Assignment 3

Please watch https://www.youtube.com/watch?v=7n3RWAIlzAI , especially the story about the great astronomical achievement of Isaac Newton, after 35:30. Newton was able to prove mathematically that Kepler's laws (emirical laws of nature) follow (in fact, are equivalent to) the universal gravitational force which falls with the quare of the distance between any two bodies.

(i) Why was that a breakthrough?

The motion of objects in the night sky was an intriguing and dynamic topic in the ancient era. It had been strongly debated by various scientists, some who claimed the objects to be revolving around the Earth at the centre of the then perceivable universe, while others like Copernicus, Kepler believed that the Sun was at the centre and that the Earth and other planets revolved around the Sun. The hitch in both of those views was that, there were no conclusive theoretical proof as to why one of the was true over the other. Though both were of different complexity, they could explain the motion about equally well by various men like Aristotle, Ptolemy, Copernicus, Kepler, Galileo, etc. Finally, Newton's work of Philosophiae Naturalis Principia Mathematica was published on July 5, 1687 [1] contained the universal law of gravity which could elegantly explain the motion of not only planets around the Sun, but also that of the satellites around planets and the objects on Earth. This theory basically explained the precise empirical results of elliptical motion of planetary objects in the sky that Kepler had formulated using Tycho Brahe's precise data. This was a huge breakthrough for Science because it revolutionised the beliefs and way of the reasoning, research starting the modern era of scientific works. 

[2] Figure 1: Title page of Newton's Philosophiae Naturalis Principia Mathematica

(ii) Study, using any materials you like, the history of that discovery. It started much earlier than the date of Halley's visit to Cambridge, shown in the documentary. There are parts not covered by the documentary, like the role of Newton's arch-enemy Robert Hooke. In the opinion of some historians, especially recently, that Hooke made important contributions, but dispised by Newton was never properly acknowledged. Describe your findings about Newton, Hooke, Halley and Wren's discussions about astronomy, who they were, where the discussions took place, and so forth.

Edmond Halley was born in 8 November 1656 in London, England [3], who's name is designated to Halley's comet was a great observer who made important measurements such as occultation of Mars by the moon and of course predicted the orbits of comets. He was very curious in the problem of an "invisible" attraction between planets in the night sky. He suggested that this force decreased proportionally to the inverse square of the distance between the Sun and the planets and also suggested that they should follow elliptical orbits, like Kepler had described! But he did not have a theoretical explanation to back his suggestions. At that time, Robert Hooke, well known for his Hooke's law describing oscillatory motions of objects attached to certain springs was born in 28 July 1635 in Freshwater, Isle of Wight, England [4]  had assured Halley that his suggestions could explain all the celestial motions [5]. This was backed also by Christopher Wren, the architect of the new St. Paul's Cathedral in London. 

[6] Figure 2: Edmond Halley enquiring Newton about a theory to explain the celestial motion

Halley, on a quest to find a theoretical explanation to the observed celestial motions when Robert Hooke had told Halley that he already had formulated that theory and that he would keep it a secret until a suitable time.  Halley, however was not satisfied with Hooke's responses and so decided to seek Newton who was at Trinity college [5] to find out if he had any idea of a theory that could explain the celestial motions. This was a revolutionary moment in the birth of classical mechanics and modern scientific era.  

Hooke was a competitor to Newton, they feud over various scientific matters. This could have been an important reason in what could have stimulated Newton to finally share his great work on the law of universal gravitation when Halley visited him 

(iii) Briefly, what was the issue between Newton and Gottfried Wilhelm Leibniz? How did this become the reason for a rift between the British and Continental science? (You may want to watch one of the youtube documentaries about Leibniz.) What are your thoughts about the issue of importance of the first realization (first discovery) vs. full formulation of a theory? If two persons claim those two contributions, who's more worthy of paraise and a place in history of science. In another situation: who's the real discoverer: a person who first made a discovery but kept it secret, or the one who made it later and announced it first?

The idea of "infinitely small" was introduced in calculus from which a new branch of mathematics was born which would later be the basis for so many practical applications. Grottfried Wilhelm Leibniz was a German mathematician [7] born in 14 November 1716. The interesting controversy with the invention of calculus is still alive among historians, some of who claim that it was Leibniz who founded calculus before Newton, reasoning with Leibniz's notations that he started working on calculus earlier than Newton. Some other historians believe it was Newton who formulated calculus. In their times, this rift between Newton's and Leibniz's claim over calculus broke into full force in 1711[8].  This was a fuel to the political fire between the Mediterranean continent and the British. 

In terms of the importance of first discovery vs full formulation of a theory, I feel that the person who formulated the full theory should deserve more importance as it would contain a lot more physics and concepts. Also, in the view of science, the importance lies with concepts and the formulation of the theory and hence the formulation of theory should be more worthy of praise. 

