A-43
The second section of distance: From 89,993° up to 2° respectively from 85 km up to 1,9917*107 km
For these area can used the first and the second simplifications.
The to solved equation is than
A-43
The calculations are take in tab. A4. Because the largeness is it divided at the columns in three tables and lines was fade out. The yellow marked cells has not partner for make a difference and its number is the equal of the neighbor-line ore is seat.
|
A |
B |
C |
D |
E |
F |
G |
H |
|
Grad |
Bogen |
W |
Delta-W |
Delta-Gamma |
co3-0 |
ta2-0 |
|
|
1 |
8,9993E+01 |
1,5707E+00 |
8,4971E+04 |
1,2139E+04 |
3,4907E-06 |
5,4837E+11 |
6,6996E+07 |
|
2 |
8,9992E+01 |
1,5707E+00 |
9,7110E+04 |
1,2139E+04 |
3,4907E-06 |
3,6737E+11 |
5,1294E+07 |
|
3 |
8,9991E+01 |
1,5706E+00 |
1,0925E+05 |
1,2139E+04 |
3,4907E-06 |
2,5801E+11 |
4,0529E+07 |
|
4 |
8,9990E+01 |
1,5706E+00 |
1,2139E+05 |
1,2139E+05 |
3,4907E-06 |
1,8809E+11 |
3,2828E+07 |
|
5 |
8,9980E+01 |
1,5704E+00 |
2,4278E+05 |
1,2139E+05 |
3,4907E-05 |
2,3511E+10 |
8,2070E+06 |
|
6 |
8,9970E+01 |
1,5703E+00 |
3,6416E+05 |
1,2139E+05 |
3,4907E-05 |
6,9663E+09 |
3,6476E+06 |
|
7 |
8,9960E+01 |
1,5701E+00 |
4,8555E+05 |
1,2139E+05 |
3,4907E-05 |
2,9389E+09 |
2,0518E+06 |
|
8 |
8,9950E+01 |
1,5699E+00 |
6,0694E+05 |
1,2139E+05 |
3,4907E-05 |
1,5047E+09 |
1,3131E+06 |
|
9 |
8,9940E+01 |
1,5697E+00 |
7,2833E+05 |
1,2139E+05 |
3,4907E-05 |
8,7079E+08 |
9,1189E+05 |
|
10 |
8,9930E+01 |
1,5696E+00 |
8,4971E+05 |
1,2139E+05 |
3,4907E-05 |
5,4837E+08 |
6,6996E+05 |
|
11 |
8,9920E+01 |
1,5694E+00 |
9,7110E+05 |
1,2139E+05 |
3,4907E-05 |
3,6737E+08 |
5,1294E+05 |
|
12 |
8,9910E+01 |
1,5692E+00 |
1,0925E+06 |
1,2139E+05 |
3,4907E-05 |
2,5801E+08 |
4,0528E+05 |
|
13 |
8,9900E+01 |
1,5691E+00 |
1,2139E+06 |
1,2139E+06 |
3,4907E-05 |
1,8809E+08 |
3,2828E+05 |
|
14 |
8,9800E+01 |
1,5673E+00 |
2,4278E+06 |
1,2139E+06 |
3,4907E-04 |
2,3512E+07 |
8,2070E+04 |
|
15 |
8,9700E+01 |
1,5656E+00 |
3,6417E+06 |
1,2139E+06 |
3,4907E-04 |
6,9664E+06 |
3,6475E+04 |
|
16 |
8,9600E+01 |
1,5638E+00 |
4,8556E+06 |
1,2140E+06 |
3,4907E-04 |
2,9390E+06 |
2,0517E+04 |
|
104 |
7,0000E+00 |
1,2217E-01 |
5,6644E+09 |
9,5285E+08 |
3,4907E-03 |
1,0227E+00 |
1,5076E-02 |
|
105 |
6,0000E+00 |
1,0472E-01 |
6,6172E+09 |
1,3324E+09 |
3,4907E-03 |
1,0166E+00 |
1,1047E-02 |
|
106 |
5,0000E+00 |
8,7266E-02 |
7,9496E+09 |
