Line of sight velocity corrections for daily rotation and annual revolution of earth during solar observation

Salman-Zade, P. KH.

English

NASA Technical Reports Server

e - 
National Aeronaut ics  and Space Adminis t ra t ion 
Goddard Space Flight Center  
C ontr act No. NAS- 5 - 92 9 9 
ST- SPHA- 10461 
CORRECTIONS FOR LINE-OF-SIGHT VELOCITIES ON 
ACCOUNT O F  THE DAILY ROTATION AND 
ANNUAL REVOLUTION OF THE EARTH 
DURING SOLAR OBSERVATIONS 
- Microfiche (MF) 
ff 853 July 65 
- 
ICATEGORYI 
2 
2 
24 M A R C H  1966 
https://ntrs.nasa.gov/search.jsp?R=19660026491 2020-03-16T20:35:49+00:00Z
ST - SFHA - 10461 
COR2ZCTIONS FOR LDE-OF-SIGHT VEmCITIES ON ACCOUNT OF 
DAILY ROTATION AND AN13UAL REVOLUTION OF THE E J m H  
DWING SOLAR OBSERVATIOI~IS * 
Vestn ik  Leninp-radskogo U n i v e r s i t e t a  
S e r i y a  Plntematiki, Melrhaniki i Is t r o n o n i i  
L E  N I N G  R A  D, 1966. 
NO. 1, vypusk 1, 166- 171, 
by F. Kh. Snlman-zade 
S U I1 M A R Y 
The ques t ion  of l ine-of-s ight  v e l o c i t y  c o r r e c t i o n s  f o r  t h e  r e l a t i v e  
motion of  the  observer  is considered he re  wi th  more d e t a i l  than  i n  preceding 
works. The au thor  hzs  recourse  t o  a more r a t i o n a l  scheme f o r  t h e i r  ca lcu la-  
t i o n ,  which is thus  proposed f o r  p r a c t i c a l  purposes. An exanple of co:Jplete 
ca1c:i lations is given f o r  a s i n i l e  case. 
* 
* +  
It is w e l l  known tliat t h e  measured s h i s t s  O Z  s p e c t r z l  l i n e s  on 
ne;.atives r e y e s e n t  on ly  the  r e f l e c t i o n  of heavenly body's l ine-of -s ight  
v e l o c i t y  r e l a t i v e  t o  observer.  In order  t o  b r i n g  the  measured s p e c t r a l  
l i n e  s h i f t s  t o  Sun, i n  p a r t i c u l a r ,  i t  i s  necessary t o  f r e e  them from t h e  
in f luence  of obse rve r ' s  motion r e l a t i v e  t o  the  Sun by way of i n t r o d u c t i o n  
of corresnonding c o r r e c t i o n s  t o  the measured l i ne -o f - s igh t  v e l o c i t i e s .  
:- s e r i e s  of works have been s p o t t e d  i n  the  A 0  05 the  Leningrad 
u n i v e r s i t y ,  concerned wi th  t h e  s tudy  of the  s h i f t  of F r a n h o f e r  l i n e s  i n  
t h e  s - l a r  s?ectrum. But il; ~.JELS found t h a t  i n  order  t o  speed up the  co::pu- 
t t . t ions  the re  a rose  tile n e c e s s i t y  o f  a more r z t i o n o l  sc5ene. T h i s  i s  Fre- 
c i s e l g  the  o b j e c t  of the uresent  work, which, man:- o t h e r  th ings ,  proFoses 
a p r - l c t i c a l  schezle f o r  t he  conputat ioc of c o x e c t i o n s  of l in ; -o9-s i rh t  velo- 
c i t i e s .  (See [I]) .  
2. 
If V is t he  t r u e  l ine-of -s ight  v e l o c i t y  at any 2o in t  Q 02 t h e  
Sun's s u r f a c e  (Fig. 11, we have 
Here V* is t he  measured l ine-of -s ight  v e l o c i t y ,  C1 is t h e  pro jec-  
t i o n  of observer ' s  motion v e l o c i t y  on a l i n e ,  linking him wi th  t h e  observed 
p o i n t  Q on the solar disk at time of observat ion,  Co is t h e  p r o j e c t i o n  of 
observer ' s  motion v e l o c i t y  on a l i n e ,  l i n k i n g  him 
v i s i b l e  c e n t e r  of t h e  inage -  a t  the nonent of t i n e  of solar d i s k ' s  c e n t e r  
observa t ion ,  A, is t h e  l imb e f f e c t * .  
