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The stellar aberration of the star y-Draconis with ether



The stellar aberration of the star y-Draconis with ether

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

The phys­i­cal aspects of the ether, when required, will be dealt with later in this doc­u­ment. The char­ac­ter­is­tics dragged ether needs to pos­sess, to explain the stel­lar aber­ra­tion, are exactly that of the known vac­uum: light moves in a vac­uum in all direc­tions with the same speed c and the impulse of pho­tons can­not be altered by vacuum.

Speed, direc­tion and mass deter­mine the impulse of an object.

I=MV

The mass M, speed V and the direc­tion deter­mine the impulse I. In com­par­i­son: a snooker ball will only change direc­tion and/​or speed when it encoun­ters the side or other balls. Pho­tons have an impulse If in the direc­tion of move­ment equal to the energy of the pho­ton divided by the speed of light c.

If=hv/​c

Where If is the impulse of the pho­ton with fre­quency v, h is the con­stant of Planck and c is the speed of light.

Assume a pho­ton com­ing from the star y–Dra­co­nis towards Earth. With dragged ether, a grad­ual tran­si­tion can be expected. When the dis­tance to the star y–Dra­co­nis increases the influ­ence of the star on the ether will decrease while the influ­ence of the Earth will increase. The influ­ence of the earth on the ether is larger when the ether is closer to the earth. Light com­ing from y–Dra­co­nis will there­fore be in tran­si­tion from ether under the influ­ence of y–Dra­co­nis to ether under influ­ence of the earth. A grad­ual tran­si­tion from ether under influ­ence of y–Dra­co­nis to ether under influ­ence of the earth can be expected.

The phys­i­cal char­ac­ter­is­tics of the ether around the star y–Dra­co­nis are the same as those of the ether around the earth. The dif­fer­ence is lim­ited to a rel­a­tive move­ment of both ethers towards or from each other; com­pa­ra­ble with mod­er­ate air flows in the atmos­phere or ocean cur­rents that grad­u­ally merge. For the observed stel­lar aber­ra­tion it is of no impor­tance over what dis­tance the tran­si­tion takes place. The effect will be the same regard­less whether or not the tran­si­tion is sudden.

Fig­ure 2 shows the sit­u­a­tion in which a pho­ton sud­denly enters the ether under influ­ence of the earth, com­ing from the ether under influ­ence of the star when the move­ment of the earth towards the star is max­i­mal. The direc­tion of the pho­ton from y–Dra­co­nis has an ele­va­tion of 75 degrees with the ellipse of the earth orbit. This angle is vir­tu­ally con­stant because the dis­tance to the star y–Dra­co­nis is infi­nitely larger than the dis­tance from the earth to the sun (no par­al­lax). The change of the real angle caused by the orbit of the earth around the Sun, the par­al­lax, is infi­nitely smaller than the stel­lar aber­ra­tion. The par­al­lax, the real change of the angle, is infi­nite small and inde­pen­dent on the stel­lar aber­ra­tion caused by the move­ment of the earth around the sun.

The impulse of the pho­ton, direc­tion and mag­ni­tude is deter­mined in ether I (fig­ure 2). Pas­sage from ether I to ether II brings the pho­ton in ether with exactly the same char­ac­ter­is­tics. The only dif­fer­ence is that ether II moves in com­par­i­son to ether I with a speed of 30 km/​second the speed of the Earth around the Sun.

The pho­ton must adjust in ether II to the new sit­u­a­tion. If the pho­ton fol­lowed the same line, there would be no stel­lar aber­ra­tion and the direc­tion and impulse of the pho­ton would be altered and that is not pos­si­ble with the char­ac­ter­is­tics of vacuum.

Fig­ure 2. The stel­lar aber­ra­tion of a pho­ton in tran­si­tion from ether I to ether II.

The pho­ton has to have a change in angle when it enters ether II, to main­tain the same direction/​impulse com­pared to the direc­tion of the pho­ton in ether I. If there is no aber­ra­tion β then the pho­ton will move in the same line in ether II. And because ether II is mov­ing com­pared to ether I with 30 km/​s, the pho­ton would be dragged to the right from its orig­i­nal path 30 km each sec­ond. The direc­tion and impulse of the pho­ton will then be changed.

