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The Mitr

Rotating Earth: the proofs or significance of Leon Foucault’s pendulum – Part 1

rotating-earth
In an earlier post, we had discussed proofs of the round shape of the Earth. This included some ancient and some modern proofs. There was, in general, a consensus that the shape of the Earth was spherical and not flat and the proofs were given since the time of ancient Greeks. Only in the middle ages, there seems to have been some doubt regarding the shape of the Earth. But amongst the learned people, there was never a doubt about the shape of the Earth. Counter-intuitive it may seem when you look at the near horizon, it is not that counter-intuitive. We can find direct proofs about it by looking around and observing keenly.
But the rotation of Earth proved to be a more difficult beast to tame and is highly counter-intuitive. Your daily experience does not tell you the Earth is rotating, rather intuition tells you that it is fixed and stationary. Though the idea of a moving Earth is not new, the general acceptance of the idea took a very long time. And even almost 350 years after Copernicus’ heliocentric model was accepted, a direct proof of Earth’s rotation was lacking. And this absence of definitive proof was not due to a lack of trying. Some of the greatest minds in science, mathematics and astronomy worked on this problem since Copernicus but were unable to solve it. This included likes of Galileo, Newton, Descartes, and host of incredibly talented mathematicians since the scientific revolution. Until Leon Foucaultin the mid-1800s provided not one but two direct proofs of the rotation of the Earth. In this series of posts, we will see how this happened.
When we say the movement of the Earth, we also have to distinguish between two motions that it has: first its motion about its orbit around the Sun, and second its rotational motion about its own axis. So what possible observational proofs or direct evidence will allow us to detect the two motions? In this post, we will explore how our ideas regarding these two motions of the Earth evolved over time and what type of proofs were given for and against it.

Even more, there was a simple geometrical fact directly opposed to the Earth’s annual motion around the Sun and there was nothing that could directly prove its diurnal rotation. (Mikhailov, 1975)

Let us consider the two components of Earth’s motion. The first is the movement around the Sun along the orbit. The simplest proof for this component of Earth’s motion is from the parallax that we can observe for distant stars. Parallax is the relative change in position of objects when they are viewed from different locations. The simplest example of this can be seen with our own eyes.
Straighten your hand, and hold your thumb out. Observe the thumb with both the eyes open. You will see your thumb at a specific location with respect to the background objects. Now close your left eye, and look at how the position of the thumb has changed with respect to the background objects. Now open the right eye, and close the left one. What we will see is a shift in the background of the thumb. This shift is related by simple geometry to the distance between our eyes, called the baseline in astronomical parlance. Thus even a distance of the order of a few centimetres causes parallax, then if it is assumed that Earth is moving around the Sun, it should definitely cause an observable parallax in the fixed stars. And this was precisely one of the major roadblock

Earth moving around an orbit raised mechanical objections that seemed even more serious in later ages; and it raised a great astronomical difficulty immediately. If the Earth moves in a vast orbit, the pattern of fixed stars should show parallax changes during the year. (Rogers, 1960)

The history of cosmic theories … may without exaggeration be called a history of collective obsessions and controlled schizophrenias.
– Arthur Koestler, The Sleepwalkers

Though it is widely believed that Copernicus was the first to suggest a moving Earth, it is not the case. One of the earliest proponents of the rotating Earth was a Greek philosopher named Aristarchus. One of the books by Heath on Aristarchus is indeed titled Copernicus of Antiquity (Aristarchus of Samos). A longer version of the book is Aristarchus of Samos: The Ancient Copernicus. In his model of the cosmos, Aristarchus imagined the Sun at the centre and the Earth and other planets revolving around it. At the time it was proposed, it was not received well. There were philosophical and scientific reasons for rejecting the model.

aristarchus-01
Aristarchus’s model of the heliocentric Universe

First, let us look at the philosophical reasons. In ancient Greek cosmology, there was a clear and insurmountable distinction between the celestial and the terrestrial. The celestial order and bodies were believed to be perfect, as opposed to the imperfect terrestrial. After watching and recording the uninterrupted waltz of the sky over many millennia, it was believed that the heavens were unchangeable and perfect. The observations revealed that there are two types of “stars”. First the so-called “fixed stars” do not change their positions relative to each other. That is to say, their angular separation remains the same. They move together as a group across the sky. Imagination coupled with a group of stars led to the conceiving of constellations. Different civilizations imagined different heroes, animals, objects in the sky. They formed stories about the constellations. These became entwined with cultures and their myths.
telescope_0013
The second type of stars did change their positions with respect to other “fixed stars”. That is to say, they changed their angular distances with “fixed stars”. These stars, the planets, came to be called as “wandering stars” as opposed to the “fixed stars”.

