Assignment 6 - Modern Astronomy

The Hubble Space Telescope - above atmosphere 

      All astronomers have had and still have a single goal in mind - that is to see the entire universe at its deepest. However, in the past technology was an issue and the astronomers were very limited in what they can actually see. After many technological advances the Hubble Space Telescope was finally launched in 1990. It is known as one of the greatest advances in humanity to this day. This is no ordinary ground-telescope, for the Hubble orbits the Earth in outer space. Its ability to give a view of the universe is remarkable due to its position in the atmosphere - blocking and distorting the light headed directly below towards Earth. It was created by NASA (National Aeronautics and Space Administration) and enabled to unlock the greatest mysteries of astronomy.

Phase of Design

The Hubble Space Telescope with the it's science instruments.
This diagram also shows the direction light hits the telescope
and its pathway. 

     It was only due to Hubble's discoveries that changed the light of modern astronomy and how the world viewed the universe. Hubble allowed us to winnow down the numerous theories that have been proposed due to speculation, while also proposing new theories. The Hubble Space Telescope was created two avoid a twofold problem. Firstly, ground telescopes on Earth produce images that are distorted by the air pockets in the Earth's atmosphere. This problem is unavoidable no matter how technologically advanced the ground telescope is. An example of the distorted view from Earth is in the way the stars twinkle when you look up at them from Earth. The second situation is the fact that the atmosphere blocks and absorbs different wavelengths of radiation emitted by celestial objects (UV rays, gamma rays, x-rays). However, the only way to fully understand any object in space is to view all radioactive elements emitted by it. Therefore, one can understand that there is no way to create a ground telescope on Earth that views the wavelengths of celestial objects when the wavelengths of radiation do not even reach Earth in the first place. Hence, NASA came up with an effective solution to avoid the atmospheric distortion - placing a telescope beyond the atmosphere, 552 kilometers away from the surface of the Earth. The mission of the Hubble Space Telescope is "to serve the community of astronomers, journalists, teachers and laypeople with the best possible science communication products, as efficiently as possible, and adapt to our strategies to suit the needs of the target group whenever needed". Although the Hubble Telescope has endless amount of objectives, some of its key ones are to publish and distribute world-class news and photos, rapid response hotline to requests from media, scientists, educators and public.
   
     The way the Hubble Space Telescope works is that every ninety-seven minutes it completes a spin around the Earth - moving at 8 kilometers per second while doing so. This speed is incredibly fast and it was shown to compare it speed by stating that one would be able to travel across United States in ten minutes. While travelling, the Hubble captures light and directs it into the rest of its machinery. Once the light has entered the telescope it hits the primary mirror and reflects off to the secondary mirror. The secondary mirror's task is to essentially focus the light through a hole in the center of the primary mirror, which ultimately leads to the telescopes instruments inside. Each of these instruments are made to view the universe in a different way from each other, and either work together or independently creating clear images. The clarity of the images lies upon two factors; the ability of the telescope to capture light (length of mirror) and the fact that the telescope is placed beyond the atmosphere.

The Launch & Problems

The launch of the Hubble Space Telescope into space with a space shuttle. 

     After many delays, the Hubble was launched on April 24, 1990. The Hubble carried five instruments when it was launched; the Wide Field/Planetary Camera, the Goddard High Resolution Spectrograph, the Faint Object Camera, the Faint Object Spectrograph, and the Highspeed Photometer. However, right after the Hubble was launched, the crew detected some errors with the primary mirror. The telescope was in no doubt providing pictures of the universe, just not to the degree it was expected - the pictures were rather blurry and were not clear as expected. The flaw of the primary mirror was something called "spherical aberration". This means that the primary mirror was the wrong shape which caused the light that reflected off the centre to not focus on the same location as the light that reflected off the edge of the mirror. Regardless of the fact that the differences in location of focus was extremely small, it caused a huge difference in the pictures produced by the Hubble.

The making of the primary mirror which was later
found to be faulty. 