1,9965E+09 |
3,4907E-03 |
1,0115E+00 |
7,6543E-03 |
|
107 |
4,0000E+00 |
6,9813E-02 |
9,9461E+09 |
3,3248E+09 |
3,4907E-03 |
1,0073E+00 |
4,8898E-03 |
|
108 |
3,0000E+00 |
5,2360E-02 |
1,3271E+10 |
6,6456E+09 |
3,4907E-03 |
1,0041E+00 |
2,7466E-03 |
|
109 |
2,0000E+00 |
3,4907E-02 |
1,9917E+10 |
1,9929E+10 |
3,4907E-03 |
1,0018E+00 |
1,2195E-03 |
|
110 |
1,0000E+00 |
1,7453E-02 |
3,9845E+10 |
3,4907E-03 |
1,0005E+00 |
3,0468E-04 |
Tab. A4: Calculation from W=84971m up to W=1,9917*1010m ; Part a
|
A |
I |
J |
K |
L |
M |
N |
|
co3-1 |
ta2-1 |
co3-2 |
ta2-2 |
co3-3 |
ta2-3 |
|
|
1 |
5,0393E+11 |
6,3326E+07 |
4,6417E+11 |
5,9949E+07 |
4,2848E+11 |
5,6835E+07 |
|
2 |
3,4114E+11 |
4,8822E+07 |
3,1735E+11 |
4,6525E+07 |
2,9572E+11 |
4,4386E+07 |
|
3 |
2,4155E+11 |
3,8786E+07 |
2,2646E+11 |
3,7153E+07 |
2,1260E+11 |
3,5621E+07 |
|
4 |
1,7724E+11 |
3,1553E+07 |
1,6721E+11 |
3,0351E+07 |
1,5793E+11 |
2,9217E+07 |
|
5 |
1,7664E+10 |
6,7827E+06 |
1,3606E+10 |
5,6993E+06 |
1,0702E+10 |
4,8562E+06 |
|
6 |
5,7401E+09 |
3,2059E+06 |
4,7855E+09 |
2,8398E+06 |
4,0314E+09 |
2,5330E+06 |
|
7 |
2,5388E+09 |
1,8610E+06 |
2,2081E+09 |
1,6957E+06 |
1,9324E+09 |
1,5514E+06 |
|
8 |
1,3377E+09 |
1,2141E+06 |
1,1945E+09 |
1,1258E+06 |
1,0710E+09 |
1,0468E+06 |
|
9 |
7,8921E+08 |
8,5401E+05 |
7,1751E+08 |
8,0147E+05 |
6,5424E+08 |
7,5363E+05 |
|
10 |
5,0393E+08 |
6,3326E+05 |
4,6417E+08 |
5,9949E+05 |
4,2848E+08 |
5,6835E+05 |
|
11 |
3,4114E+08 |
4,8822E+05 |
3,1734E+08 |
4,6525E+05 |
2,9571E+08 |
4,4386E+05 |
|
12 |
2,4155E+08 |
3,8785E+05 |
2,2646E+08 |
3,7153E+05 |
2,1260E+08 |
3,5621E+05 |
|
13 |
1,7724E+08 |
3,1553E+05 |
1,6721E+08 |
3,0351E+05 |
1,5793E+08 |
2,9217E+05 |
|
14 |
1,7665E+07 |
6,7826E+04 |
1,3606E+07 |
5,6993E+04 |
1,0702E+07 |
4,8562E+04 |
|
15 |
5,7402E+06 |
3,2058E+04 |
4,7856E+06 |
2,8397E+04 |
4,0315E+06 |
2,5330E+04 |
|
16 |
2,5388E+06 |
1,8609E+04 |
2,2081E+06 |
1,6956E+04 |
1,9325E+06 |
1,5514E+04 |
|
104 |
1,0214E+00 |
1,4219E-02 |
1,0201E+00 |
1,3387E-02 |
1,0189E+00 |
1,2582E-02 |
|
105 |
1,0155E+00 |
1,0318E-02 |
1,0145E+00 |
9,6140E-03 |
1,0134E+00 |
8,9355E-03 |
|
106 |
1,0106E+00 |
7,0514E-03 |
1,0097E+00 |
6,4735E-03 |
1,0089E+00 |
5,9207E-03 |
|
107 |
1,0066E+00 |
4,4116E-03 |
1,0059E+00 |
3,9583E-03 |
1,0053E+00 |
3,5297E-03 |
|
108 |
1,0036E+00 |
2,3920E-03 |
1,0031E+00 |
2,0620E-03 |
1,0026E+00 |
1,7567E-03 |
|
