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The stellar aberration and dragged ether



The stellar aberration and dragged ether

When you are inter­ested in physics you must read “Unbe­liev­able”!

A pho­ton can be accred­ited an impulse in the direc­tion of move­ment equal to:

Impulse of the pho­ton in the X– and Y– direc­tion in ether II for the observer in rest with ether II is (fig­ure 2):

Because ether II moves always side­ways with speed v respec­tively to ether I, the impulse of the pho­ton for the observer in rest with ether I in the X-​direction, when the move­ment is max­i­mal v towards the star (fig­ure 4 and 5 the move­ment in Y-​direction is zero), will be:

(Bradley only mea­sured the stel­lar aber­ra­tion in the X-​direction; the ver­ti­cal aber­ra­tion. When the move­ment towards the star is zero {speed in X-​direction is zero and the move­ment in the Y-​direction is there­fore v} the hor­i­zon­tal aber­ra­tion, not mea­sured by Bradley is maximal)

In the Y-​direction the impulse of the pho­ton is not changed, because the speed of both ether to each other in that direc­tion is zero:

For the observer in ether II the impulse of the pho­ton, after pen­e­trat­ing ether II from ether I, will not change. The vac­uum has not the qual­ity to change the impulse. Con­sid­er­ing this the stel­lar aber­ra­tion can now be deter­mined by the fol­low­ing equations:

The reduced for­mu­las are:

The stel­lar aber­ra­tion and the Doppler-​effect in the X-​direction, due to the pas­sage of the pho­ton from ether I to ether II, is described by the equations:

These for­mu­las only describe the stel­lar aber­ra­tion and Doppler-​effect caused by the speed in X-​direction towards or from the star (ver­ti­cal aber­ra­tion). Bradley did not mea­sure the hor­i­zon­tal aber­ra­tion caused by the speed of the Earth in the Y-​direction; side­ways to the star. The vec­tor sum­ma­tion of the ver­ti­cal aber­ra­tion caused by the speed of the Earth in the X-​direction and the hor­i­zon­tal aber­ra­tion caused by the speed of the Earth in the Y-​direction gives the total aber­ra­tion of the star y–Dra­co­nis.

Con­sid­er­ing these for­mu­las we observe a small dif­fer­ence when we cal­cu­late ß for v and the reverse speed –v. This small devi­a­tion between both cal­cu­la­tions of the aber­ra­tion β for v and –v is caused by the math that does not describe the actual physics exactly. The sum­ma­tion of both β for v and –v should be exactly zero. The for­mu­las above describe the sit­u­a­tion where the speed changes instan­ta­neous from zero to v or –v. In real­ity the speed grad­u­ally increases from zero to v and than grad­u­ally to –v. This sec­ond order effect, not described by the for­mu­las, is respon­si­ble for the slight dif­fer­ence between the cal­cu­lated ß with v or –v.

Next chap­ter: The drag coef­fi­cient of Fresnel

When you are interested in physics you must read “Unbelievable“!

A photon can be accredited an impulse in the direction of movement equal to:

Impulse of the photon in the X- and Y- direction in ether II for the observer in rest with ether II is (figure 2):

    

Because ether II moves always sideways with speed v respectively to ether I, the impulse of the photon for the observer in rest with ether I in the X-direction, when the movement is maximal v towards the star (figure 4 and 5 the movement in Y-direction is zero), will be:

(Bradley only measured the stellar aberration in the X-direction; the vertical aberration. When the movement towards the star is zero {speed in X-direction is zero and the movement in the Y-direction is therefore v} the horizontal aberration, not measured by Bradley is maximal)

In the Y-direction the impulse of the photon is not changed, because the speed of both ether to each other in that direction is zero:

For the observer in ether II the impulse of the photon, after penetrating ether II from ether I, will not change. The vacuum has not the quality to change the impulse. Considering this the stellar aberration can now be determined by the following equations:

        

        

The reduced formulas are:

       

The stellar aberration and the Doppler-effect in the X-direction, due to the passage of the photon from ether I to ether II, is described by the equations:

These formulas only describe the stellar aberration and Doppler-effect caused by the speed in X-direction towards or from the star (vertical aberration). Bradley did not measure the horizontal aberration caused by the speed of the Earth in the Y-direction; sideways to the star. The vector summation of the vertical aberration caused by the speed of the Earth in the X-direction and the horizontal aberration caused by the speed of the Earth in the Y-direction gives the total aberration of the star y-Draconis.

Considering these formulas we observe a small difference when we calculate ß for v and the reverse speed –v. This small deviation between both calculations of the aberration β for v and -v  is caused by the math that does not describe the actual physics exactly. The summation of both β for v and -v should be exactly zero. The formulas above describe the situation where the speed changes instantaneous from zero to v or –v. In reality the speed gradually increases from zero to v and than gradually to –v. This second order effect, not described by the formulas, is responsible for the slight difference between the calculated ß with v or –v.

Next chapterThe drag coefficient of Fresnel

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