     Fortunately, NASA's scientists were able to quickly find a solution where they would use numerous small mirrors to direct the reflecting light to the correct location, allowing the light to reflect to the telescope's science instruments. These small mirrors were called The Corrective Optics Space Telescope Axial Replacement (COSTAR) and the scientists were required to replace another instrument within the Hubble with this. In order to precisely fix the telescope, the scientists spent almost a year training for the work required to correct the lens. Finally, on December 2, 1993 the crew of seven was ready to go out in space to the Hubble that required five days to repair. In order to repair the Hubble, they removed the High Speed Photometer and replaced it with COSTAR while also replacing the Wide Field/Planetary Camera with a newer version. A newer version was installed because it had small mirrors that would also compensate for the spherical aberration. By the time the crew was all finished with the Hubble it was December 9, 1993 and this allowed NASA to release exceptional high resolution pictures by January 13, 1994. The following years, many astronauts went back to the Hubble for routine check ups and to add new features.

Late Phase

    It all sounds all good - man has created a telescope to observe far beyond what anyone can see from Earth, creating spectacular high resolution images and changing the scientific community. Nevertheless, at one point in the near future the Hubble telescope will eventually degrade to the point where it completely shuts down. However, even when the Hubble stops working it will still continue to orbit the Earth. It will continue to orbit the Earth until the Hubble's orbit also decays and when this occurs the Hubble will come falling towards the Earth. But not to fear, because NASA is still working on a robotics mission to aid in degrading the telescopes orbit and guiding its plunge down to Earth.

The degradation of the Hubble Space Telescope over time. 

Hubble's Great Moments

The change of the brightness of a star due to a planet's orbit. 

     The Hubble Space Telescope had made countless contributions to the astronomic community and will always be looked as one of humanities greatest moments. An example of a breakthrough because of Hubble occurred due to the discovery of extra-solar planets. These planets have been discovered by ground-telescopes by observing tiny wobbles in the motion of a star as a planet pulls at it or by the dimming of light when a planet passes by it's parent star. For this, the Hubble allows us to have a more depth view of these planets blocking light. The periods when the lights are blocked by a planet are called transits. Until this day, Hubble is the first to make observations about planets around stars other then the Sun. Through these observations the Hubble has discovered atmospheres with sodium, carbon and oxygen, as well as a planet with a tail that has hydrogen evaporating. Also, methane was found in an extra-solar planet that was the size of Jupiter - the first organic molecule found on any other planet. Hubble also was able to take a picture of an extra-solar planet that is now known as Fomalhaut b and they were also able to observe a disk of gas and dust surrounding this planet. Afternumerous observations, scientists strongly believe that this star has its own planets.

The Andromeda Galaxy - Milk Way
Galaxy's closest neighbor. 

     The Hubble Space Telescope also assisted in following the galactic histories. It was thought that galaxies in the earlier universe collided, causing the galaxies that we now see to arise - evolving. Our galaxy is called Milky Way Galaxy and the closest galaxy next to is called Andromeda Galaxy. In Andromeda's halo (perimeter region of the galaxy containing stars) the Hubble was able to distinguish individual stars. It is known that halos only develop during the early formations of galaxies and so astronomers predicted that the Andromeda Galaxy's stars would be extremely old. However, when observing from the telescope they were able to tell that the stars were in fact varying in age - some 13 billion years old and other 6 billion years old. The most plausible explanation for this is that Andromeda was created through collisions of various other galaxies, and the Hubble provided substantial evidence for this.
 
      Lastly, another great breakthrough by the Hubble Space Telescope is it's ability to observe the universe's rate of expansion. When trying to study how old the universe really is, astronomers look for Cepheids. Cepheids are a special type of stars that are pulsing and their cycles of intensity show their brightness. Astronomers use Cepheids by comparing how bright they actually are with how faint they appear, and then finally determine the distance of their galaxy. Before the Hubble was created, astronomers have predicted that the universe's age was approximately 20-30 million years old. Hubble was able to observe 31 Cepheid stars and narrowed the age of the universe to approximately 13.7 billion years old (plus or minus 100 million years). The Hubble was able to narrow down the large interval and we are now able to develop a time scale and predict how the universe actually formed.