Ancient Greeks called these lights πλάνητες ἀστέρες (planētes asteres, “wandering stars”) or simply πλανῆται (planētai, “wanderers”),from which today’s word “planet” was derived.
Planet

So how does one make sense of these observations? For the fixed stars, the solution is simple and elegant. One observes the set of stars rising from the east and setting to the west. And this set of stars changes across the year (which can be evidenced by changing seasons around us). And this change was found to be cyclical. Year after year, with observations spanning centuries, we found that the stars seem to be embedded on inside of a sphere, and this sphere rotates at a constant speed. This “model” explains the observed phenomena of fixed stars very well.
The unchanging nature of this cyclical process observed, as opposed to the chaotic nature on Earth, perhaps led to the idea that celestial phenomena are perfect. Also, the religious notion of associating the heavens with gods, perhaps added to them being perfect. So, in the case of perfect unchanging heavens, the speeds of celestial bodies, as evidenced by observing the celestial sphere consisting of “fixed stars” was also to be constant. And since celestial objects were considered as perfect, the two geometrical objects that were regarded as perfect the sphere and the circle were included in the scheme of heavens. To explain the observation of motion of stars through the sky, their rising from the east and setting to the west, it was hypothesized that the stars are embedded on the inside of a sphere, and this sphere rotates at a constant speed. We being fixed on the Earth, observe this rotating sphere as the rising and setting of stars. This model of the world works perfectly and formed the template for explaining the “wandering stars” also.
These two ideas, namely celestial objects placed on a circle/sphere rotating with constant speed, formed the philosophical basis of Greek cosmology which would dominate the Western world for nearly two thousand years. And why would one consider the Earth to be stationary? This is perhaps because the idea is highly counter-intuitive. All our experience tells us that the Earth is stationary. The metaphors that we use like rock-solid refer to an idea of immovable and rigid Earth. Even speculating about movement of Earth, there is no need for something that is so obviously not there. But as the history of science shows us, most of the scientific ideas, with a few exceptions, are highly counter-intuitive. And that the Earth seems to move and rotate is one of the most counter-intuitive thing that we experience in nature.
The celestial observations were correlated with happenings on the Earth. One could, for example, predict seasons as per the rising of certain stars, as was done by ancient Egyptians. Tables containing continuous observations of stars and planets covering several centuries were created and maintained by the Babylonian astronomers. It was this wealth of astronomical data, continuously covering several centuries, that became available to the ancient Greek astronomers as a result of Alexander’s conquest of Persia. Having such a wealth of data led to the formation of better theories, but with the two constraints of circles/spheres and constant speeds mentioned above.
With this background, next, we will consider the progress in these ideas.
A stabilised image of the Milky Way as seen from a moving Earth.

 

The Mitr

Can Stars Be Seen in Daylight?

