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When it comes to light aberration, many people may think it is very simple, but in fact it is not simple. It plays a very important role in people's understanding of the speed of light and the establishment of special relativity. Therefore, the things involved in aberration are worthy of in-depth study.

01. From raindrops to sound, for ease of understanding, let's start with a common thing.

Many people have this kind of life experience, when riding with an umbrella or walking quickly in the rain, in order to avoid getting wet, the umbrella should lean forward a little, like this.

This involves a simple but profound physical problem.

To put it simply, you will understand it as soon as you say it. Profoundly, because it involves the relativity of velocity in classical mechanics, it is based on the space-time transformation hypothesis of classical mechanics-Galileo transformation.

In the ground reference system, the raindrop velocity is downward, as shown in figure (b) below, while in the view of the moving person, the raindrop velocity is oblique to the rear. Figure (c) below.

The mathematical expression of this law is that r, g and m are taken from the initials of rain, ground and man, respectively, so it is the speed of rain relative to people, the speed of raindrops relative to the ground, and the speed of the ground to people. According to the triangle rule of the vector, the drawing is

If the angle between and is measured, then the velocity of the raindrop can be calculated as

If the rain is replaced with a sound, the sound is transmitted from the top, the relative air is fixed, and the person moves eastward at a horizontal speed, then similarly, the speed of the sound will also be oblique backward.

However, from raindrops to sound, the span is still a little big! Because the former is a ballistic object, while the latter is a wave! The wave itself is not an object, but the propagation of a vibrational state.

Therefore, you may wonder whether the relativity of the above raindrop motion is also true for waves.

It is true, of course, which can be explained by plane waves.

Suppose that the plane wave travels vertically and you move horizontally relative to the medium. Since some part of the wave, such as the crest of the wave, moves vertically relative to the medium, then in your opinion, those peaks have another partial velocity in the horizontal direction, and the direction of the velocity becomes oblique.

So, when you stare at a wave crest, you will find that it passes through a diagonal line, which is the so-called direction of wave velocity, that is, the wave line! Now that the wavefront is tilted, so is the perpendicular surface, the wavefront. Therefore, the whole wave in the movement of your point of view, as a whole turned an angle!

So, whether it is a wave or an object, such as a particle or fluid, there is a change in the direction of velocity caused by the motion of the observer. Whether the raindrop or the sound, the speed will become oblique to the rear, as if there is a kind of wind blowing back in the air, it is it that blows the raindrop or sound backward.

02. The concept and formula of aberration in history, there are two main views on the understanding of the nature of light. People represented by Newton support the theory of particles (corpuscle model), while those represented by Robert Hook and Christian Huygens support the theory of fluctuation (wave theory of light).

If light is thought to be a moving ballistic particle, then according to the above image of raindrops, it is natural to know that when the observer moves relative to the star, and when the velocity has a component along the vertical direction of his line with the star (hereinafter referred to as lateral motion), he will see the direction of starlight deflect.

If you think that light is a wave, then the situation is a little more complicated. Because a medium must be found for light, otherwise the speed of light cannot be explained, and it is unknown to whom the observer is moving.

In order to understand the propagation mechanism of photoluminescence waves, wave theory holds that there is an invisible medium in the universe, which endows the wave velocity of light. This substance is called aether, and it is to light what air is to sound.

Therefore, if you replace the sound in the above example with light, the result is similar: the observer who travels to the right in the ether will see that the light originally shot from the top of the head is now oblique and downward, as if a gust of wind has tilted the light back. This is the so-called "etheric wind".

By the way, the ether is not a monopoly of wave theory. Although Newton insisted on the theory of particles, he did not reject the ether, but his ether did not provide wave velocity, but a matter full of absolute space whose density varied with gravity. Therefore, people who support the theory of particles will often talk about the ether.

In short, whether light is thought of as particles or waves, in theory, observers of lateral motion will see the direction of light deflect.

According to the etheric fluctuation point of view, the formula for calculating this deflection angle is given below.