t he  first is condi t ioned by t h e  d a i l y  r o t a t i o n  of the  3 a r t h  and t he  second-  
by the  nnxual r e v o l u t i o n  of t he  Sun a-ound t h e  Sar th .  Let us pause at t h e s e  
two co r rec t ions .  
wi th  t h e  p o i n t -  t h e  
The motion of t h e  observer  r e l a t i v e  to Sun is rietermined by two p a r t s :  
1 . - T h e  c o r r e c t i o n  f o r  t he  d a i l y  r o t a t i o n  of the  S a r t h ,  expressed 
i n  km/sec and added t o  the o'nserved v e l o c i t y ,  is given by the  express ions  
Here 9' i;; the h e l i o c e n t r i c a l  l a t i t u d e  of the  observer ,  r i z  t he  
d i s tnnce  from the observer  t o  the  center  of t h e  Ear th ,  t a k i n g  i n t o  account 
hi6 l o c a t i o _ ?  above s e a  l e v e l  (expremed i n  km). I f  t h e  l a t t e r ' s  h e i c h t  is 
- h, we have 
r / - " + / I ,  (::\ 
where ro 
Earth.  The value of ro is found from the  expres3 ion:  
is the  d i s t m c e  ire--- .-A the ?o in t  a t  sea l e v e l  t o  the cen te r  of t h e  
r,, -- a (0.998320 + O.OUlG84 cos 2? - 0 . 0 0 0 0 0 4 ~ 0 ~  43). (4) 
In fornul;  (4) a i s  the  ecjustor ia l  raZiuc of t he  Z x t h  expressed 
' i n  km, Cp i s  the p e o ~ r a p h i . c a l l a t i t u d e  of the  place of observat ion;  as t o  <p , 
e n t e r i n p  i n  (2), i t  is  determined from the  e--.I)rt.snj.on: 
p - 695.65 sin 2~ -/- 1",17 Sln b- 6) 
I n  formula 2 : 1) the  c j u m t i t j  36164.1 is the  numb-r of mean s01.z.r 
seconds in s ide rea l  days; 2)  $ i s  the v i s i b l e  d e c l i n a t i o n  of  the po in t  Q 
* By li.;?b e f f e c t  we understan6 the dif- .erence i n  :he p o s i t i o n  Of SpeCTral 
l i n e s  o? the l imb ax6 a t  Sun's center.  
3 .  
a t  time of observa t ion ;  3) H = s -  41 is the  hour angle ;  4) a - is  t h e  
v i s i b l e  r i g h t  ascension of t he  poin t  Q a t  t h e  nonent of o5:ervatian; 
5 )  s is t h e  m e a  s i d e r e a l  time. 
Note t h a t  $ and a v  determined 
r e l a t i v e  t o  t h e  true equa to r  andequinox, 
are found by zdding c o r r e c t i o n s  A q  and 
MY A Q  t= t h e  vis%ble eq;nnt-r-jfi c=;rdfnn= 
t L : j  of t he  cen te r  of  t he  s o l a r  d i sk ,  
and 
t he  c o r r e l a t i o n s  : 
do 
s o  ; t t izse correctiDnx a r e  given by 
(6) 
AT - - - h cos 9 sec C,,, 
1; - 0 sin 3. 
Here is the  p o s i t i o n  angle of Fig. 1 
the  p o i n t  Q, measured from the  west end of the  d a i l y  p s r n l l e l  (Ti;.l), 8 
is tl-e angle  fortled L:r rays l inkin;-  the  ob;erver w i th  the  g o i n t s  Q 2nd t:ie 
v i s i b l e  c e n t e r  of Sun's image 0. If J is t h e  d i s t znce  from 4 t o  tfie cen- 
t e r  of  Sua's im-.ye, 
r a d i u s  of the Sun, we hLve 
po is t he  r a d i u s  of Sun's i n q e  anci S is thn anqular 
It shouli be gated, th2.t :Ihen the  S u . 7 ' ~  h e i r k t  is l e c b  thLm 30°, 
nccou:~t shoulr! be tnken O S ;  the  d i f f e r e n t i a l  r e f r a c t i o n  when determining jl 
and. 6. 
t 8 ?'or a f i x e d  p h c e  W is co;lstcint s o  t h a t  t he  c o r r e c t i o n  C1, whick 
llas E? naxi  .m vclue of ~ 0 , 4 6 h / s e c ,  can be t a b u l a t e d  f o r  every day by the  
a r y u a e n t s  and H. 