The constellations that we saw at night half a year ago are now overhead in the daytime. Six months later they will again adorn the night sky. The sunlit atmosphere of the Earth screens them from the eye because the air particles-disperse the sun-rays more than the rays emitted by the stars. (The observer located on the top of a high mountain, with the densest and dustiest layers of- the atmosphere below, would see the brighter stars even in daytime. For instance, from the top of Mt. Ararat (5 km. high), first-magnitude stars are clearly distinguished at 2 o’clock in the afternoon; the sky is seen as having a dark blue colour.)
The following simple experiment will help explain why the stars disappear in daylight. Punch a few holes in one of the sides of a cardboard box, taking care, however, to make them resemble a familiar constellation. Having done so, glue a sheet of white paper on the outside. Place a light inside the box and take it into a dark room; lit from the inside; the holes, representing stars in the   night sky, are clearly seen. But, switch on a light in the room without extinguishing the light in the box and, lo, the artificial stars on our sheet of paper vanish without trace: “daylight” has extinguished them.
One often reads of stars being seen even in daylight from the bottom of deep mines and wells, of tall chimney-stacks and so on. Recently, however, this viewpoint, which had the backing of eminent names, was put to test and found wanting.  As a matter of   fact, none of the men who wrote on this subject, whether the Aristotle of antiquity or 19th-century Herschel, had ever bothered to observe the stars in these conditions. They quoted the testimony of a third person. But the unwisdom of relying on the testimony of
“eye-witnesses,” say in this particular field, is emphasized by the; following example. An article in an American magazine described daylight visibility of stars from the. bottom of a well as a fable. This was hotly contested by a farmer who claimed that he had seen Capella: and Algol in daytime from the floor of a  20-metre high silo. But when his claim was checked it was found that on the latitude of his farm neither of the stars was at zenith at the given date and, consequently could not have been seen from
the bottom of the silo.
Theoretically, there is no reason why a mine or a well should help in daylight observation of stars. We have already mentioned that the stars are not seen in daytime because sunlight extinguishes them. This holds also for the eye of the observer at the bottom of a mine. All that is subtracted in this case- is the light from the sides. All the particles in the layer of air above the surface of the mine continue to give off light and, consequently, bar the stars to vision.
What is of importance here is that the walls of the well protect the; eye from the bright sunlight; this, however, merely facilitates observation of the bright planets, but not the stars. The reason why stars are seen through the telescope in daylight is not because they are seen from “the bottom of a tube,” as many think, but because the refraction of light, by the lens or its reflection in the mirrors detracts from the brilliancy of the part of the sky under observation, and at the same time enhances the brilliancy of the stars (seen as points of light). We can see first-magnitude and even second-magnitude stars in daytime through a 7 cm. telescope. What has been said, however, does not hold true for either wells, mines, or chimneys.
The bright planets, say, Venus, Jupiter or Mars, in opposition, present a totally different picture. They shine far more brilliantly than the stars, and for this reason, given favourable conditions, can be seen in daylight.
From Astronomy for Entertainment – Yakov Perelman Pg: 135-137
Available here.

The Mitr

Reason and Faith – Misconceptions in Science Education

Reason does not work in matters of faith. But it may have a chance at clearing misconceptions.
via Tehelka

Truly so. In case of my field of study, namely science education research, it may be the other way round. The classic studies in science education aim at identifying the misconceptions that the learners have regarding a particular subject and then finding a mechanism by which they could be addressed.
This was a very simple but very basic presentation of  what most studies try to achieve, though the methodology may be different. There are some studies which present us with a conceptual framework so that all the responses and the problems with the learners can be seen in light of a theoretical construct. This they say will enable us to make sense of what we see in the classrooms, and what is present as representation in the learners mind. What I think they are trying to say is that we need to get to the conceptual structures that lead to formation of the misconceptions.
Now mind you that many of these misconceptions in science are very stubborn and people are very reluctant to give them up. The reason may be that many of these misconceptions come from direct factual experience in the real world. And from what I know about Philosophy of Science, we might want to make a case that all science is counter-intuitive to our everyday experience. This would explain why misconceptions in science arise. But would this case explain all the known misconceptions?
Let us do some analysis of how a particular misconception might arise.There can be two different reasons for a misconception to arise, if we adhere to deductive logic. That is to say we assume that we have a set of starting statements that are given, whose authenticity is not questioned. And from these set of statements we make certain deductions regarding the world out there. Now there can be two problems with this scenario, one is that the set of statements that we are taking for granted might be wrong, the other is that in the process of deduction that we have followed we made a mistake. The mistake is learnt only when the end result of our analysis is not consistent with the observations in the real world. Or it might be even the case that the so called misconception will lead to a correct answer, at least in some cases.  In these cases we have to resort to more detailed analysis of the thought structure which lead to the answers. Another identifying characteristic of the misconceptions is presence of the inconsistencies across different areas known to the learners. Whereas they might get a particular concept clearly and correctly, in applying same thing for another concept they just might revert to a completely opposite argument and in doing this they do not realise the inconsistency.
We will be clearer on this issue when we talk with a few examples. Suppose that we have a scenario in which we are trying to understand the phenomena of day and night, its causes and consequences. A typical argument in our class goes like this:

How many have seen the Sun set?

Almost all hands would go up, then comes the next question:

How many have seen the Sun rise?

