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And (a 1 - a 2)/ a 2 = (0 / ) 2/3 1
Or (a 0 a)/ a = ( 0 / ) 2/3 1
And [(a m a e)/ a e] 0
= [(a 0 a)/ a] (v 0 /r 0) ' 0 = [(a 0 a)/ a] ' 0
Modern and Nobel error # 16 is: [( 0 / ) 2/3 1] ' 0
= 70.75 [(88/365.26) 2/3 -1] = 43 arc sec/100y
Modern and Nobel error # 33 is : - 2 sine 2 {[cosine -1 ( 0 / ) 2/3 ]/2} ' 0
= - 2 sine 2 {[cosine -1 (88/365.26) 2/3 ]/2} 70.75 = 43 arc sec/100y
6.9 - Newton's distance historical mistake II
Newton force is F = k/r 2 = G m M/r 2 = m v 2/r
And velocity of a celestial object measured from the sun is = (GM/r) 1/2
With r 3 0 = (GM/v 2 0); r 0 = (GM/v 2 0)
And r 3 = (GM/v 2); r = (GM/v 2)
Modern and Nobel error # 17 = [(r 0 - r)/r] ' 0 = {[(GM/v 2 0)/ (GM/v 2)] - 1} '0
= [(v/v 0)2 - 1] '0 = [(29.8/47.9) 2 - 1] x 70.75 = 43 arc sec/100y
Modern and Nobel error # 34: = - 2 sine 2 {[cosine -1 (v/v 0)2]/2} ' 0
= - 2 sine 2 {[cosine -1 (v/v 0)2]/2} ' 0
6.10 - Newton's velocity historical mistake II
Newton force is F = k/r 2 = G m M/r 2 = m v 2/r
And v 0 = (GM/r 0) ; v = (GM/r) 1/2
Modern and Nobel error # 18 = [(v 0 - v)/v] ' 0 = [(GM/r 0) 1/2 / (GM/r) -1] '0
= [(r/r 0) 1/2 - 1] '0 = [(149.6/58.2) 1/2 - 1] x 70.75 = 43 arc sec/100y
Modern and Nobel error # 35: = - 2 sine 2 {[cosine -1 (r/r 0) 1/2 ]/2} ' 0
= - 2 sine 2 {[cosine -1 (149.6/58.2) 1/2 ]/2} 70.75 = 43 arc sec/100y
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6.11 - Newton's surface gravity historical mistake II
Newton force is F = k/r 2 = G m M/R 2 = m g
And g 0 = Gm 0 /R 2 0 ; g = Gm/R 2
Modern and Nobel error # 19 = [(g 0 - g)/ g] ' 0 = {[(Gm 0 /R 0 2) - (Gm/R 2)]/ (Gm/R 2)} '0 = {[(m 0/ R 0 2) - (m/R 2)]/ (m/R 2)} '0
= [(g 0 - g)/ g] ' 0 = [(3.8/9.8) -1] 70.75 = 43 arc sec/100 years
Note: [(m 0 / R 0 2)/ (m/R 2) (29.8/29.335) 2 -1] '0 = 43 arc sec/100y
Modern and Nobel error # 36:
= - 2 sine 2 {{cosine -1 [(m 0/ R 0 2)/ (m/R 2)]}/2} ' 0
= - 2 sine 2 {{cosine -1 [(0.33/ 2440 2)/ (5.97/6371 2)]}/2} 70.75 = 43 arc sec/100y
6.12 - Le Verrier mistake II
Modern and Nobel error # 21 is: [(v +/- v ) /v 0)] ' 0 = (v /v 0) [1- (v /v)] ' 0
Modern and Nobel error # 37 : - 2 sine 2 {{cosine -1 (v /v 0) [1- (v /v)]}/2} ' 0
= - 2 sine 2 {{cosine -1 (29.8 /48.14) [1- (0.4651/29.8)]}/2} 70.75 = 43 arc sec/100y
6.12 - Le Verrier distance mistake II
And v = [G M 2 / (m + M) r] 1/2 = (G M / r) 1/2 ; m
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6.13 - Le Verrier signal time mistake II
With (r/r 0) 1/2 [1- (v /v)] ' 0 = [(r 0 /c) /(r /c)] 1/2 [(1- (v /v)] ' 0
Modern and Nobel error # 23 is: (T 0 /T) 1/2 [(1- (v /v)] ' 0
= (194 /498.67) 1/2 x 0.98 x 70.75 = 43 arc sec/100y
Modern and Nobel error # 39 :- 2 sine 2 {{cosine -1 (v /v 0) [1- (v /v)]}/2} ' 0
= - 2 sine 2 {{cosine -1 (194 /498.67) 1/2 x 0.98}/2} x 70.75
6.14 - Le Verrier orbital period mistake
Keplers law: a/T = k = constant
Or, r 0/ 0 = r/ = k; r 0 / r = ( 0 / ) 2/3