[9] Figure 3: A picture of Newton (on the left) and Leibniz (on the right)

In terms of the real discoverer, I feel that the person who made the discovery should deserve more importance though they kept it secret because it is the thinking that matters and just because someone happened to share it before them shouldn't really be of much importance from a science point of view.

References:

[1] http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation

[2] http://www.library.usyd.edu.au/libraries/rare/modernity/images/newton5-1.jpg

[3] http://www.space.com/24682-edmond-halley-biography.html

[4] http://en.wikipedia.org/wiki/Robert_Hooke

[5] http://www.pbs.org/wgbh/nova/newton/principia.html

[6] http://www.lookandlearn.com/blog/1564/birth-of-edmond-halley/

[7] http://en.wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz

[8] http://en.wikipedia.org/wiki/Leibniz%E2%80%93Newton_calculus_controversy

[9] http://deskarati.com/2011/03/10/leibniz-and-newton-calculus-controversy/

Assignment 2

(i) the Earth is spinnig around its axis every day, while the immense distant world of stars is motionless

Nicolaus Copernicus was one of the greatest astronomer of his historic period. He had given quite a lot of proofs correcting the beliefs people had in his period. Most of these proofs have been recorded on his book, De Revolutionibus. This short paper summaries the proofs of some of the theories which helped the people get the correct perspective of the solar system. 

One of the proof he produced was for the Earth spinning around its axis everyday. Most of the ancient astronomers believed in the Earth being stationary and at the centre of the known "universe". Ptolemy argued that the things that were not attached to the Earth would all appear to move to the west. This was the commonly accepted belief. But Copernicus responded that all falling bodies that were made of Earth shared a rotational component with the Earth and a radial component velocity towards the centre of the Earth.  This is shown in Figure 1. Below is a quote of Copernicus giving a logical reasoning based on the motion of ships floating on an ocean.

Figure 1: Rotational and radial component

[1]"For when a ship is floating calmly along, the sailors see its motion mirrored in everything outside, while on the other hand they suppose that they are stationary, together with everything on board. In the same way, the motion of the earth can unquestionably produce the impression that the entire universe is rotating."


(ii) the Earth is a planet orbiting the Sun once a year like the other planets, so it is not in the center of the universe

Similar to the belief about the rotationless Earth, Ptolemy argued that since only half of the stars on the sky at any given time, the Earth had to be in the centre. But Copernicus debated that it is because of the distance between the centre of our solar system and the Earth is small that it doesn't produce any noticeable effects. Copernicus also opened up the possibilities of Earth being just another normal rocky body in our solar system which was a huge shift in the position of Earth in our Universe that people had in mind. 

[2]Copernicus argued that the Earth moved as a whole in a circular orbit around the centre of the solar system because of the observed retrograde motion of planets like Mars which could not be so accurately and elegantly explained by other models. He also used the reasoning that parallax could not be applied to all observed bodies in our solar system which suggested that perhaps Earth is not the centre of the solar system and that it orbits the Sun 360 degrees in one year (by definition) similar to other planets. 

(iii) the Sun does not orbit around the Earth, but remains motionless in the center of the planetary system.

Figure 2: This is a script of Copernicus portraying the centre Sun solar system

Copernicus came up with a unique and very interesting proof of how the difference in the brightness of Mars cannot match the observations if we were in a Geo-centric system and that the observations of the difference in the brightness of Mars can be explained with a Helio-centric system.  The Figure 2 shows the Helio-centric model which Copernicus used to explain the observations which is a revolutionary proof for the Helio-centrism of the solar system.

This proof is not only accurate, but also elegant and convincing to say that helio-centrism is perhaps what our solar system is. In the sixth century BC, Pythogoras had suggested this idea of helio-centric solar system and few centuries later, Aristarchus also backed this idea of the Sun being motionless at the centre of our planetary system. [3]





I consider the third proof the most important. This is because, firstly it is beautifully elegant and precise. It is simple to understand and hence easy for scientists to agree with. I also consider it important because it is a revolutionary piece of work which helped in the change of the mindset of people from thinking that Earth was the special body in space and that everything else acted around Earth to the actual reality of Earth being a rocky body revolving around the Sun. I feel it is a point where scientific arguments were encouraged and this work is a perfect example of such a reasoning. It is also an example of the Occam's Razor principle where a theory which is elegant and simple to understand is much better than a theory with complicated arguments. [4]



References:

[1] Nicholas Copernicus, On the Revolutions of the Heavenly Spheres, Johns Hopkins University Press, 1992.
[2] http://www.geocentricity.com/conference/Frank/epicycle_conference_bible_2_final.pdf

[3] Andrew Dickson White, A History of the Warfare of Science with Theology in Christendom,  D.Appleton and Company, 1896. 

[4] Steven Dutch, 21st Century Geocentrism, Natural and Applied Sciences, University of Wisconsin - Green Bay