From the relativity of velocity, the velocity of light wave relative to the earth is equal to the sum of the speed of light wave relative to the ether and the speed of the ether relative to the earth, where l, e and an are taken from the initials of light, earth and aether, respectively. When the star is directly above, the light is vertically downward relative to the ether, which corresponds to the following vector triangle

When the star is not directly above, the speed of light in the ethernet is oblique downward, which is slightly more complicated. Suppose the angle between the speed of light in the ether and the ground is, the angle between the speed of light and the ground seen on the earth is, and the vector triangle of the above velocity is

In the etheric, the speed of light is c, and the speed of the etheric relative to the earth is the speed of the etheric relative to the earth.

According to Galileo transformation, the above tangent can be obtained by dividing the speed of light in the etheric reference frame K and the speed of light in the earth reference system K'.

And then according to the triangular relationship,

This angle is the angle at which the light is deflected by the etheric wind. Because of its existence, when we look up at the star, what we see is not itself, but a virtual image of it, such as the star on the right in the following picture.

This phenomenon that the position of the star deviates due to the motion of the observer is called stellar aberration (Stellar Aberration) or stellar aberration (Aberration of light). The angle at which the speed of light is relative to the speed of light in the ether is the so-called aberration angle.

Note that stellar aberration and stellar aberration essentially have the same meaning, but the two emphasize different meanings. The former emphasizes that "the virtual image of the star deviates from the real position", while the aberration emphasizes that "the light of the star deviates from the original direction".

Although the theoretical expression of the aberration angle above is accurate, it is not commonly used, because the angle directly observed is the inclination of the starlight seen on Earth rather than the real inclination of the star, that is, the angle in the previous picture.

So can it be used to represent the aberration angle of light?

From the trigonometric knowledge, when very small, it can be approximately regarded as an open angle of the radius of the arc pair, so although it looks the same in form as the formula expressed above, note that it is an approximation!

Because the aberration angle of the star is actually very small, the accuracy of this formula is very high, so it has become a common formula for the aberration angle. And because the speed of the earth is much less than the speed of light, the denominator is negligible, so this formula can be approximated to that if you choose a star at the zenith, the aberration angle satisfies the theoretical formula.

This is the most commonly used classical aberration formula, which is discussed later in this paper.

If the particle-based theory of light is based on the velocity of the flow of light particles from the star and the velocity of the earth relative to the star, the law and formula of light difference are the same as in the case of etheric fluctuations mentioned above.

Therefore, the above concept and formula of aberration of light are applicable not only to the theory of light fluctuation, but also to the theory of light particles. However, in theory, the meaning of aberration is different between the two viewpoints, which will be discussed later.

03. Bradley's observation according to the classical aberration formula, it is obvious that the speed of light in the ether can be obtained if the aberration angle of a star confirmed to be at the zenith can be measured.

This is the basis on which the 18th century English physicist James Bradley (James Bradley,1693~1762) measured the speed of light.

At first, Bradley's main goal was not to measure the speed of light, and he didn't even know there was a light aberration at the time. Because he himself is the discoverer of aberration.

Bradley's work began in 1725. He was supposed to observe stellar parallax (stellar parallax). Stellar parallax means that when viewed from different positions, the position or direction of the star looks different, usually using the angle at which the radius of the earth's orbit opens to the star as parallax, as shown in the following image.

It can be seen that although the difference between stellar parallax and stellar aberration is only one word, the meaning is different. But they all prove the fact that the earth revolves around the sun as evidence of Copernicus's heliocentric theory, which was one of Bradley's original research goals.

If you look at a low-altitude star, its light is oblique, and the starlight experiences a longer distance in the atmosphere than the starlight from the high sky, considering that there is more water vapor and dust near the surface, and the starlight is scattered so that the observation error is very large. in order to minimize the impact of this problem, stars at the zenith should be selected to observe.

Bradley specially chose a second-class star named γ-Draconis (γ-Dra, formerly known as Eltanin in Chinese, belonging to the Dragon constellation, as pictured above). It is located at 51 °29'N, while London is at 51 °30 °N, so when it sweeps past the meridian, it happens to be at the zenith of London.

Bradley's client designed a sophisticated telescope that belongs to the zenith telescope (zenith telescope). As shown in the image below, the main body of the telescope is a 24.5ft long optical tube that passes through the roof through a chimney.