With (r 0 /r) 1/2 [(1- (v /v)] ' 0
Modern and Nobel error # 24 is: ( 0 / ) 1/3 [(1- (v /v)] ' 0
= (88/365.26) 1/3 x 0.98 x 70.75 = 43 arc sec/100y
Modern and Nobel error # 40 :
= - 2 sine 2 {{cosine -1 ( 0 / ) 1/3 [(1- (v /v)}}/2} 70.75
= - 2 sine 2 {{cosine -1 (88 / 149.6) 1/3 [(1- (0.4561/29.8)}}/2} 70.75
= 43 arc sec/100y
6.15 - Le Verrier gravity mistake
And 0 = g 0 = Gm 0 /r 20; = g = Gm/r 2
And ( / 0) = (g/g 0) = (Gm/r 2)/ (Gm 0/r 20) = (m r 20 / m 0 r2)
And (r 0 /r) = (m 0g/g 0m) ; (r 0 /r) 1/2 = (m 0g/g 0m) 1/4
With (r/r 0) 1/2 [1- (v /v)] ' 0
Modern and Nobel error # 24 is: (m 0g/g 0m) 1/4 [1- (v /v)] ' 0
= (0.33 x 9.8/3.8 x5.97) 1/4 0.98 x 70.75 = 43 arc sec/100y
Modern and Nobel error # 41 :
=- 2 sine 2 {{cosine -1 (m 0g/g 0m) 1/4 [1- (v /v)]/2} ' 0
= - 2 sine 2 {{cosine -1 (0.33 x 9.8/ /3.8 x5.97) 1/4 [(1- (0.4561/29.8)}}/2} 70.75 = 43 arc sec/100y
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Chapter 7: Fourier Light signal processing
r = r 0 e t
Distance r in real time is r = r 0 e i ( + t)
With r 2' = h = r 0 2'0; ' = '0 e -2 i ( + t)
At = 0; Perihelion
r = r 0 e t
Taking r = c t and r 0 = c t 0
Then (t/t 0) = e i t
And the Fourier transform is:
= (1/2 ) {- e i t d t}
And = (1/2 ) 0 0 e i t d t
= (1/2 ) [e i 0 -1]/ i
= (1/2 ) [cosine 0 + i sine 0 - 1]/ i
Along the line of sight
x = (1/2 ) [sine 0]/
x [100 / 0] = (100 /2 ) [sine 0 / 0] per 100
With 0 = arc tan ( v 0/c); 100 = 1 century = 36526 days
x [100 / 0] per century = (100 /360) {sine [arc tan ( v 0/c)] / [arc tan ( v 0/c)]}
x [100 / 0] per century
= (36526days /360degrees) {sine [arc tan ( v 0/c)] / [arc tan ( v 0/c)]}
In arc seconds per century: x [100 / 0] per century
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= (36526x 24 x 3600 /360 x 3600) {sine [arc tan ( v 0/c)] / [arc tan ( v 0/c)]}
x [100 / 0] per century
= (36526x 24 x 3600/360 x 3600) {sine [arc tan ( v 0/c)] / [arc tan ( v 0/c)]}
Where v 0 = 47.9 km/second; c = 300,000 km/second
Modern and Nobel error # 42 :
x [100 / 0 ] = (36526 /15) {sine [arc tan (47.9/300,000)] / [arc tan (47.9/300,000)]}
= 42.5 arc seconds per century
Modern and Nobel error # 43 :
x [100 / 0 ] = (36526 /15) {sine [arc tan (29.8/300,000)] / [arc tan (29.8/300,000)]}
= 42.5 arc seconds per century
Angular velocity ' in real time is ' = ' 0 e - 2i ( + t)
Taking '= 2 f and ' 0 = 2 f 0
Then (f/f 0) = e - 2i ( + t)
At = 0; Perihelion
And (f/f 0) = e- 2i t
And the Fourier transform is:
= (1/2 ) {- e - 2i t d t}
And = (1/2 ) 0 0 e - 2i t d t
= (1/2 ) [e - 2i t -1]/ - 2
= (1/2 ) [cosine 2 0 + sine 2 0 - 1]/ - 2
Along the line of sight
x = - (1/2 ) [sine 2 0]/ 2
x [100 / 0] = (100 /2 ) [sine 2 0 / 2 0 ] per 100
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With 0 = arc tan ( v 0/c); 100 = 1 century = 36526 days
x [100 / 0 ] per century
= (100 /360) {sine 2 [arc tan ( v 0/c)] / [arc tan ( v 0/c)]}
x [100 / 0] per century
