Thursday, 12 February 2015

Assignment 3



Assignment 3: Universal gravitation. Discovery disputes.


(i) Why was that a breakthrough?
Newton proving mathematically that Kepler’s laws follow the universal gravitational force was a breakthrough. Many scientists before him believed that the forces between the Earth and the Moon were independent from the external forces observed in space. Newton unified the forces and stated that this invisible force observed throughout the universe as the universal law of gravitation. He came to this conclusion though his thought experiment. This experiment consisted of firing a cannon ball from a high point on earth in a straight line. He was aware that the cannon ball would move in a straight line and that the cannon ball would also fall down towards earth due to gravity. He then thought of firing the cannon at high speeds will make the cannon ball be balanced between going in a straight line and falling hence orbiting earth, like the moon. This breakthrough unified the gravitational force observed on Earth and in the universe.

(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.

Robert Hooke, famous for Hooke’s law, had contributed a great amount towards astronomy. He claimed that he had come up with key theories regarding gravity before Newton and that he should be credited for them. Robert Hooke had sent Newton letters that included his hypothesis of the inverse square force and its relation to the orbit of the planets around the sun, and how further planets revolved at a slower rate. Newton replied stating he hadn’t heard of such a theory and was intrigued, so Newton focused on proving it mathematically and was successful. However Newton did not share his progress of proofing the inverse square law to Robert Hooke, since he viewed him as a rival.
Edmund Halley, an astronomer famous for predicting the orbit of a comet, had met with both Robert Hooke and Christopher Wren at a coffee shop to discuss theories regarding astronomy. These three individuals were all interested in the inverse square law of attraction. At the meeting they discussed if the inverse square law was the result of the elliptical orbits. At this point Christopher Wren offered a prize to the mathematician who would proof this theory. This resulted in Edmund Halley to approach Newton regarding the topic of inverse square law. There Newton showed his proof of inverse square law. Halley’s questions was what lead Newton to the idea of universal gravitation. Halley then insisted that Newton publish his work. Newton had eventually published his work in the book The Principia. Newton states that Hooke’s letters resulted in his motivation to study orbits however he denies that it had anything to do with universal gravitation. Newton viewed these individuals as rivals because they all independently suggested the inverse square law.

(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 praise 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?

Gottfried Wilhelm Leibniz, was a mathematician in Germany who is viewed a one of the fathers of calculus. However Isaac Newton, known to be inventor of calculus, had claimed that his ideas were stolen by Leibniz. This accusation resulted in a rivalry between the two individuals.  The issue between Newton and Leibniz was they both believed that they alone were the inventors of calculus. Newton had claimed that he had discovered theories for calculus before Leibniz however Newton was reluctant to publish his findings. Leibniz published his findings in 1684 while Newton published his in 1687. In this case Leibniz had published his findings first while Newton claimed to have discovered his theory ahead of time but did not publish his work. I believe that both Newton and Leibniz should be credited for discovering the principles of calculus. However I believe that it is important to publish any new discoveries or theories in advance, since it is crucial for the scientific community to discuss their findings publicly. In the end the individual who publishes their findings first should be praised for their work rather than the individual that finds a discovery but doesn’t share it.


Sources
http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html
http://www.space.com/24682-edmond-halley-biography.html
http://www.pbs.org/wgbh/nova/newton/principia.html
https://thonyc.wordpress.com/2011/09/28/the-man-who-inverted-and-squared-gravity/
http://www.britannica.com/EBchecked/topic/335266/Gottfried-Wilhelm-Leibniz
http://upload.wikimedia.org/wikipedia/commons/4/41/NewtonsPrincipia.jpg
https://www.learner.org/courses/physics/visual/img_lrg/figure6.jpg
http://upload.wikimedia.org/wikipedia/commons/5/50/Sir_Isaac_Newton_by_Sir_Godfrey_Kneller,_Bt.jpg

Tuesday, 20 January 2015

Assignment 1



Eratosthenes expertized in various professions such as mathematics, geography, poetry, astronomy, and music theory. He is predominantly known for his contribution to the study of astronomy as he is the first individual to calculate the circumference of the Earth accurately. In addition, he was the first astronomer that calculated the tilt of the Earth’s axis. Adding to his contribution to the study of Astronomy, he had also calculated the distance from the Earth to the Sun and introduced the concept of leap day. Furthermore with his understanding of geography during his era, he was able to form the first map of the world with parallels and meridians. 

Apart from astronomy, he had invented scientific chronology by organizing events after the siege of Troy. Eratosthenes had contributed to mathematics as well, particularly to the study of number theory. He presented a technique to pinpoint prime numbers called the sieve of Eratosthenes. Throughout his life, Eratosthenes has contributed valuable information to science.

Eratosthenes calculated the circumference of the Earth by measuring the altitude of the sun at Alexandria during noon. Using the known fact that on June 21st at Syene the sun is directly overhead. The zenith distance at Syene was 0 degrees while at Alexandria it was 7 degrees. In addition to this Eratosthenes was aware of the distance between Alexandria and Syene, hence he used geometry and the zenith to calculate the circumference of the Earth. 



Eratosthenes was able to approximate the circumference of the Earth to a percent error of 16.3% from what the current measurements is today. He calculated the size of the Earth to be approximately 46,620 km.

I believe it was a success due to the incredible accuracy considering the time Eratosthenes calculated the circumference of the earth. Despite the lack of accurate tools and measurements he was able to approximate the circumference with a high degree of accuracy. In addition he was the first astronomer to calculate the Earth’s circumference with much accuracy. By using the method of calculation that Eratosthenes used alongside with the data available today, the result would be 40,074 km which has a remarkable precision of 0.16%. 

Sources:
http://www.britannica.com/EBchecked/topic/191064/Eratosthenes-of-Cyrene
http://www.math.wichita.edu/history/men/eratosthenes.html