Bradley installed the telescope on the inner wall of a house called Kew, southwest of London, not far from the Greenwich Observatory, where the author carefully checked that the longitude was-0.297954, almost the location of the prime meridian.

The telescope is also known as the zenith sector (zenith sector), so named because the optical tube is located in the vertical plane of the local meridian, and the telescope looks at a small sector above the meridian. In other words, the projection of the optical tube on the ground is parallel to the meridian, and its inclination can only be fine-tuned along the meridian in the north-south direction.

The purpose of this is to observe only those stars that reach just above the meridian every day, and when those stars are observed, they are at the zenith as much as possible.

The observer lies on the sofa in the house, watching the target star by adjusting the eyepiece. The Vernier scale next to the eyepiece gives the angle of the star in the north-south direction.

According to the image above, because γ-Dra is slightly to the left above the ecliptic, the earth moves closer and closer to γ-Dra from December to June of the following year, so the latitude of γ-Dra should increase-albeit weakly. So, in order to see it, the tube of the telescope should keep moving northward. From June to the end of the second year, the process is the other way around-the pipe should move south.

Friendly Tip: the above picture contains a lot of information and is worth tasting carefully.

Since Hook had given a parallax of about 23 angular seconds for γ-Dra in 1674, Bradley predicted that the shift of γ-Dra in the north-south direction would vary with time as follows.

However, the results of the measurements puzzled Bradley, who did not observe the expected parallax at all, but observed something completely unexpected.

In fact, it is no wonder that parallax has not been observed, because according to the known distance between γ-Dra and the earth is 154light-years, the Radian of parallax is less than 21 milliseconds, which is three orders of magnitude smaller than Hook's original value, which is almost equivalent to standing in Guangzhou to observe the height of a person in Heilongjiang or Xinjiang. Bradley's telescope can't see it at all.

So what did Bradley find out?

Bradley did observe a change in the height of γ-Dra, but the change for the whole year was completely different from what the parallax expected. His observations are as follows

From December to March, γ-Dra moves southward in the meridian; by March, it shifts about 20 "from its starting position; from March to June, it moves northward back to its starting position; then from June to September, it continues northward until it finally reaches 20" north of its starting position; finally, from September to December, it moves southward back to its starting position.

Explanation of stellar aberration Bradley thought that one day when he was sailing on the Thames, he noticed that the direction of the wind had not changed, but because the course of the ship changed, the direction of the indicator flag on the mast changed, and he understood at once.

It occurred to him that light is a stream of particles from a star (Bradley Benedict believes in the particles of light), similar to the change in the direction of raindrops seen by travelers in the rain. When the earth moves relative to the star, the direction of the particle flow of these light will also shift, so the light will always deflect an angle in the opposite direction of the earth's rotational speed.

Yes, Bradley's thoughts are similar to those described in Section 2 of this article, except that he thinks based on the theory of particles of light. He regarded the speed of the earth orbiting the sun as the speed of the earth relative to the star, so he got the aberration formula and became the first person in history to study and explain the aberration phenomenon.

Bradley's idea of "direction shift of light", if understood in terms of etheric fluctuations of light, is, of course, the same result-the etheric wind blowing back blows the light from the top of the head, deflecting it back, as shown in the image below.

Because of the deflection of light, to observe a star, the direction of the tube must be adjusted accordingly, otherwise the light it emits will not be able to reach the bottom of the tube. This is shown in the following figure.

Therefore, in order to see γ-Dra at the corresponding time every day, Bradley must adjust the direction of the optical tube of the telescope so that its deflection angle is consistent with the aberration angle.

Therefore, the relationship between the deviation angle and time obtained by Bradley is actually the variation of the aberration angle of γ-Dra with time.

Er, the variation of the aberration angle of γ-Dra with time is periodic, to be exact, a change in the form of sine or cosine function.

So how do you explain this?

Next, it may be more a question of geography or astronomy.

Although the etheric wind always points in the opposite direction of the earth's rotation speed, the direction of the etheric wind felt on the ground changes from time to time because the earth's revolution is curvilinear and the earth is spinning. For observers in London, the etheric wind can lead to different observations at different times.

Let's take a look at the period from December to March.

During this period, the direction of the earth's movement on the ecliptic gradually changed from north to west, so the etheric wind gradually changed from south to east.

