Abstract

Shifts z and z′ toward the red of the galaxy NGC 5668 for a beam of 21 cm, z measured in radioastronomy with a frequency meter and z′ measured in optics with a spectrograph, not being equal, it follows that the speed of light from a galaxy c¯ is not equal to that of a galaxy c which is measured on earth from stationary source. The Doppler empirical formula cannot be explained in classical mechanics since it is in contradiction with it. As for the theory of relativity c¯ = c from a postulate and z′ = z. If we consider the universe represented on a three-dimensional space (H), non-Euclidian, with Euclidian connection plunged in a Riemannine four-dimension space (E), a certain universal time, like that of an astronomer, can be defined and its course calculated in relation to this time: it will necessarily be confounded with the atomic clock time, but c¯c and z′ ≠ z: the Doppler formula is not accurate. However, c¯ and c as well as z′ and z are so close in all the experiments carried out on earth, even when an artificial satellite is used, that the errors made in using the Doppler formula are clearly inferior to experimental errors.

© 1968 Optical Society of America

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Figures (4)

Fig. 1
Fig. 1

Dérive annuelle: 0.64489 sec; maximum d’oscillation: 0.0016 pour l’angle 90° + 20 min.

Equations (45)

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τ 1 = τ 1 1 + V R / c
z = ( τ 1 - τ 1 ) / τ 1 = V R / c ;
( λ 1 - λ 1 ) / λ 1 = V R / c .
d sin α k = K λ ,
λ 2 / λ 1 = ( c / c ) ( 1 + V R / c ) = [ ( c - V R ) / c ] ( 1 + V R / c ) = ( c / c ) [ 1 - ( V R / c ) 2 ] ;     z 1 = ( c / c - 1 ) - ( c / c ) ( V R / c ) 2 ;
c ¯ = c [ 1 + 2 M G / c 2 R - 2 m G / c 2 R 1 + ( V / c ) 2 ] 1 2 ,
z = λ 3 c / λ 1 c ¯ - 1 = V cos φ / c ,
λ 3 / λ 1 = z + 1 = ( 1 + V cos φ c ) c ¯ c = ( 1 + z ) c ¯ c ,
z = ( 1 + V cos φ c ) c ¯ c - 1 = [ c ¯ / c ) - 1 ] + V cos φ c c ¯ c ,
z = ( 1 + z ) [ 1 + 2 M G c 2 R - 2 m G c 2 R 1 + ( V / c ) 2 ] 1 2 - 1 ,
z = ( 1 + z ) [ 1 + 2 M G / C 2 R + ( V / c ) 2 ] 1 2 - 1.
( 1 + z ) / ( 1 + z ) = c ¯ / c > 1 , done z > z .
d sin α κ c ¯ τ 1 = d sin α k c τ 1 c c = d sin α k λ 2 n = K ,
λ [ 1 - ( 2 M G / c 2 R ) 2 ] 1 2 = λ ( 1 + ( 2 M G / c 2 R ) 2 / 2 + ) = λ
z = ( 1 + z ) [ 1 + ( V / c ) 2 ] 1 2 - 1 ,
z + 1 = λ 3 / λ 1 = ( 1 + β cos φ ) ( 1 + β 2 ) 1 2 = 1 + β cos φ + 1 2 β 2 + β 3 2 cos φ - 1 8 β 4 ,
λ 3 = λ 1 ( 1 + β cos φ + 1 2 β 2 + β 3 2 cos φ - β 4 / 8 + ) .