The view of Cepheid from the Hubble Space Telescope and their variable brightness. 

     The reason why I chose these three specific great moments of the Hubble Space Telescope is because by finding extra-solar planets and their compositions we may be able to see if there is indeed life on other planets as well. Also the Hubble was able to show us that galaxies grow and evolve by colliding into each other, indicating that there is constant change within our universe. Lastly, by being able to understand the birth of cosmology, one is able to measure the rate of expansion of the universe, and ultimately unfold how the universe was made along with its compartments.

References

Historical Milestones of the Hubble Project. (2009). Retrieved from http://www.nasa.gov/mission_pages/hubble/story/timeline.html

ESA. (2014) The Hubble Space Telescope. Retrieved from http://www.spacetelescope.org/about

Space Telescope Science Institute. (2008). Hubble Space Telescope. Retrieved from http://www.stsci.edu/hst
All pictures are from public domain.

Assignment 5: Discoverer of Expanding Universe

Alexander Friedmann's Life 

Alexander Friedmann (1888-1925)

     Alexander Friedmann was born in Saint Petersburg, Russia on June 16 1888. His parents were both involved in the arts community for his father was a ballet dancer and his mother was pianist. Nevertheless Friedmann was a mathematician who studied at Saint Petersburg State University where he had studied for four years. He was known to be an exceptional student throughout both high school as well as university. While in university Friendmann also attended seminars based on modern physics, and soon after completed his master's degree through conducting research based on aeronautics, Earth's magnetic field, mechanics of liquid, and also the theoretical meteorology.

     Over the course of many years, Friedmann was appointed many jobs for his various talents. In 1913 he received a position at the Aerological Observatory, where he was able to study meteorology. For the next several years he took part in several flights in airships to make meteorological observations. However, when the first world war started in 1914, he decided to participate in the Russian air force as a technical expert and a bomber pilot. Friedmann then returned to Saint Petersburg in 1920 when the Red Army took over Perm University where he had been a professor at. Here he took up many positions as a professor and a researcher at various institutes and universities.

Cosmological Works/ Einstein 

Expanding universe 

     In 1920, Friedmann became familiar with Albert Einsteins General Theory of Relativity, and 2 years later he had discovered the expanding universe solution to Einstein's general relativity field equations. Scientists had always viewed the universe as "static" meaning that it had always been the same size in the past and will also be the same size in the future. Einstein adjusted his field equations to match the static model of the universe in 1917 by adding the repulsive force of a cosmological constant to eqaulize the inward pull of gravity. However, five years later Friedmann published extensive solutions to Einstein's equations. The resulted in him arriving at the possibility of a dynamic universe that changes over time. In his paper he had hypothesized that the universe's radius of curvature is either one increasing steadily or increasing as a periodic function of time. His model was focused on a variable type of universe that included the stationary universe case as well. The Friedmann's equation is such that it explains the expansion of the universe. In this equation G represents the gravitational constant, R represents the universe's radius, c is the speed of light, p is the patter density of the universe while lastly k represents the curvature of the universe.

Friedmann equation 

     However, since Einstein had reported in 1917 that the universe contracts instead of the universe expanding, Friedmann was quick to send his findings out. He titled it "On the curvature of Space" and sent his findings to a scientific journal called Zeitschrift fur Physik in 1922. Einstein who was focused on his equations that were well fit to the static universe was not pleased and had given great criticism. However Friedmann wrote back showing an extensive explanation of his calculations. He also requested that Einstein proof read all the calculations and then provide feedback. He also stated that if he were to find errors then his critique will be valid but if he didn't find any errors, he requested Einstein to fix his previous criticism. After looking through his letters and proof reading Friendmann's work, Einstein corrected his previous criticism of Friedmanns work, after realizing that Friedmann indeed was correct.
     In 1928 Lemaitre who was also an exceptional scientist had also discovered that the universe was in fact not static but expanding - he proposed the Big Bang Theory, ultimately stating that the universe had begun as an atom.