At noon on the first day (December 17), γ-Dra was at the zenith of London. according to the relationship between sidereal day and solar day, γ-Dra appeared at the zenith about 3 minutes and 56 seconds earlier than the day before, until around March 18, when γ-Dra reached the zenith at 6 a.m.

Bradley observes gamma-Dra at this point every day, and his task is to adjust the optical tube of the telescope to record the north-south deflection of the star.

Considering that the earth rotates from west to east, between December and March, when γ-Dra is above the meridian, the etheric wind felt in London begins eastward and then gradually shifts northward.

At 6 o'clock in the morning on March 17 or 18, when γ-Dra is directly above the meridian, and the speed of the earth's revolution is just south of the ground, the speed of the northward etheric wind on γ-Dra reaches its maximum, that is, the speed of the earth's revolution. This northward strongest etheric wind blows gamma-Dra light northward, causing the illusion of gamma-Dra to deviate southward to the farthest.

Tip: considering that the rotation and rotation of the earth are from west to east, combined with the previous picture of the movement of the earth on the ecliptic, the above rule can be obtained. Please think about it carefully.

So, from London, γ-Dra deviates from the west at first and then to the south. In order to make the telescope see γ-Dra all the time, the optical tube should first deviate to the west, and the deviation degree is the largest, and then the deflection angle gradually decreases and then gradually deviates to the south, and the deviation angle increases gradually.

The problem becomes simpler if you only focus on the offset of the star in a particular direction. Bradley only records the movement of γ-Dra in the north-south direction, that is, the effect of the etheric wind blowing northward, and he found that around March 17, γ-Dra deviated south by about 20 ".

If we continue to look at the period from March to June, the etheric wind on the zodiac gradually changes from east to north, and the etheric wind corresponding to the observation points on the earth gradually changes from north to west. Since Bradley only focused on the movement of stars in the north-south direction, he found that the etheric wind to the north gradually weakened to zero, which reduced the shift of γ-Dra to the south until it fully returned to its original position in December.

The analysis method is the same from June to September and from September to December, leaving it to the reader to practice.

If we look at the four stages together, we can see that the deviation of γ-Dra in the north-south direction shows a periodic law, and Bradley's observation results are completely understandable!

05. Bradley's contribution Bradley pointed out that he is only concerned with the deviation of stars in the north-south direction, and if he is also concerned about the deviation of stars in the east-west direction, then the observation will become much more complicated. He believes that if deviations in all directions are taken into account, the virtual image of the star will cross a circle at the zenith-a small ellipse to be exact.

You may ask: why do most people, including Bradley himself, only care about the north-south direction of γ-Dra, regardless of the east-west deviation?

Because the earth rotates around the north-south axis, the star is at the zenith only if it is just within a small range above the local meridian, and this moment can be predicted based on the difference between the stellar day and the solar day, which provides an accurate time window for observing the aberration of γ-Dra.

In other words, since you want to use the best moment when the star is directly above the meridian to observe its deviation, it seems a bit troublesome to observe its deviation in this direction.

This is a bit like the "control variable method" mentioned when we study the relationship between mass, force and acceleration in high school physics. Only by fixing a quantity can we study the relationship between the two external quantities. If you let several quantities change at the same time, your research will certainly be very troublesome.

In fact, according to the literature, Bradley lacked a high-precision clock, the stellar clock, to time according to the stellar day, otherwise he would have been able to measure the deviation of γ-Dra along the east-west direction. As you all know, relying on the sophisticated GPS clock, it's all right to do this now!

Of course, if the earth rotates from north to south and other conditions remain the same, Bradley will surely choose to observe the star's deviation from east to west. Because in that case, the east-west direction becomes latitude and the north-south direction becomes longitude.

The aberration angle of γ-Dra obtained by Bradley is 20.2 ". Since then, by observing the deviations of different stars in the direction of longitude and latitude, astronomers around the world have obtained more aberration angles of stars and found that these values are almost the same.

This is easy to understand because these stars have one thing in common-they are all very far away from Earth and are located at the zenith of the observatory, so they all obey the simplified formula of the aberration angle.

At present, the exact value of the annual aberration angle of a star is 20.49552 ", which is applicable to the aberration angle of light along both longitude and latitude.