2. - The co r rec t ion ,  expressed i n  kn/sec, f o r  t h e  o r h i t a l  r n t a t i o n  
of t h e  Zar th ,  which mast a l s o  be added t o  t h e  observed v e l o c i t y ,  is, zccordi i i r  
t o  F. Sc les inge r  [2], piven 5s' the e.xpression: 
C; - 1732,34 ( A x  C O S  ? C O S  a' - / -  A Ycos  2' sill d + -LZ sin C'). (7) 
j;ci-,z I:, Y ,  Z a r e  the  'yeocentr ical  r e c t a n s l g a r  ec_uatol-izl coordina- 
t e s  of the cecLcr of t i le  '_,un, determined r e l a t i v e  t o  m e a  C o w t o r  and equinox 
. 
4. 
m d  r e l a t e d  t o  a c e r t a i n  egoch, f o r  example ir, t h e  case of i n t e r e s t  t o  us, 
t o  t;;e yea r  1963. AX,  AY, AZ CY:  the v e l o c i t y  coTponents of this motion, i n t e r -  
po la t ed  t o  the  moment 0- ob:;ex-rtFon r e s p e c t i v e l y  i n  the d i r e c t i o n s :  1) paral- 
l e l  t o  t h e  e q u i n o o t i a l  l i n e ,  2) p a r a l l e l  t o  t he  e q u a t o r i a l  plane,  3 )  perpen- 
d i c u l a r  t o  t h e  e q u a t o r i a l  plane.  
A l l  these  six q u a n t i t i e s  a r e  t abu la t ed  i n  t h e  Ast ronoxica l  Yearbook 
for every day z t  00 00 hours ep5ener i s  tine. Q' and 6 1  i n  forxula (7) are  
t h e  e c u a t o r i n l  conrd ina te s  of the poin t  of observa t ion ,  l e t e r z i n e d  r e l a t i v e  
the same :c,uator and equinox as X, Y, Z. 
According t o  [l], we have f o r  t h e  c c r t c r  01 t h c  Sun : 
T h e  corrcsyonding equator i ; i l  coo rd ina te s  X I  Land 8' 01 p o i n t  Q 
a r e  founcl by adding the  qua -n t i t i e s  
t o  t h e  v i s i b l e  e q u a t o r i a l  coor7 ina tcs  02 the cen te r  cf the  Sun ab and &\ 
a t  t im of ob-;ervetion of the  p o i n t  9. 
T a k i g F  i n t o  account t h e  above-said, tile c o r r e c t i q n  i n  km/sec f o r  
t h e  mof-ion v e l o c i t y  cozponent of %he observer  zlong the  visual ray t o  t he  
p a i n t  C, w i l l  have t:,e form 
2-r co\ cp' 
hblG 4 1  c, c;+c: = - -- cos a sin H -  1732,34 (AX cos I;' cos 9' 4- 
+ .Ll' .os i ' s lna '+AZsin?) .  (9) 
The c o r r e c t i o n  I_- -:!I: ?-;-re-:;ic.r, (7) f n r  obscr-.-i.r's ? lo t ion  a lona  
t h e  l i n e  l i n k i n g  him wi th  t!,e po in t  0 ( a t  t h e  t i n e  of obse;vation of t h e  disk's 
c e n t e r )  i s  found by s u 3 s t i t u t i n . y  i n t o  formula ( 9 )  t h e  r e s -ec t ive  e o u a t o r i a l  
coorrlin-ites of the  Sun's c e n t e r  m d  of the  q u z a t i t i e s  AX, A-Y, AZ ;It t h e  t i ne  
w5en the  Sun's spectrum is observed. 
SuimarizinT the  above-expounded rnct;;od of c! - . tcrr i inatfon of t h e  correc-  
t i o n  for obse rve r ' s  motion v e l o c i t y  conponent a l o n r  t h e  v i s u a l  r a y  toward 
t h e  ?oizL- of observxt ion,  we nay rcduce i t  t o  t h e  p?rIor..iiEc 01 the fo l lowing  
o p e r a t i o m  : 
5. 
1. - a. 
moncnts of t h e  of obnervat ions*.  
2.- The p o s i t i o n  m g l e  3/ of t h e  po in t  of observa t ion  on the  Sun's 
and so of t h e  center  of Sun's d i s k  are i n t e r p o l a t e d  t o  the  
d i s k  is measured ( f o r  the p o i n t s  of t h e  e a s t e r n  and western ends of the  equa- 
t o r  t he  anF1e i s  r e s p e c t i v e l y  equal t o  1800 + P and P , where P is the  pa- 
s i t i J n  an,yle of the  Sun's r o t a t i o n  axis, c o q u t e d  from t h e  nor thern  meridian 
point] .  
