Tuesday, February 10, 2015

Universal Gravitation - Discovery Disputes

Sir Issac Newton was a mathematician and physicist who studied at Cambridge University. He was and still is the most intelligent being of our time for he discovered the basis of all knowledge today. Not only was he the first to use calculus, he also published a book based on light and optics. However, his most important discovery was based on gravity, a force that attracts a body towards any other physical body having mass.

Philosophiae Naturalis Prinipia Mathematicia,
Mathematical Principles of Natural Philosophy
     Of his numerous phenomenal achievements, Newton's astronomical achievement lead to answers of questions that have been asked for years. Issac Newton mathematically proved that empirical laws of nature follow and are equivalent to the universal gravitational force. When questioned about planetary orbits Newton showed mathematical proof using calculus that the planets did not orbit the sun in perfect circles, but rather in elliptical orbits. He also stated that the planet obeys the inverse square law of gravity and so must travel in an elliptical orbit. The inverse square law says that if a planet is twice as far from the sun, the gravitational attraction is four times weaker.
After publishing his book "Mathematical Principles of Natural Philosophy", people realized Newton was discussing a new framework for understanding the universe. He built on many scientists work prior to him such as Galileo. Galileo suggested that objects on
Thought Experiment - Canon ball shot
from top of mountain and demonstrates
elliptical orbits.
Earth and celestial objects' motion were completely different and so required different methods. However, Newton disagreed and stated that the same laws governed motion on Earth and the heavens. This led him to create three laws of motion that would be true anywhere (on Earth and outer space). These laws have strongly impacted our understanding of objects and their motion that they are widely used today and without them many discoveries may have not been made. However, in order to explain how the planets orbited around the sun, Newton used the thought experiment. This experiment involved him imagining a canon ball being fired both strongly and weakly. He concluded that since all objects move in a linear motion and that gravitational forces have an effect, if the canon ball is fired strong enough it will continue in an orbit just like that of the moon. This breakthrough led to the idea that gravitational forces are a result the elliptical orbits and the motion of the planets.

Inverse Square Law 
     Robert Hooke is widely known for being Newton's arch enemy. This is because Hooke believed that he had a huge role in Newton's discovery of gravitational forces and the planets orbits around the sun, and feels as if he did not receive the credit he deserved. By 1670 Hooke believed that the Sun and planets were attracted to each other an
d the attraction increased as the two got closer. He also believed that the inverse square law would be linked with the celestial bodies and gravitational attraction. He was also the first scientists to really argue that gravity is a universal force. Edmond Halley and Sir Christopher Wren were also scientists who concluded that the inverse square law determined the attraction between two celestial bodies. However, no one had mathematical evidence to explain the inverse square law. Determined to find a way to figure out the mathematical evidence Wren, Halley and Hooke met at a coffee shop in London. Wren explained that he would offer a reward to whomever could find this mathematical evidence within the next 2 months. Hooke said he had mathematical evidence but could not find it and so Halley took it upon himself to find the evidence. He then went to Newton who appeared with the evidence a few months later. After publishing his work, Newton did not credit Hooke for having any insight on the inverse law and so there was a huge dispute. However, Newton believed that Hooke`s work was almost negligible and did not further his work as much as Hooke believed it did.

     Newton stated that he developed the theory of calculus in the early 17th century but decided not to publish it until 1693. Leibniz on the other hand was more than happy to publish his work in 1684. So the problem here was that both scientists claimed to have independently arrived at the theory of calculus, and so it was a dilemma to decide who to credit. Eventually the Royal Society gave credit to Newton as first discovery and Leibniz as first publication. However, later on due to a very biased outlook, the Royal Society accused Leibniz of plagiarism. This dispute between the two scientists eventually brought a rift between British and Continental science because Newton was English whereas Leibniz was from German, resulting in two different sides for the public to take.
 I personally believe that the person who published the theory first should be credited. This is because anyone can state that they developed a theory without publication - publication is the only evidence that shows that if someone has actually developed an original idea.

References
https://www.newton.ac.uk/about/isaac-newton/life
http://www.pbs.org/wgbh/nova/newton/principia.html
http://www.uiowa.edu/~c22m025c/history.html

All pictures are from public domain.