This is impos­si­ble because vac­uum, the ether, has no char­ac­ter­is­tics to achieve a change in impulse. To com­pre­hend this per­cep­tion one must under­stand that an observer in ether II is by def­i­n­i­tion at rest with the dragged ether II and there­fore also mov­ing with 30 km/​s in com­par­i­son to ether I.

The impulse of a pho­ton in a cer­tain direc­tion can be deter­mined by split­ting up the impulse and speed. The speed or impulse of the pho­ton is ana­lyzed in two direc­tions: ver­ti­cal and par­al­lel to the move­ment of the earth towards or from the star. The impulse of the pho­ton ver­ti­cal to the move­ment of ether II (Y-​direction) is unchanged. There is no dif­fer­ence in speed of the two ethers in that direc­tion. For the deter­mi­na­tion of the impulse and speed of the pho­ton in ether II in the direc­tion of the move­ment of the earth towards the star y–Dra­co­nis, the speed of the earth around the sun has to be added (X-​direction in fig­ure 2).

The speed of ether II, com­pared to ether I in the X-​direction is respon­si­ble for the appar­ent change in direc­tion: the stel­lar aber­ra­tion. By adding the speed in the X-​direction at the moment the pho­ton enters the ether under influ­ence of the earth, the impulse of the pho­ton towards the observer on the earth is kept the same whether the pho­ton is trav­el­ing in ether I or ether II. By adding the speed of the earth towards the star in the X-​direction when the pho­ton enters ether II we keep the same impulse for the observer, whether the pho­ton is in ether I or ether II.

By adding 30 km/​s in the X-​direction we how­ever change the speed of the pho­ton. The total speed of the pho­ton, the vec­tor sum of the speed of the pho­ton in both direc­tions, changes when we add 30 km/​s in the X-​direction. Expe­ri­ence tells us that the mea­sured speed of light in vac­uum (ether) never exceeds c.

The tran­si­tion of the pho­ton enter­ing ether II from ether I, as it is described above, can there­fore not be com­plete. The speed of the pho­ton now exceeds the speed of light. The speed of light has to be adjusted because the observed speed in vac­uum is always c.

The cor­rec­tion is achieved by reduc­ing the speed of the pho­ton, after adding 30 km/​sec in the X-​direction, to c. In fig­ure 2 this is achieved by reduc­ing the vec­tor sum of the speed in X– and Y-​direction to the cir­cle with radius c. When we do this we change the impulse of the pho­ton in both direc­tions (X and Y). By look­ing at the for­mula of the impulse I of a pho­ton we have only one vari­able by which we can change the impulse, and that is the fre­quency v; h and c are nat­ural con­stants and there­fore by def­i­n­i­tion deter­mined. The impulse of a pho­ton I is:

I=hv/​c

When we reduce the speed of the pho­ton, after adding 30 km/​sec in the X-​direction, to c and at the same time increase the fre­quency v with the same fac­tor the impulse and direc­tion of the pho­ton for the observer in ether II will be the same whether the pho­ton is trav­el­ing in ether I or ether II. The increase or decrease of the fre­quency of the pho­ton when the earth is mov­ing towards and from y–Dra­co­nis is called the Doppler effect. In fig­ure 2 we have drawn the sit­u­a­tion where the Earth is mov­ing with 30 km/​s towards the right-​angled pro­jec­tion of y–Dra­co­nis on the orbit plane. Imag­ine that the speed towards the pro­jec­tion of y–Dra­co­nis declines from 30 km/​s to 0 and after that the speed decreases fur­ther to –30 km/​s in the oppo­site direc­tion. The aber­ra­tion ß will also decline to 0 and fur­ther to –ß when the speed is com­pletely reversed.

Fig­ure 3. The the­o­ret­i­cal stel­lar aber­ra­tion of the incli­na­tion of y-​Draconis.