3.-  The co r rec t ions  A a m d  A 8  a r e  conputed by formulas ( 6 ) .  
4.- The e q u a t o r i a l  coordinates  u and 6 of the  observa t ion  poin t  
z r e  obta ined  by adding ba a b  A6 t o  t h e  above-obtained va lues  of Ho and 
$ 0  
5.- The s idereal  t h e  6 i s  determined f o r  every moment of time of . 
observa t ion ,  and then the  hour angles  H = s - @  of the observed po in t s  on 
the  Sun's  d i s k  a t  t h a t  noaent. 
5 . -  r and cp' 
7.- F i n d l y  the  value of 
a r e  determined fro::: t h e  express ions  ( 3 ) ,  ( 4 ) ,  ( 5 ) .  
2nr cos y' -
Sli 164;i- ' 
bein?  cons t an t  €or the  p lace  of observet ion,  i s  coix:luted. 
8.- -Lfter f i x d i n g  the rezpcc t ive  t r igonometr ic  f u n c t i o n s  of 6 and H 
en te r in r .  i r . t o  fornuln  (21, we compute the c o r r e c t i o n  CI1. 
anc', t>-e i r  f i r s t  d i f r e r e n c e s  4X, AY, AZ, on thc  day 0: observa t ion  a t  0000 
hou-s eyhemeris time; then these  q u a n t i t i e s  a r e  i c t e r p o l a t e d  t o  the  t i a e s  of 
obnervbt ions of t he  S u n ' s  d i s k  points.  
9.- From t he  f s t r o n o n i c a l  Yemkook we wri te  t h e  coord ina tes  X, Y, Z 
10. - 3y fornu1r.s ( 2 )  we detern ine  
11.- By formulas ( 6 )  we determine AU' and A6' 
t o  t h e  above-obtaincd va lues  of a. and 8 o s  we f i n d  
and 5b. 
an5 then by adding then 
a' and &'. 
a' and 6' 
' 1 
12.- Upon f i n d i n r  tke r e spec t ive  t r i r o n o n e t r i c  func t ions  of 
tl 
entering- i n t o  forinula (71, we compute the  co r rec t ion  C 1. ' 
13.- The f i n n l  co r rec t ion  C1, being  the sun of C 1 and C'i, is then 
determined. 
14.- F i n a l l y  t:;e c o r r e c t i o n  C, is determined by subntit:-.tio:: of t h e  . 
cor ;-:Toniing e q u a t o r i a l  coordin?.tcs of Sun's cen te r  (y!, 00, CO) 2nd 02 t 5e  
q u a n t i t i e s  AX, AY, A 2  i n t o  iornuln  ( 9 )  a t  the n o m n t  of t h e  when t h e  
S:-ectrum 01 t h e  Sun's  cen te r  i s  observed ( f o r  tlis s tudy  03 s h i f t s ) .  
I -. 
c 
3 
c 
2 
c : 
c 
P 
c 
0, 
c 
9> 
c 
\ 
< 
ro 
6 .  
7. 
The curves of C1 v a r i a t i o n  f o r  t he  e a s t e r n  and western ends of 
the  equator  and nor thern  and southern ends of t he  po le s  of the Sun are 
p l o t t e d  i n  F i g . 2  as a func t ion  of observat ion time, which i n  the given 
case  correspond t o  4 and 10 October 1963. As may be seen from the drawing, 
t h e  curves 1 and 2 s h i f t e d  l i t t l e  r e l a t i v e  t o  one another  w i th in  the  l i m i t s  
of  six days, and t h a t  is why the values  of C1 (and even of Co) f o r  t h e  i n -  
t e rmedia te  days a r e  found by i n t e r p o l a t i o n .  
I n  r e a l i t y  c o r r e c t i o n  for  the motion of the  c e n t e r  of gravity of 
t h e  system Zarth-l.Ioon should be e f fec ted .  Bowever, t h i s  co r rec t ion  is s m a l l  
and i s  disregarded i n  t h i s  czse. 
I n  conclusion. we present ,  as an example, a coxplete  c a l c u l a t i o n  
of two i n d i c a t e d  co r rec t ions  f o r  t h e  e a s t e r n  end of the  equator  on 4 October 
1963, u s in?  the  scheme proposed by us, which is p r a c t i c a l  f o r  c a l c u l a t i o n s  
( see  Tables  1 and 2). 
* * *  T I I E  E N D  * * +  
T k R L E  . -  _ . . -  1
M 
a. 