109 |
1,0015E+00 |
9,8761E-04 |
1,0012E+00 |
7,8023E-04 |
1,0009E+00 |
5,9729E-04 |
|
110 |
1,0003E+00 |
1,9498E-04 |
1,0002E+00 |
1,0967E-04 |
1,0001E+00 |
4,8740E-05 |
Tab. A4: Calculation from W=84971m up to W=1,9917*1010m; Part b
|
A |
O |
P |
Q |
R |
S |
T |
|
co3-4 |
ta2-4 |
co3-5 |
ta2-5 |
L-querF |
dBetaF |
|
|
1 |
3,9636E+11 |
5,3958E+07 |
3,6737E+11 |
5,1294E+07 |
5,1036E+03 |
|
|
2 |
2,7601E+11 |
4,2392E+07 |
2,5801E+11 |
4,0529E+07 |
4,5011E+03 |
7,8558E-02 |
|
3 |
1,9984E+11 |
3,4182E+07 |
1,8809E+11 |
3,2828E+07 |
4,0260E+03 |
7,0266E-02 |
|
4 |
1,4931E+11 |
2,8145E+07 |
1,4132E+11 |
2,7131E+07 |
3,6417E+03 |
6,3559E-02 |
|
5 |
8,5683E+09 |
4,1873E+06 |
6,9663E+09 |
3,6476E+06 |
1,5574E+03 |
2,7181E-01 |
|
6 |
3,4278E+09 |
2,2734E+06 |
2,9389E+09 |
2,0518E+06 |
1,1019E+03 |
1,9232E-01 |
|
7 |
1,7008E+09 |
1,4248E+06 |
1,5047E+09 |
1,3131E+06 |
8,5377E+02 |
1,4901E-01 |
|
8 |
9,6402E+08 |
9,7586E+05 |
8,7079E+08 |
9,1189E+05 |
6,9719E+02 |
1,2168E-01 |
|
9 |
5,9819E+08 |
7,0995E+05 |
5,4837E+08 |
6,6996E+05 |
5,8928E+02 |
1,0285E-01 |
|
10 |
3,9636E+08 |
5,3958E+05 |
3,6737E+08 |
5,1294E+05 |
5,1036E+02 |
8,9074E-02 |
|
11 |
2,7601E+08 |
4,2392E+05 |
2,5801E+08 |
4,0528E+05 |
4,5011E+02 |
7,8559E-02 |
|
12 |
1,9984E+08 |
3,4182E+05 |
1,8809E+08 |
3,2828E+05 |
4,0260E+02 |
7,0267E-02 |
|
13 |
1,4931E+08 |
2,8145E+05 |
1,4132E+08 |
2,7131E+05 |
3,6417E+02 |
6,3560E-02 |
|
14 |
8,5684E+06 |
4,1872E+04 |
6,9664E+06 |
3,6475E+04 |
1,5574E+02 |
2,7182E-01 |
|
15 |
3,4279E+06 |
2,2733E+04 |
2,9390E+06 |
2,0517E+04 |
1,1020E+02 |
1,9233E-01 |
|
16 |
1,7008E+06 |
1,4248E+04 |
1,5048E+06 |
1,3131E+04 |
8,5383E+01 |
1,4902E-01 |
|
104 |
1,0178E+00 |
1,1802E-02 |
1,0166E+00 |
1,1047E-02 |
1,0032E+00 |
1,7510E-02 |
|
105 |
1,0124E+00 |
8,2823E-03 |
1,0115E+00 |
7,6543E-03 |
1,0023E+00 |
1,7494E-02 |
|
106 |
1,0081E+00 |
5,3928E-03 |
1,0073E+00 |
4,8898E-03 |
1,0016E+00 |
1,7480E-02 |
|
107 |
1,0047E+00 |
3,1258E-03 |
1,0041E+00 |
2,7466E-03 |
1,0009E+00 |
1,7470E-02 |
|
108 |
1,0022E+00 |
1,4758E-03 |
1,0018E+00 |
1,2195E-03 |
1,0005E+00 |
1,7462E-02 |
|
109 |
1,0007E+00 |
4,3878E-04 |
1,0005E+00 |
3,0468E-04 |
1,0002E+00 |
1,7456E-02 |
|
110 |
1,0000E+00 |
1,2185E-05 |
1,0000E+00 |
|||
|
5,5549E+00 |
Tab. A4: Calculation from W=84971m up to W=1,9917*1010m; Part c
(The yellow marked field is the limit of W to table A3.)