Tuesday, February 3, 2015

Assignment 2: The Copernican Revolution


1473-1543 CE
Nicolaus Copernicus was not only a mathematician but also an astronomer. Although he graduated from university with a mathematics degree, he spent his life as a priest at a roman catholic church (Artymowicz, 2015). During his time, it was the Ptolemaic Model that astronomy was based on; the Earth was the center of the universe. Overtime, Copernicus became interested in astronomy due to his colleague and soon found himself exploring the universe's boundaries on his free time (Artymowicz, 2015). After reading many books on astronomy, Copernicus began to develop a celestial model of his own. However, he was skeptical about publishing his ideas at first because of the academia professors who would've rejected him (Artymowicz, 2015). Copernicus introduced numerous concepts and wanted to demonstrate his ideas using reasoning and evidence. He proves that (1) the Earth spins on it's axis and the stars in the distant remain motionless, (2) Earth being a planet orbits the Sun just like the other planets and therefore it is not located in the centre of the universe, and finally (3) the Sun does not orbit the Earth, but instead stays motionless in the centre of the solar system (Artymowicz, 2015).

Heliocentric Theory

  Among his famous theories was the theory of the heliocentric solar system. Copernicus' belief that uniform motion should only be performed by the planets led him to reject the Ptolemaic Model and insisted in the heliocentric model (Fitzpatrick, 2010). This theory was speculated and debated upon among other scientists before Copernicus. In order to prove this model, he observed that both Venus and Mercury were always in close approximation to the sun; they are never in opposition to the Sun (Fitzpatrick, 2010). Therefore, he claimed that both Venus and Mercury are closer to the Sun than the Earth is (Fitzpatrick, 2010). He concluded by stating that the Sun must be the center of the universe since it's the center of this motion (Fitzpatrick, 2010).
   
     Additionally, he observed retrograde motion which is the notion that the planet seemed to move in an opposite direction relative to other solar system bodies (Fitzpatrick, 2010). Copernicus explained that this was due to the fact that the Earth was moving faster along its orbit than the other planets were, and so from time to time it overtakes and passes the other planets (Maher,2009). This explained why the planet apparently moved in the opposite direction of the other bodies in the system. He also stated that the different planets were at different distances away from the sun due to the brightness at conjunctions and oppositions (Maher,2009).

     Another discovery he made that contributed to his model was that he claimed the Earth rotated on its own axis and his proof for this was based on his own observations (Maher,2009). He stated that the changes that one observes from the Earth are either due to movement of the observer or the object being observed (Maher,2009). Concluding that the observed changes were due to the Earth (object being observed), he also said that everything outside of the Earth contained an endless amount of substance and that these substances all moving along the same direction was impossible (Fitzpatrick, 2010). Another observation he made was that the Sun and the Moon both rise in the east and set in the west (Fitzpatrick, 2010). This showed a uniform movement of objects in the sky stating that the Earth was moving on its own axis.
     Finally, Copernicus stated that the Sun was motionless and in the center of the universe due to symmetry. The Sun which was located at the center of the universe created symmetry among the motion of the planets (Fitzpatrick, 2010). It made sense that the largest body the Sun, occupied motionless central space of the solar system, which also determined the periods of the planets relative to the sun.
     Even though Copernicus was fully credited for the heliocentric theory, Aristarchus as well as Pythagoras were the first to describe the Sun as being the center of the solar system, not the Earth (Maher, 2009). However, Copernicus was the first to create such a detailed model with justifications.

Scientists Before Copernicus
    Even though Copernicus created the Heliocentric model of the solar system, his ideas for this creation were based on astronomers of the past (Aristarchus, Heracleides, and Pythagoras). Pythagoras had stated that the Earth and Sun, along with other planets orbited a central structure called the "Central Fire" (Maher, 2009). He stated that the Earth would rotate around this central fire once every day. Through his observations he realized that the Sun and moon (stars) would rise and set throughout the day and therefore came up with the assumption that the Earth rotated on it's axis. Heracleides also believed that the Earth rotated on it's axis but thought that this occurred every twenty four house from a specific direction (west to east) (Fitzpatrick, 2010). Aristarchus on the other hand was the first to depict a model of the solar system where the Sun was in the centre and not the Earth, also stating that the Earth was in motion, orbiting around the Sun (Maher, 2009).

     The most important discovery made by Copernicus was that the Sun and not the Earth was the center of the solar system. This changed everything because it was widely accepted that the Earth was the center of the solar system. Using this, different observations were made about not only the Earth, but the other planets as well. This led to new discoveries about how the Earth differed from the other planets and what caused it to be unique and similar compared to them.




References

Artymowicz, P. (2015). The Origins of Modern Astronomy: The Copernican Revolution. Retrieved from http://planets.utsc.utoronto.ca/~pawel/ASTB03

Fitzpatrick,R. Copernicus's Model of the Solar System. (2010). Retrieved from http://farside.ph.utexas.edu/Books/Syntaxis/Almagest/node4.html

Maher,P. (2009). Copernicus on the Earth's Orbit Around the Sun. Retrieved from http://patrick.maher1.net/317/cope1.html

All pictures are from public domain.