-k An' 
a' 
, sina' 
COS a' 
a = sin 8' 
cos E' 
' = cos 8' cos a' 
=COS 6' sin a' 
AX 
AY 
dZ 
, A X . 0  
I 
' AY-c 
f - A Z , r r  
P 
d 
ci ( K A f / k r  ) 
.c, (X*/SfUr,) 
-0.984 3070 
0.16; 9537 
-0.071 1015 
- 1 0 1'38.d 
$7'0 1:. 
--4" 1 1'4215 
1.2146 
1.9931 
1.2215 
1 3h37m49f'l 
- 
+ 5 7 3  
1 2113am46:~ 
-0.1683 
--0.9t(57 
-0.0731 
$0.9973 
-0.9830 
-0.lb78 
, 0.003 351s 
-0.015 4676 
-0.006 7073 
-0.003 2948 
+0.002 5954 
+O.OOO 4903 
-0.000 2091 
+0.362 
0.549 
0.983 7858 
0.165 8867 
--4"07'31'5 
-07 ' 0412 
-4"14'35:7 
-0.071 9398 
i.? 1 98 
- 
1.9929 
1 2269 
1 P 3 8 m  17 :O
- 
+57'5 
1 ?1139m 14$5 
- 0.1704 
-0.9854 
-0.0740 
$0.9973 
-0.9827 
-0.1699 
+0.003 3879 
-0.0154614 
-0.006 7047 
-0.003 3293 
+0.002 6360 
+O.ObO 4961 
--o.noo 2063 
-;-0.357 
$0.391 
8. 
~ _ _ _ _  
-0.983 3601 
-0.167 8190 
-u.vi.: 1 I I I - . -- 
-4 10'24:8 
~ 07'04'2 
-4 17'2910 
- 
1.2248 
1.9927 
, 1.2321 
12h38m44?0 
+ 5 7 3  
12i1391n41?5 
-0.1723 
-0.9851 
-0.0748 
+0.9972 
-0.9823 
-0.1718 
+0.003 4240 
-0.006 7020 
-0.015 4553 
-0.003 3634 
-k0.002 6552 
-i-0.000 3013 
- 0.000 2069 
+0.358 
4-0.220 
T A B L E  - 2 
I 3' 
-U.!183 't29S 
-0.169 is06 
r. n-r.7 c 9 c 1  
-u.vIJulrlJ 
-4 13'18f0 
- -07'0 k:2 
-4 20'2212 
1.2297 
1 .!!925 
1.2372 
12h39ml If0 
- 
-1-5755 
12i140m08?5 
0.1i.i 2 
-0.9547 
--0.0757 
+ 0 . W  1 
-0 9818 
-0.1 737 
$0.003 4fill i 
-0.015 44'12 
--0.oo6 6993 
-0.003 3971 
-:-0.002 6835 
+O.OOO 5071 
-0.000 2065 
+0.358 
$0.126 
R E F ' .  3 2  N C E S  -- 
8 
Contract  110. NAS-5-9299 
Consul ta .n t s  and D e s i < - n e r s ,  Inc. 
i l r l i n y t o n ,  V i r g i n i a  
GODDkRI) SPACE F.C. 
100 
110 
400 
610 
611 
612 
613 
614 
61s 
640 
643 
, 630 
252 
256 
CLARK, TOi3TSEND 
STROUD 
BOURi>EXT 
EE3ZED I T H  
l'icDOI1ALD 
LBR-3ItJ4, BOLDT 
VICB * WILL 1,'JG 
S Z R r n I T S  os 
EEPL'IER 
mss 
KUPFERIAET C3 3 
t.%ITE 
FROST 
WO LFF 
B3ITR IIJG 
B*-iJ%? 
GOLDBEEG 
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RESS 
1.z -2J) 
CJJXRON 
NOR Ti'IiAOP 
IvT S EN 
SQUIRES 
L I B R  .'RY 
F X . 8  
G I  f o r  SS c3 3 
9. 
Trans la ted  by AIDRE L. BRICHAMT 
on 22-23 March 1966 
DI S T R I  B U T  I O N  -- 
- N A S A  . H Q S  OWEX CENT= 
A R C  
SONETT 
LIBR .LRY 
La R C 
AD ixs or1 
SEATON 
XE i'-TREf., M I  
JP L 
NE:?BURN 
FJYCKOFF 
U. IGIIA 
-
v m  -+.LIEN 
U. BERELEY 
FIELD 
u. P:ICEIGAN 
B!J?llZTT 
s: IC cs 
JOHNS ON 


Corrections for line-of-sight velocities on account of the daily rotation and annual revolution of the earth during solar observations

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