To make duplicate the calculations in the table, here given the instructions for calculation of the columns too.
A: Numbering of lines because the coordination of the table-parts
B: Degree: Input is the entry-angle of the sun-rays in the 1m-layer (Angle measured from radial-ray). To hold the length of table in limit, are stepped the angles different long. Begin is at 89,993°, stepped arrangement in (1/1000)°-steps up to 89,990°, (Line 1 up to 4)
stepped arrangement in (1/100)°-steps from 89,99° up to 89,90°, (Line 5 up to 13)
stepped arrangement in (1/10)°-steps from 89,9° up to 89,0°, (Line 14 up to 22)
stepped arrangement in (1/1)°-steps from 89° up to 2°, (Line 23 up to 109)
Numbers for the angle 1° aim at only to make a difference. The angle B can act as γmax too.
C: Arc: Conversion to arc: C=(B/180)*π
D: Length of way W, calculated by radius of the sun and γmax : D=695500000/TAN(3,141592654*B/180) . The angle B is here used as γmax (see fig. A2 too).
E: Delta-W: Difference of the length of way W between two angle-numbers: E=Di-Di-1
F: Delta-Gamma: A fifth of the angle-difference: F=( Ci-1-Ci)/5. These more fin stepping was take, to make not longer the table and nevertheless to calculate with higher precision. These more fin stepping is therefore calculated in the columns (Column G up to R).
The follow columns connect with the part
of the above for these table given equation. Each angle between two lines of the table above is five times divided, by which result 6 sections. On these way is increase the precision of the calculation. From these 6 sections is formed a middle number of the term
for the one line. The middle number
represent the middle length of course of the particles
in the 1m-layer for the distance from W1 to W2, that is from one line to the next.
G: co3-0: (co3 mean cos3 , the follow number mean one of the 6 sections, here the section 0)
G=1/(cos(C))3
H: ta2-0: (ta2 mean tan2 )
H=(tan(C))2
I: co3-1: I=1/(cos(C-F))3
J: ta2-1: J=(tan(C-F))2
K: co3-2: K=1/(cos(C-2*F))3
L: ta2-2: L=(tan(C-2*F))2
M: co3-3: M=1/(cos(C-3*F))3
N: ta2-3: N=(tan(C-3*F))2
O: co3-4: O=1/(cos(C-4*F))3
P: ta2-4: P=(tan(C-4*F))2
Q: co3-5: Q=1/(cos(C-5*F))3
R: ta2-5: R=(tan(C-5*F))2
S: LquerF: S=2/3*((G-1)/H+(I-1)/J+(K-1)/L+(M-1)/N+(O-1)/P+(Q-1)/R)/6
The factor 2/3 from the to solved equation A43 is here already contain.
T: dBetaF: T=S*(ARCTAN((Di-1+Ei-1)/695500000)-ARCTAN(Di-1/695500000))
Here mean i the acute line.
The sum of the column T is the in equation A-43 searched sum
multiplied with the factor 2/3. The result of the table A4 is: 5,5549.
To Chapter 2.5 Connection between the 3K-radiation and the deflection of light by the sun