Although Bradley did not observe the stellar parallax but observed the stellar aberration, the periodicity of the stellar aberration is also conclusive evidence of the earth's motion around the sun, so the stellar aberration provides the first empirical proof for Copernicus's heliocentric theory.

In addition to achieving these goals, Bradley achieved another goal that was later added-he wanted to prove that the speed of light was limited. In fact, he gave a more accurate picture of the speed of light for the first time. With this work, Bradley ushered in the peak of his life, and his name was permanently recorded in the annals of human science and technology.

Before that, the Danish astronomer Ole R ø mer gave a wide difference in the speed of light-214000 km / s-by observing the solar eclipse of one of Jupiter's moons in 1675.

Bradley measured the maximum deviation angle of γ-Dra to the south and north is 20.2 ", which is the deviation angle of the light of γ-Dra, which is converted to 0.00561 °. Bradley calculated the average speed of the earth's revolution based on the radius of the earth's orbit (what value he used at that time, which was not found) and the number of seconds in a year, and the calculated value of the speed of light is 301000 km / s.

The error between this value and the standard value of light speed 299792.458 km / s is within 0.4%, which shows that Bradley's optical aberration theory is reliable and the measurement accuracy is relatively high.

If we use the standard value of the speed of light, considering that the average speed of the earth is about 29.79km / s, it is very close to 1/10000, which is called the optical aberration constant, which is the tangent of the aberration angle.

06, other types of aberration this section is mainly written for the integrity of the content, you can skip if you are not interested.

The above so-called optical aberration should be called "annual aberration", because it occurs during the earth's revolution cycle, so what is in the formula is the average speed of the earth's revolution. The annual light aberration constant is the ratio of the earth's rotation speed to the speed of light, and the corresponding angle is 20.49552 ".

If the earth's rotation is taken into account, it will lead to the so-called "solar aberration", which refers to the maximum angle at which the star's light is deflected in a day. Since the maximum rotation velocity of the earth is at the equator, about 0.465km / s, this value is two orders of magnitude smaller than the rotation speed, and the corresponding angle is about 0.319 ". The optical aberration constant at latitude φ is 0.319 "cos φ.

Furthermore, the motion of the solar system can also lead to aberration. Because the motion of the solar system is almost constant, this aberration is constant for a long time, so it is called "long-term aberration".

In the observable time, the long-term aberration angle is constant, and even if its value is larger than the annual aberration angle, it is not easy to see, because its effect on stellar aberration is consistent globally. So in general, this kind of aberration is ignored.

07. Is this it? The classical theory of aberration has indeed been finished, it looks very simple!

However, more than 100 years later, it will be subject to all kinds of skepticism, because the classic aberration contains some assumptions. For example, it is thought that the earth will not drag the ether, but the stars and the ether remain stationary.

In addition, according to the particles of light, the speed of light should be related to the speed of stars, that is, when you look at different stars, you should see different angles of aberration.

All these questions plagued the geniuses of that era, and all kinds of smart brains appeared on the stage, including Arago, Eli, Thomas Young, Fesso, Michelson and Morey. Their ingenious ideas and wonderful designs continue to inspire people, until the aberration is finally given a new explanation, leading to a wonderful theory of relativity.

For all these follow-up experiments, thinking, and related history, we will not miss any highlights and details, step by step, firmly secure, and analyze each of these mysteries one by one. Try to avoid "easy to know", "easy to get", "easy to prove", "not difficult to find", "obviously have" and "have the same reason", but also readers with clear physical thinking and historical context.

This reply is based here. If you want to know what kind of legends there are in the world, it is natural to listen to the next decomposition!

reference

Liu Jueping, Electrodynamics, Beijing, higher Education Press, 2004.7.

Https://en.wikipedia.org/wiki/Aberration_(astronomy)

Https://en.wikipedia.org/wiki/James_Bradley

Https://www.geocentrismdebunked.org/geocentrism-and-stellar-aberration/

Http://www.royalobservatorygreenwich.org/articles.php?article=1065

Https://www.secretsofuniverse.in/speed-of-light-ole-roemer/

This article is from the official account of Wechat: University Physics (ID:wuliboke), by Xue Debao.

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