= (36526days /360degrees) {sine2 [arc tan ( v 0 /c)] / 2 [arc tan ( v 0/c)]}
In arc seconds per century:
x [100 / 0] per century
= (36526x 24 x 3600 /360 x 3600) {sine 2[arc tan ( v 0/c)] / 2[arc tan ( v 0/c)]}
Where v 0 = 47.9 km/second; c = 300,000 km/secondModern and Nobel error # 44 :
x [100 / 0] = (36526 /15) {sine 2[arc tan (47.9/300,000)] / 2[arc tan (47.9/300,000)]}
= 42.5 arc seconds per century
Modern and Nobel error # 45 :
x [100 / 0] = (36526 /15) {sine 2[arc tan (29.8/300,000)] / 2[arc tan (29.8/300,000)]}
= 42.5 arc seconds per century
Modern and Nobel error # 46 :
x [100 / 0] = (36526 /15) {sine 2[arc tan (0.4651/300,000)] / 2[arc tan (29.8/300,000)]}
= 42.5 arc seconds per century
Chapter 8: Descartes and LaGrange failures
8.1 = x + y = 0 e t
Along the line of sight x = 0 cosine t
Then x (seconds) = x - t
= - 2 t sine {[arc tan (V r m - V r e)/ ( 2c)]/ 2} = 43
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And in arc x (arc seconds) = x - t
= - 30 t sine {[arc tan (V r m - V r e)/ ( 2c)]/ 2} = 43
Where r = V r; and r = V ; and V r = 2 r r; and V = r
The confusion is and was r = ; V r = 2 V ; and taking V r = ( 2) V And taking V r = V r (Mercury) - V r (Earth) = V r m - V r e
And V = V r / 2
Modern and Nobel error # 47 : x (Arc second) = x - 0
= - 30 t sine {[arc tan (V r m - V r e)/ ( 2c)]/ 2} = 43 arc second /century
8.2 La Grange historical mistake
Angular velocity with respect to center of mass ' c m = v c m /r
Angular velocity with respect to Sun ' s = v s/r
And Astronomers observed: ' s = v s/r
Angular velocity with to the sun
And v c m = [GM/ (m + M) a]; m = 0.32 x10 24 kg; and M = 2.0 x10 30 kg
And v s = (GM/a)
And (' cm - s) / s = [(2 /T c m) - (2 /T s)]/ (2 /T s)
= (T c m /T s) 1 = (v s/v c m) 1
= [ (GM/a)] / { [(m + M) a/ GM]} - 1
= [(m + M)/M] - 1
= [1 + (m/M)] - 1
1 + (m/2 M) 1 m/2 M
And (' cm - s) / s (m/2 M); and (' cm - s) = (2 /T s) (m/2 M)
And (' cm - s) T s = (2 + - 2 ) = m/ M; = m/ M
Multiplying by [(180/) (3600) (26526/ 0)]
Modern and error # 48 = (m/ M) [(180/) (3600) (26526/ 0)] = 43
= (0.32 x 10 24 /2x 10 30 ) [(180/) (3600) (26526/ 0)] = 43
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Modern and Nobel error # 49 is
(per century) = - 2 x 15 0 sine 2 arc tan (v/c); 0 = 100 years
= - 30 (100 x 36526 x 24 x 3600) sine 2 tan -1 (48.14/300,000) = 43 arc sec/100y
Chapter 9: Axial tilt processing
In Chapter 7 Fourier analysis said that planet Mercury's Perihelion has nothing to do with planetMercury but has something to do with Earth.
Astronomers measure with an axial tilt of 23.44 0 because they measure from Earth and use theSun as reference point. Parallaxes are shifted by an angle of 23.44 0
Meaning measurements are shifted by a factor of: (1 - sine 23.44 0)
Modern and Nobel error # 50 : (1 - sine 23.44 0) ' 0
= (1 - sine 23.44 0) 70.75 = 43 arc sec/ 100y
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