The Three Universe Models

The universe models 

     Freidmann's findings ultimately led to the fact that the universe's shape changes according to its own gravitational force. This results in three different models of the universe. The three different models arose from the speed of the initial expansion, and the amount of matter in the beginning universe.
     The first model called "Closed" states that the universe will eventually stop expanding at some time in the future - this means that it will collapse in on itself. The reverse of expansion (collapse) is due to the high density and strong gravitational attraction. This arises from a positive space-time curvature.  Therefore, this model explains that the univere has a limited lifetime even though it may be long, and is also termed "Big Crunch".
     The second model called "Einstein - deSitter" i when the universe is geometrically flat. In this model it shows that the universe continuously expands until there is a slow decline. This is due to a space-time curvature of a negative value and the rate of gravity would ultimately slow down expansion. It is said that we are living in such a universe, and it is termed the "Big Freeze".
     The third model is called "Open" model and instead of its geometry being flat its a hyperbola. This model is known as the "Big Rip" and this type of universe is known to expand infinitely. This is a result of a space-time curvature of zero, which is a result of low density and high rate of expansion - allowing for density to never surpass expansion.
     However due to political issues between the United States and the Soviet Union Friedmann's findings were not accepted until Lemaitre had independently discovered it who was a Belgian astronomer.

George Gamow 

George Gamow (1904 - 1968)

     Friedmann had many students, one of which was George Gamow who was a Russian American nuclear physict. This scientist provided a lot of evidence to support the Big Bang Theory. He met Friedmann while he was attending the Leningrad University. After graduation he seeked out to see if the newly formed quantum theory could also apply to the nucleus of an atom. He developed his own theory in 1928 on radioactivity due to his immense interest for the quantum theory. While Gamow was in Washington he developed the theory of the internal structure of red giant stars. From he developed two scientific theories with his colleague, one being the theory of the so-called Urca process and the other being the theory of the origin of chemical elements by process of successive neutron capture. In 1954 Gamow began his interest in the biological phenomena and published several papers based on information storage and transfer in living cells. Here is where he proposed the genetic code that is now confirmed through laboratory work. His most important work however involved his theory that described the radioactive alpha particles decay of atomic nuclei. He was most known for his popular writings on science that introduced millions of readers to concepts of relativity and atomic and nuclear physics which have been translated into numerous different languages. Due to his incredible scientific writings the UN awarded him the Kalinga Prize in 1956.

References

George Gamow. (2014). Retrieved from http://www.britannica.com/EBchecked/topic/225123/George-Gamow

Mastin, L. Alexander Friedmann. (2009). Retrieved from http://www.phsyicsoftheuniverse.com/scientists_friedmann.html

The Life and Career of George Gamow. (2013). Retrieved from http://www.phys.colorado.edu/public-outreach/distingushed-life-and-career

All pictures are from public domain.

Assignment 4: The Changing Pluto

Pluto and its three moons. 

    Pluto is the furthest from planet Earth and therefore very little is known about this planet's physical characteristics. It is known to have less than 20% of Earth's diameter, consisting of a rocky core that is surrounded by a mantle of water ice. Pluto was previously thought of as the ninth planet of the solar system, as well as being the smallest. Today it is known as a dwarf planet which orbits the Sun just like any other planet, but is much smaller - so small that it cannot clear objects out of it's path. Pluto is nearly 40 times as far from the Sun as the Earth. It orbits the Sun in an oval and therefore sometimes seen as closer to the Sun and other times further - even during its closest point to the Sun, it is billions of miles away. It was also discovered that Pluto is located in a region called the Kuiper Belt. Here there are thousands of small icy objects like Pluto. Pluto also has 3 moons - Charon, Nix, and Hydra; Charon being the largest of the three. The reason that triggered the thinking of Pluto not being an actual planet of the solar system is the discovery of Eris. In 2003, an astronomer thought he had discovered a new planet just beyond Pluto, that was larger than Pluto itself. Therefore, Pluto became a dwarf planet due to its size and location in the solar system.
 