The alter­ation of the ele­va­tion angle θ, the aber­ra­tion of the star y–Dra­co­nis mea­sured by Bradley, with dragged ether is the­o­ret­i­cally accord­ing to fig­ure 3 dur­ing the year. The the­o­ret­i­cally cal­cu­lated stel­lar aber­ra­tion matches the mea­sured aber­ra­tion by Bradley per­fectly. The chart of fig­ure 3 shows the the­o­ret­i­cal changes (ß) of the ele­va­tion of the star dur­ing the year. Bradley only mea­sured the ele­va­tion of the star y–Dra­co­nis dur­ing the year. The azimuth part of the aber­ra­tion was ini­tially not recorded by Bradley.

The derived for­mu­las for the stel­lar aber­ra­tion are of gen­eral use. The stel­lar aber­ra­tion of a star is depen­dent on the ele­va­tion (θ) of the star with the orbit of the earth. In fig­ure 4 the max­i­mum aber­ra­tion of the ele­va­tion (θ) of any star is given as a func­tion of the incli­na­tion. At 90 degrees the star is ver­ti­cally posi­tioned to the orbit of the earth around the sun.

Fig­ure 4. The max­i­mum stel­lar aber­ra­tion of the incli­na­tion of a star as a func­tion of inclination.

When we include the stel­lar aber­ra­tion in the orbit plane (the azimuth part) we are able to cal­cu­late the exact stel­lar aber­ra­tion of any star any time dur­ing the year.

Next chap­ter: The appar­ent change of angle in a force-​free ether

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

The physical aspects of the ether, when required, will be dealt with later in this document. The characteristics dragged ether needs to possess, to explain the stellar aberration, are exactly that of the known vacuum: light moves in a vacuum in all directions with the same speed c and the impulse of photons cannot be altered by vacuum.

Speed, direction and mass determine the impulse of an object.

I=MV

The mass M, speed V and the direction determine the impulse I. In comparison: a snooker ball will only change direction and/or speed when it encounters the side or other balls. Photons have an impulse If in the direction of movement equal to the energy of the photon divided by the speed of light c.

If=hv/c

Where If is the impulse of the photon with frequency v, h is the constant of Planck and c is the speed of light.

Assume a photon coming from the star y-Draconis towards Earth. With dragged ether, a gradual transition can be expected. When the distance to the star y-Draconis increases the influence of the star on the ether will decrease while the influence of the Earth will increase. The influence of the earth on the ether is larger when the ether is closer to  the earth. Light coming from y-Draconis will therefore be in transition from ether under the influence of y-Draconis to ether under influence of the earth. A gradual transition from ether under influence of y-Draconis to ether under influence of the earth can be expected.

The physical characteristics of the ether around the star y-Draconis are the same as those of the ether around the earth. The difference is limited to a relative movement of both ethers towards or from each other; comparable with moderate air flows in the atmosphere or ocean currents that gradually merge. For the observed stellar aberration it is of no importance over what distance the transition takes place. The effect will be the same regardless whether or not the transition is sudden.

Figure 2 shows the situation in which a photon suddenly enters the ether under influence of the earth, coming from the ether under influence of the star when the movement of the earth towards the star is maximal. The direction of the photon from y-Draconis has an elevation of 75 degrees with the ellipse of the earth orbit. This angle is virtually constant because the distance to the star y-Draconis is infinitely larger than the distance from the earth to the sun (no parallax). The change of the real angle caused by the orbit of the earth around the Sun, the parallax, is infinitely smaller than the stellar aberration. The parallax, the real change of the angle, is infinite small and independent on the stellar aberration caused by the movement of the earth around the sun.

The impulse of the photon, direction and magnitude is determined in ether I (figure 2). Passage from ether I to ether II brings the photon in ether with exactly the same characteristics. The only difference is that ether II moves in comparison to ether I with a speed of 30 km/second the speed of the Earth around the Sun.

The photon must adjust in ether II to the new situation. If the photon followed the same line, there would be no stellar aberration and the direction and impulse of the photon would be altered and that is not possible with the characteristics of vacuum.

Figure 2. The stellar aberration of a photon in transition from ether I to ether II.

