parameters. b.ven though t~ pressure pg = 4.609 t~"a is ptescribed i'or
every ~~ro~iuction rep,ime, it is clear the~ xithin Lhe tolerances set by the
reguluting organs, proceas changes lead to varigtions in this pressure $nd to
corresponding changes in the operating charact~ristics.
Civer~ the complexity of the steam separation process and the lack of suitgble
formulas for this type of ateem generator, ae developed an approximate method
for eslculnting steam aeparation in the steam apace only, neglecting t}:~ ten-
dency tc separation in the louvered separators mounted in the upper part of
the drum, Which s+ould be most pronounced primarily at high humidities (51.
'Phe calculations vere nade for various changes in the main operating parameters
und partfcularly for changes in the xater level h~ above the upper row of ex-
change tubes. 1't~e final steam dryness resulting from mixture of gteam from
various sectora in the outlet collector is shoan in Fig. 4 as a fLnction of
the height h~ for the desiFn peremeters; separation in the entire sLeFm
:?pgce was Laken intc account. ralloWii~g analysis of the corputation nnd
30
FOR O~FICIAI. Il5E Oh'LY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000100050024-9

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-44850R000100054424-9
~nk n~~ictnt. us~ ornY ~
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