Tuesday, 10 February 2015

Assignement 3: Universal gravitation & Discovery Disputes

Newton’s Work and the Breakthrough (Based on the youtube link)




Newton owned more than 30 bibles where he connected religion to astronomy, and he re-dated ancient history drawing up elaborate charts and chronologies that show symbolizations dated back to 1980BC.   Newton coned the bible for keys to the future, of when the end will come (when Christ will return), and he predicted it would be the year 2060.  Edmond Halley is what triggered a question about planetary orbits, which changed science forever.   Through years, scientists discovered that planets move around the sun in slightly elongated elliptical orbits, but they could not prove why that is the case.  Halley and other scientists had begun to suspect that some kind of force is what caused the planets to be attracted to the sun, however the force grew weaker with distance.  This mathematical relation was formulated as the inverse square law.  The inverse square law states that if the planet is twice as far form the sun, the gravitational attraction it feels is 4x weaker, however no one was able to prove that this was the cause for the elliptical orbits.  Several months later, Newton sent Halley proof stating that a planet obeying the inverse square law of gravity must travel in an elliptical orbit, and he used calculus to arrive to this conclusion, but Newton wanted more than mathematical proof so he did not publish it just yet.  So he worked on a further explanation for 18 months.  He finally submitted a 500-page book of his masterpiece named Naturais Principia Mathematica.  Newton believed that the same laws that governed motion on earth is also applicable in the heavens, so he wrote a book called the Axioms (Laws of Motion), which included his three laws of motion.  His first law states that an object in motion would remain in motion forever unless acted on upon an external force.  His second law of motion states that an object rate of acceleration is proportional to the force exerted on it, and lastly his third law of motion states that for every action there is an equal and opposite reaction.   To show how gravity works on earth and the skies, Newton developed a thought experiment. 
 
This diagram illustrates Newton's breakthrough in Astronomy 

Newton’s breakthrough was to see that the moon’s orbit around the earth and the same law of gravity governed the cannonball’s motion on earth.  Cannonballs falling from the earth and the moon falling on the earth follow the same law of physics, which is gravity.  If gravity governed motion on the earth and it’s moon, why not be the same motion for Jupiter and it’s moons, and the entire solar system for that matter of fact.  Newton finally proclaimed that this invisible force operates all around the universe, which is called the universal law of gravitation. 
References used for Newton:



https://www.youtube.com/watch?v=7n3RWAIlzAI

https://pegsandtails.files.wordpress.com/2013/03/enoch_seeman__sir_isaac_newton_01a.jpg
Robert Hooke (1635-1703)




Hook specialized his work in various fields such as astronomy, chemistry, biology, and geology to even architecture.  He is popularly known for inventing the universal joint, iris diaphragm along with an early prototype of the respirator which invented an anchor escapement and the balance spring (which made more accurate clocks possible).  He also worked out the correct theory of combustion by devising an equation describing the elasticity that is still currently used today as the “Hooke’s Law”.  He assisted Robert Boyle in conducting the study in the physics of gases.  He was referred to as the “virtuos” since he was able to contribute findings of the importance regarding various fields in science as a whole.  He was also the one who discovered the term “plant cells”, along with examining fossils with a microscope.

References used for Hooke:

http://www.ucmp.berkeley.edu/history/hooke.html

Edmond Halley


Halley is a well-known astronomer and mathematician who was the first individual to calculate the orbit of a comet (which was then later named after him).  Halley was determined to compile an accurate catalog of the southern stars in the Southern Hemisphere.  After a long struggle, he had finally recorded the celestial longitudes and latitudes of 341 stars along with observing a transit of Mercury across the Sun’s disk, alongside making numerous mendulum observations as well in January 1678.  Halley was the first to publish a star catalog in which contained telescopic determination of locations within the Southern stars, whch was a huge milestone in identifying himself as a solid astronomer.  He was elected as a fellow of the Royal Society in 1678, and was granted the M.A degree by the University of Oxford.

References used for Halley:
http://www.britannica.com/EBchecked/topic/252812/Edmond-Halley

http://www.staff.science.uu.nl/~gent0113/astrology/images/edmond_halley_1687.jpg

Christopher Wren


Christopher Wren was a well known astronomer and architecture.  He first started off with a passion for mathematics and astronomy and became a professor of Astronomy at Gresham College in London.  He was one of the first members to make the well-proclaimed Royal Society for astronomers.  After significant amount of years in scientific research, he became Savilian Professor of Astronomy at Oxford in 1661.  Physics and mathematics is the foundation of determining his passion for architecture.  He is arguably the best-known architect of St. Paul’s Cathedral along with other prominent London churches.

References used for Halley:

http://www.rmg.co.uk/explore/astronomy-and-time/astronomy-facts/history/christopher-wren-architect-and-astronomer

http://ad009cdnb.archdaily.net/wp-content/uploads/2014/10/54446aa7c07a80762d0004ac_spotlight-sir-christopher-wren_via_history_of_surgery.jpg

Newton vs. Leibniz: The Calculus Controversy



Both Newton and Leibniz were recognized figures in the contribution to the work of calculus.  However there is a controversy on the debate of who really does get the true recognition for calculus.  Newton was the author of Principia (1687) as well as a host of equally esteemed published works, however he went much further in exploring the applications of calculus compared to Leibniz.  It is important to note that Leibniz and Newton both had very different views of calculus. Newton’s theory was based on limits and concrete reality, while Leibniz’s theory focused more on the infinite and the abstract.  Leibniz has published the first account of differential calculus in 1684 and then published the explanation of integral calculus in 1686 (Boyer, 1968), but Newton did not officially publish his findings until 1687.  However, there is evidence in which shows that Newton discovered his theories of fluxional calculus in 1665 and 1666, along with the fact that Newton was also the first to establish the general method called the "theory of fluxions".  He was the first to state the fundamental theorem of calculus, along with being the first to explore applications of both integration and differentiation in a single work (Struik, 1948). 
Therefore, it is clearly notable that Newton deserves the recognition and the title of the discovery of calculus.
References used for Newton/Leibniz:
http://www.angelfire.com/md/byme/mathsample.html


http://tikalon.com/blog/2012/Leibniz_Newton.jpg