λ 3 = λ 1 ( 1 + β cos φ ) ( 1 - β 2 ) 1 2 = λ 1 ( 1 + β cos φ + 1 2 β 2 ) + β 3 2 cos φ + ( 3 8 ) β 4 + .
mesur e ´ e optiquement { 1780 ± 50 ( Sandage ) , soit de de 1730 a ` 1830 1665 ± 88 ( Humason ) , soit de 1577 a ` 1753 Valeur pond e ´ r e ´ e 1741 ± 11 km / sec .
( z + 1 ) / ( z + 1 ) = 1.00580 1.00526 = 1.0005372 = c ¯ / c ;             c ¯ = c + 182.04 km / sec .
c ¯ c = [ 1 + 2 × 7.72 × 10 - 8 + ( V / c ) 2 ] 1 2 = 1.0005372 ;             c ¯ c = ( 1 + 15.44 × 10 - 8 ) 1 2 ,
V / c = 0.03483 ; V = 0 , 1044 × 10 5 = 10449 km sec . V R / c = z = 0.00519 , d ' o u ` V R = 1577 ; 1577 = 10449 cos φ ; cos φ = 0.1513 φ = 51 ° , 0 8 .
( z + 1 ) / ( z + 1 ) = c ¯ / c ( 5 )
z = c ¯ z / c + ( c ¯ / c - 1 )
τ = τ 1 + Δ τ 1 = τ 1 + ( e / 4 π m ) ( τ 1 ) 2 H ,
( τ 1 / τ 1 ) - 1 = z = ( e / 4 n m ) ( τ 1 ) 2 H .
z = V R / c et z = ( c ¯ - c ) / c + ( c ¯ / c ) · V R / c .
c ¯ c < 1 + 1 2 ( V 2 c ) < 1 + 1 2 ( 30 3 10 - 5 ) 2 = 1 + 5 × 10 - 9 .
r = a ( 1 - e 2 ) 1 + e cos φ , et r 2 d φ d t = h = 2 π a 2 T ( 1 - e 2 ) 1 2 = a 2 1 ;
t = 1 ( 1 - e 2 ) 2 0 φ d φ ( 1 + e cos φ ) 2 ;
u + u = μ 2 c 2 M G 2 h 1 + 2 M G u 2 c 2 ; r 2 d θ d t 1 = h 1 ,
p 4 d θ d t 1 = c 2 ( 1 - α r ) d θ d t 1 = λ c 2 ,
θ = λ 0 t 1 d t 1 1 - ( α / r ) = λ 1 ( 1 - e 2 ) 2 × 0 φ 1 d [ 1 - ( α / a 1 ) ] ( 1 + e cos φ ) ( 1 + e cos φ ) 2 ,
D 1 ( 1 - e 2 ) 2 = ( λ c 2 μ 2 - 1 ) 0 φ 1 d φ ( 1 + e cos φ ) 2 + λ c 2 μ 2 ( α a 1 ) 2 × 0 φ 1 d φ 1 1 - α / a 1 ( 1 + e cos φ 1 ) + λ c 2 α μ 2 a 1 0 φ 1 d φ 1 + e cos φ .
2 π D a c 2 α T ( 1 - e 2 ) 2 = 0 φ 1 d φ 1 + e cos φ = 10.112 D = 1 1 - e 2 2 arc tan ( ( 1 - e ) ( 1 + e ) 1 2 tan φ 1 2 ) ;
10.112 D = ( λ c 2 / μ 2 - 1 ) a 1 / α 0 φ 1 d φ ( 1 + e cos φ ) 2 + λ c 2 / μ 2 0 φ 1 d φ 1 + e cos φ ,
10.112 D = e 1 - e { - 2 ( 1 - e ) 1 2 arc tan ( [ ( 1 - e ) ( 1 + e ) 1 2 ] tan φ 1 2 ) + sin φ 1 1 + e cos φ 1 } ,
d ( ν i ( d a i / d θ ) d θ + ν α d a α ω α i d θ     d θ = - 1 2 ν i ( p 4 ) a α + p 4 ω α 4 d θ
( n 2 - 1 ) / ( n 2 + 2 ) = a 2 + Σ i M i / ( ω 2 - ω i 2 ) ,
n 2 = a 2 + Σ i M i ( c τ ) 2 - ( c τ i ) - k ( c τ ) 2 - h ( c τ ) 4 = f 2 ( c τ ) ;
F ( c λ 3 / c ¯ ) = K λ 3 ,
F ( c λ 3 / c ¯ ) = [ ( 2 K + 1 ) / 2 ] λ 3
F ( c λ 31 / c ¯ ) λ 31 - ( F c λ 32 / c ¯ ) λ 32 = i .
f ( c λ 31 / c ¯ ) / λ 31 - f ( c λ 32 / c ¯ ) = i / 2 e .
HZ 4 ; c ¯ = c + 69 , 003 ; V R = 36 , 008 ; V = 45.6 km / sec HZ 10 + 43 , 000 37 , 853 41.3

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