Discovery of Pluto 

Solar system with 9 planets - Pluto included

  It wasn't only until 1930 that Pluto was discovered by an astronomer by the name of Clyde Tombaugh. This was because Pluto was so small that a very powerful telescope would be needed to see it. Clyde Tombaugh was born in 1906 in the United States on a farm. He grew up with a passion in stargazing due to the encouragement of his uncle and father. Tombaugh had been dissatisfied by his telescopes he had purchased and so decided to build one himself. Over his lifetime, he had built more than 30 telescopes. In 1928, he had built a very accurate 23 centimeter reflector which was the telescope that had allowed him to make detailed drawings of both Mars and Jupiter. After creating these drawings, he had submitted them to Lowell Observatory where they subsequently offered him a position as a junior astronomer. Once he accepted the job, he had joined the search for Lowell's Planet X - a planet beyond Neptune which was a big project they were working on. His task consisted of him taking a picture of a small portion of the night sky each day which was then later compared to each other in order to identify a moving point of light that may be a planet.He displayed one image and then blinked the second image to see if any objects had moved from night to night. On February 18th 1930 Tombaugh saw an object moving at a certain speed which was then named Pluto by a young school girl. After viewing 65% of the sky along with monthly observations, he discovered an object which was then later named as Pluto. Even after the discovery, Tombaugh went back to school at University of Kansas and obtained his masters in astronomy. However, while doing so he would go back to the observatory every summer to continue on his work. Tombaugh also had immense insight in Mars for he described the surface of Mars - full or craters. He had also taught at two universities.

Pluto - Dwarf Planet 

Pluto's orbital inteference with Neptune, along with Eris'
orbit. 

     In August 2006, Pluto was demoted to a dwarf planet due to its relevant size to the other planets. It was then realized that Pluto was neither a Terrestrial planet or a Jovian planet and so people wondered how to classify objects such as Pluto - it was just a large icy body orbiting the Sun. The first essential change to how we view Pluto started with the findings of the first Trans-Neptunian object. These Trans-Neptunian objects have an orbit that is beyond that of Neptune. In 2003, scientists at Palomar Observatory used a telescope to observe the night sky, where they had discovered what is now known as a dwarf planet called Eris. Even though it was larger than Pluto, it had a moon orbiting around it just like Pluto itself. It was also considered a planet - the tenth planet. However, the Astronomical Union changed their definition of a planet and Eris had become a dwarf planet. This caused massive speculation about Pluto's status as a planet. Therefore, in 2006 a vote was held to decide whether Pluto was a planet or a dwarf planet. Regardless of the small voting percentage (3% for planet and 4% for dwarf planet), it was decided that Pluto was too a dwarf planet. This led the organization to set parameters to allow astronomers to identify planets from other celestial objects. According to the union, a planet requires and orbit around the sun, enough gravity to allow the object itself to become of a spherical shape, and finally the object must clear of all debris in its path.

Plutinos

Orcus and Ixion - Plutinos in the Kuiper Belt. 