The photon has to have a change in angle when it enters ether II, to maintain the same direction/impulse compared to the direction of the photon in ether I. If there is no aberration β then the photon will move in the same line in ether II. And because ether II is moving compared to ether I with 30 km/s, the photon would be dragged to the right from its original path 30 km each second. The direction and impulse of the photon will then be changed.

This is impossible because vacuum, the ether, has no characteristics to achieve a change in impulse. To comprehend this perception one must understand that an observer in ether II is by definition at rest with the dragged ether II and therefore also moving with 30 km/s in comparison to ether I.

The impulse of a photon in a certain direction can be determined by splitting up the impulse and speed. The speed or impulse of the photon is analyzed in two directions: vertical and parallel to the movement of the earth towards or from the star. The impulse of the photon vertical to the movement of ether II (Y-direction) is unchanged. There is no difference in speed of the two ethers in that direction. For the determination of the impulse and speed of the photon in ether II in the direction of the movement of the earth towards the star y-Draconis, the speed of the earth around the sun has to be added (X-direction in figure 2).

The speed of ether II, compared to ether I in the X-direction is responsible for the apparent change in direction: the stellar aberration. By adding the speed in the X-direction at the moment the photon enters the ether under influence of the earth, the impulse of the photon towards the observer on the earth is kept the same whether the photon is traveling in ether I or ether II. By adding the speed of the earth towards the star in the X-direction when the photon enters ether II we keep the same impulse for the observer, whether the photon is in ether I or ether II.

By adding 30 km/s in the X-direction we however change the speed of the photon. The total speed of the photon, the vector sum of the speed of the photon in both directions, changes when we add 30 km/s in the X-direction. Experience tells us that the measured speed of light in vacuum (ether) never exceeds c.

The transition of the photon entering ether II from ether I, as it is described above, can therefore not be complete. The speed of the photon now exceeds the speed of light. The speed of light has to be adjusted because the observed speed in vacuum is always c.

The correction is achieved by reducing the speed of the photon, after adding 30 km/sec in the X-direction, to c. In figure 2 this is achieved by reducing the vector sum of the speed in X- and Y-direction to the circle with radius c. When we do this we change the impulse of the photon in both directions (X and Y). By looking at the formula of the impulse I of a photon we have only one variable by which we can change the impulse, and that is the frequency vh and c are natural constants and therefore by definition determined. The impulse of a photon I is:

I=hv/c

When we reduce the speed of the photon, after adding 30 km/sec in the X-direction, to c and at the same time increase the frequency v with the same factor the impulse and direction of the photon for the observer in ether II will be the same whether the photon is traveling in ether I or ether II. The increase or decrease of the frequency of the photon when the earth is moving towards and from y-Draconis is called the Doppler effect. In figure 2 we have drawn the situation where the Earth is moving with 30 km/s towards the right-angled projection of y-Draconis on the orbit plane. Imagine that the speed towards the projection of y-Draconis declines from 30 km/s to 0 and after that the speed decreases further to -30 km/s in the opposite direction. The aberration ß will also decline to 0 and further to -ß when the speed is completely reversed.

Figure 3.  The theoretical stellar aberration of the inclination of y-Draconis.

The alteration of the elevation angle θ, the aberration of the star y-Draconis measured by Bradley, with dragged ether is theoretically according to figure 3 during the year. The theoretically calculated stellar aberration matches the measured aberration by Bradley perfectly. The chart of figure 3 shows the theoretical changes (ß) of the elevation of the star during the year. Bradley only measured the elevation of the star y-Draconis during the year. The azimuth part of the aberration was initially not recorded by Bradley.

The derived formulas for the stellar aberration are of general use. The stellar aberration of a star is dependent on the elevation (θ) of the star with the orbit of the earth. In figure 4 the maximum aberration of the elevation (θ) of any star is given as a function of the inclination. At 90 degrees the star is vertically positioned to the orbit of the earth around the sun.

Figure 4.   The maximum stellar aberration of the inclination of a star as a function of inclination.

When we include the stellar aberration in the orbit plane (the azimuth part) we are able to calculate the exact stellar aberration of any star any time during the year.

Next chapter: The apparent change of angle in a force-free ether

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