Almost same number of hands go up, excepting a few, who are late risers like me. Some of the more intelligent and the more knowledgeable would say,
“Wait! Sun doesn’t rise and set, it is the Earth that is moving, so it causes the apparent motion of Sun across the sky, the start and end of which we call as day and night. So in conclusion the Sun doesn’t rise and set, it is an illusion created by motion of Earth.”
To this all of the class agrees. This is what they have learned in the text-book, and mind you the text-book represents truth and only truth, nothing else. It is there to dispel your doubts and misconceptions and is made by a committee of experts who are highly knowledgeable about these things. Now let us continue this line of reasoning and ask them the next question in this series.

Does the Moon rise? If so, does it rise everyday?

The responses to this question are mixed. Most of them would say that it does not rise, it is always there, up in the sky. Some would gather courage and say that it does rise.

Does the Moon set?

Again to this the response is mixed, and mostly negative. Most of them are adamant about the ever presence of the moon in the sky. The next question really upsets them

Do the stars rise and set?

Now this question definitely gets a negative response from almost all of them. Even the more knowledgeable ones fall. They have read different parts of the story, but have not connected them. They tell you the following: “No the stars do not move, they are there all the time.” They also tell you that there is something called as the fixed stars and this is in the text-book, which cannot be wrong. And when asked:

Why are we not able to see the stars during the day time?

They tell you “Of course you cannot see the stars during the day time. This is because our Sun, which is also a star, is too bright and the other stars too far away and hence are dim. So our Sun’s brightness, overwhelms the other stars, and hence they are not visible during the day time, but they are there nonetheless. In the night time, since the Sun is no longer visible, the stars become visible. Have you never noticed that during the evening twilight the stars become visible one by one, the brighter ones first. Whereas in the morning the brightest are the last ones to disappear.”
Of course, the things said above and the reasoning given sounds good. So much so that the respondents are convinced that they understand how things work, and have an elaborate reasoning mechanism to explain the observed things, in this case the formation of day and night and appearance / disappearance of stars during night and day respectively.
You ask them:

Don’t you think there is a problem with what you have just said?

