Example 3 ​Propagation of a Beam of Light in the radial-directionof the Sun from the Gravitational Radius of the sun until the Earth with the speed of light
c=
1
ϵ0μ0
​within a Radial Gravitational Field G1 oriented in the radial-direction of the Sun with accelleration G1 = g[r] , resulting in Gravitational Redshift
v
Grav-1
(GRS) caused by the: Gravitational Field of the Sun
TherearetwokindsofRedshiftcausedbythegravitationalfieldofthesun.
​​​1)
Redshift
1
caused by the Gravitational Field within the fusion core of the sun(this is the area where the emitted light of the sun has been created). This has been calculated in Example 32)
Redshift
2
caused by the Gravitational Field outside the fusion core of the sun. This will be calculated in Example 4​The total RedShift caused by the Gravitational Field of the sun is the sum of
Redshift
1
+
Redshift
2
Book:
RisingoftheJamesWebbSpaceTelescopeanditsFundamentalBlindnes
:Page46,Equation(73)​​ExampleofaSphericalBeamofLight ,propagatingintheradial-direction(r-direction)​​withthespeedoflightc=
1
ϵ0μ0
.​​TheinputfortheElectricFieldIntensity{E(x,y,z,)=ev}andtheMagneticFieldIntensity{H(x,y,z,)=mv}havebeensubstitutedintheFieldEquationfortheElectromagneticFieldwithinaconstantgravitationalfieldwithaccellerationginthez-direction.(BookEquation73,page46).​​​​
- 
1
2
c
∂
¯
E
×
¯
Η

∂t
+
ε
0
¯
E
∇. 
¯
E
−
ε
0
¯
E
×∇×
¯
E
+
μ
0
¯
Η
∇. 
¯
Η
−
μ
0
¯
Η
×∇×
¯
Η
+
1
2

2
ε
μ
¯
E
 . 
¯
E

+
ε
2
 μ

¯
H
 . 
¯
H

¯
g
= 0
Equation
(73)
​​​​Whichcanbewrittenas:​​​​
term1
=
-
1
2
c
∂
¯
E
×
¯
Η

∂t
​​​​term2=
ε
0
¯
E
(∇. 
¯
E
)
​​​​term3=
−
ε
0
¯
E
×(∇×
¯
E
)
​​​​term4=
μ
0
¯
Η
∇. 
¯
Η

​​​​term5=
−
μ
0
¯
Η
×∇×
¯
Η

​​​​term6=
-
1
2

2
ε
μ(
¯
E
 . 
¯
E
)
+
ε
2
 μ
(
¯
H
 . 
¯
H
)
¯
g
​​​​Equation(73)equals:​​​​
term1+term2+term3+term4+term5+term6
=
0
In[]:=
ϵ0=.
In[]:=
μ0=.
In[]:=
x=.
In[]:=
y=.
In[]:=
z=.
In[]:=
t=.
In[]:=
Get["VectorAnalysis`"]
General
:VectorAnalysis` is now obsolete. The legacy version being loaded may conflict with current functionality. See the Compatibility Guide for updating information.
In[]:=
Get["Calculus`DSolve`"]
Get
:Cannot open Calculus`DSolve`.
Out[]=
$Failed
In[]:=
InverseFunctions->True
Out[]=
InverseFunctionsTrue
In[]:=
Needs["DifferentialEquations`NDSolveProblems`"]
In[]:=
Needs["DifferentialEquations`NDSolveUtilities`"]
In[]:=
Needs["DifferentialEquations`InterpolatingFunctionAnatomy`"]
In[]:=
Get["Calculus`DSolveIntegrals`"]
Get
:Cannot open Calculus`DSolveIntegrals`.
Out[]=
$Failed
In[]:=
SetCoordinates[Cartesian[x,y,z]]
Out[]=
Cartesian[x,y,z]
In[]:=
G1=.
In[]:=
ϵ0=.
In[]:=
μ0=.
In[]:=
fg=.
In[]:=
Msun=.
Thelightbeingemittedbythesunhasbeencreatedby
nuclearfusioninthecoreofthe thesun
.​​OutsidetheGravitationalRadiusoftheSun,(thedistanceofthecenterofthesunwherethegravitationalaccellerationofthesunchangesfromincreasingintodecreasing),thegeneratedlightwillpropagatewiththespeedoflight:​​c=
1
ϵ0μ0
​​oppositelydirectedtowardsthegravitationalaccellerationoutsidethe​​sun.Thegravitationalaccellerationoutsidethesunwillincreaseproportionalto:​​​​g2[r]=K2
1
2
r
=
f
g
M
Sun
4π
1
2
r
​​withinaRadialGravitationalFieldg[r]oriented​​intheradial-directionoftheSunwithaccellerationg[r]resultinginthe​​GravitationalRedshiftcausedbythe GravitationalFieldoutsidetheSun.​​​​The
GravitationalIntensityShift
forthelightemittedbythesunequalsaccordingtheBook:Page64,Equation(111)​​​​
I
NGR
=
-
K2ϵ0μ0
z

​​​​InsteadofSphericalCoordinates(r,θ,φ)forthelight emittedSphericallywithinthesun,forthefarfield (withinasmallarealikethedimensionsofaSpaceTelescope),​​CartesianCoordinates(x,y,z)arebeingused.
Results for the electromagentic force densities in resp x-direction, y-direction, z-direction:
Out[]=
69634000