“Where is the problem?”, they tell you. “We just explained scientifically how things are in heaven.”
Then you open the Pandora’s box,
“Well you have just said that the Sun doesn’t move really, it is the Earth that moves, and hence we see the apparent Sun rise and Sun set.”
Then they say, “Yes, that is the case. The Sun doesn’t move, but the Earth does.”
You ask, “How do you know this? Do you see that the Earth is moving?”
They say, “The textbook tells us so ” Some of the more knowledgeable ones say that “Galileo proved that the Earth moves and not the Sun. Since we are on Earth, we see only apparent motion of the Sun.”
You say: “But wait, just now you said that the Moon does not move, it is always in the sky. Also you said that the stars do not move, they are there all the time. Now if the Earth moves, then all these bodies should also move, if only, apparently.Then the stars must also move, just like the Sun does, do not forget that Sun is a star too! So other stars should also just set and rise like the Sun, and so should also the Moon!”
Or you can argue just the opposite: “I claim that it is the Sun that moves, Earth does not move. Isn’t it a lot more easier to explain this way, why we do see the Sun moving, because it moves. And we anyway do not see Earth moving! How will disprove me?”
Then the grumbles start. They have never thought about this. They knew the facts, but never connected them. This lead to the misconceptions regarding these things. They were right in parts, but never got a chance to connect the dots, metaphorically speaking.The reason for these misconceptions is the faith in the text-books, but if the text-books fail to perform the job of asking them the right question, where the reasoning alone can get rid of many of the misconceptions.
If we choose the alternative question, of challenging them to disprove that the Earth is stationary, almost most of them are unable to answer the question of disproving that the idea that the Sun moves and not Earth. They would suggest that we can see this from the satellite in the sky (Can we really?).
Most of us take the things for granted and never question many (or as in most cases, any) of them. And many times the facts are something we do not question. We say that “It is a fact.” This statement basically posits that the information which we think is out there can be unquestionable. But there are many flavours of the post-modern philosophy which challenge this position. They think that the facts themselves are relative, that is to say that one culture has different science than another one.  But let us leave this, and come back to our problem of the stars and the Sun and Moon.
Lets put out the postulates for the above arguments and try to deduce deductively the results that were obtained.
Claim 1: Sun doesn’t move.
Claim 2: Earth moves.
Observation 1: We see the Sun moving across the sky daily, it rises and it sets.
Explanation 1:  Since the Earth moves, and the Sun is stationary, we see that Sun moves apparently. This apparent motion of the Sun is seen as the Sunrise and the Sunset by us. This is what causes the day and night.
But we can have Observation 1 explained by another set of claims, which is exactly opposite, namely, that the Earth doesn’t move but the Sun moves.
Claim 3: The Sun moves.
Claim 4: The Earth does not move.
Explanation 2: Since the Earth does not move, and the Sun does, we just see the Sun passing by in the sky, around the Earth. This causes day and night.
We see that Explanations 1 and 2 are both valid for Observation 1, if the claims 1 and 2, 3 and 4 are true then the respective deductions from them, in this case the Explanations 1 and 2 respectively are also true.So in this case the logical deduction is correct, provided that the Claims or assumptions are correct. But this process does not tell you whether the claims themselves are true or not. But both set of assumptions, cannot be true at the same time. Either the Earth moves or it does not, it cannot be in a state of both. If at all we had an explanation which came from these assumptions which did not correspond with the observations, but was logically deducible, then we can question the assumptions or premises as philosophers call them.
Of course, the things said above and the reasoning given sounds good. So much so that the respondents are convinced that they
understand how things work, and have an elaborate reasoning mechanism
We can have one example of this type.
Assumption 5: Stars do not move, there are so called “fixed stars”.
Assumption 5: During the day time the Sun is too bright, as compared to the other stars.
Now in this case combining Assumption 5 (A5) with Observation 1 (Ob1) we would get the following:
Explanation 3: The stars are too dim as compared to Sun, hence we cannot see them during the day time, but they are present. Hence they do not move.
In Explanation 3 (E3) above the deduction has a problem. The deduction does not follow from the assumption. This is the other problem in which we talked about above.
Most of the people who would suggest these responses have mostly no background in astronomy. Even then the basic facts that Earth goes round the Sun and not the other way round are forced upon them, without any critical emphasis on why it is so. Neither are they presented at point with the cognitive struggle of another view point, namely the geo-centric view. So presenting the learners with opportunities that will make them observe things and make sense of the explanations in light of the assumptions that were made, will enhance the reasoning and help them to overcome some of their misconceptions.
But there is another observation which can be made of the skies. And it can be either done in the classroom with the aid of Free Softwares like Stellarium. After the round of above questions, we usually show the class the rising of the stars from the east. In a darkened room with a projector the effect is quite dramatic for those who have not witnessed such a thing before. So you can show the class, just as the Sun rises, all other celestial bodies like the Moon and the stars also must rise and this is an observed fact.
Observation 2: The stars and planets and the Moon also rise and set everyday.
So how do we make sense of this observation, Ob2 in the light of the assumptions that we have.
Assumption 6: Sun is a star.
Explanation 4: We observe that Sun moves during the day, from East to West. Sun is a star, hence all other stars should also move.
Now why this should be the case will be different for the geo-centric and the helio-centric theories. In case of H-C theory the explantion is simple. The Earth moves hence the stars appear to move in the opposite direction. And this applies to all the objects in the sky.
Since the Earth moves all other celestial objects will appear to move. In case of G-C theory we have to make an assumption that the
stars are “fixed” on some imaginary sphere, and the sphere as a whole rotates.
But coming back to the misconceptions, it is just the ad-hoc belief that the stars do not move (“fixed stars”) in conjunctions with another observation that in presence of too bright objects dim objects cannot be seen leads to belief that the stars are immobile and do not rise and set as the Sun does. There is another disconnection from another fact that they know, or are told in the textbooks, that  the apparent movement of the Sun is caused by the actual movement of  the Earth. There is no connection between these two facts which is  made explicit.
We think that providing opportunities for direct observation aided by software, Stellarium in this case, which help in visualizing the movements of celestial bodies will help in developing the skill of reasoning and explaining an observed phenomena.

The Mitr

We are stardust…

The amazing thing is that every atom in your body came from a star that exploded. And, the atoms in your left hand probably came from a different star than your right hand. It really is the most poetic thing I know about physics: You are all stardust. You couldn’t be here if stars hadn’t exploded, because the elements – the carbon, nitrogen, oxygen, iron, all the things that matter for evolution – weren’t created at the beginning of time. They were created in the nuclear furnaces of stars, and the only way they could get into your body is if those stars were kind enough to explode. So, forget Jesus. The stars died so that you could be here today.

via Lawrence M. Krauss – Wikiquote.