     In 2008 it was decided that such objects that are similar to Pluto should be called Plutoids. Plutinos on the other hand are small icy bodies similar to Plutoids but differentiated from them because of the way they orbited around the Sun. Plutino was derived from the planet Pluto and it means little Plutos. It is in this Plutino region that is home to dwarf planets including Pluto. As Neptune moved further away from the Sun, it started to interfere with orbital motions of many objects, one of them being Pluto. The interference resulted in the objects' (including Pluto's) orbit becoming locked to the orbit of Neptune. However, the two planets do not collide for their periods of revolution are at different ratios. Every two times a Plutino orbits the Sun, Neptune orbits the Sun three times. Orbits and orbital  periods of Plutinos are similar to those of Plutos. Examples of Plutinos are Orcus and Ixion. Orcus is referred to as anti-Pluto because it appears on the opposite phase of Pluto - when Pluto is closest to the Sun, Orcus is at its furthest point to the Sun. Orcus is also found in the Kuiper Belt, having a radius of 800km and an orbital period of 245 years. It is colder than Pluto by 10 degrees Celsius (-240 degrees Celsius). Due to its extensive ice coverage on the planet, Ocrus has the highest albedo (reflection of sunlight) compared to any other object in the Kuiper Belt - including Pluto. On the other hand, Ixion is the 5th largest Plutino and is composed of ice and tholin. It also has a longer orbital period than Pluto itself for Pluto's orbital period is 247 years whereas Ixion's orbital period is 249 years. All plutinos are Plutoids but only those Plutoids with orbital periods with Neptune are Plutinos. The three known plutoids are Pluto, Eris, and Makemake.

Theoretical Prediction or Not

     However, Pluto wasn't a true theoretical prediction based on celestial mechanics since it was discovered on the basis of the irregular orbits of Neptune and Uranus. There was a hypothesis stating that there must be another gaseous body beyond Neptune that causes deviations within the elliptical orbit. However, once it was found that Pluto was too small to make changes in these large planets (Uranus and Neptune), they realized the deviations in their orbits were due to an overestimation of Neptune's mass. The Titius-Bode's Law was used to predict a planet around 38.8 AU, beyond Uranus. Beyond Uranus they had found Neptune so their prediction of another planet beyond Uranus was accurate, however the Titius Bode's Law was not because Neptune was found at 30.1 AU and not at 38.8 AU. Unlike this discovery of planet Neptune, the discovery of Pluto was not based on theoretical predictions. The inaccurate Titius Bode's Law predicted that Pluto was 30 AU further than its actual distance. Lowell's predictions using mathematics that was created through the observation of both Neptune and Uranus was not able to predict the true orbit of Pluto. Tombaugh had found Pluto by chance and not due to Lowell's predictions which did not help find the planet's location.

A view of the Kuiper Belt and its distance relative to the other planets. 

References

http://nineplanets.org/pluto.html

http://www.universetoday.com/13872/interesting-facts-about-pluto/

http://www.loc.gov/rr/scitech/mysteries/pluto.html

All pictures are from public domain. 

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.

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.

Assignment 1: Ancient Astronomy - Size of the Earth

Eratosthenes

Eratosthenes 276 BC - 194BC

     Eratosthenes was not only a Greek scientist but also had many other occupations (Abreu, 2012). He was a mathematician, geographer, poet, astronomer, music theorist, and the chief librarian (Abreu, 2012). He invented many tools and technology that we still use today. If it hadn't been for Erathosthenes` intelligence, many of today's concepts about a wide range of subjects may not have progressed as well as they have. However from everything he has accomplished, Erathosthenes was best known for calculating the circumference of the Earth (Abreu, 2012).

One of his many accomplishments was that he was the founder of chronology (Ast, 2014). This is the science of arranging events in a timely order. This contributed to the discipline of earth history, and the study of the geologic time scale (Ast, 2014). Time keeping is an important concept because it allows for radiocarbon dating as well as dendrochronolgy (Ast, 2014). This allows for the estimation of living things relative to the proportion of carbon isotopes and estimation of the age of trees, respectively (Ast, 2014). These are two major methods of scientific research for it allows us to order events of all kind in chronological order.

Geography & Mathematics

     Eratothenes was also known as the father of Geography. Due to his interest in the geography of the Earth along with his exceptional knowledge of the Earth, he made a book called Geographika (Freedman et al, 2010). This book consisted of three volumes, and outlines different climate zones across the Earth - two freezing zones, two temperate zones, and a final zone. He also listed hundreds of cities in this book, as well as their locations and distances from one another (Freedman et al, 2010). It is here where he had come up with longitude and latitude system.
     One of his major accomplishments in mathematics is Sieve of Eratosthenes, which is a straightforward algorithm that helps recognize prime numbers (Freedman et al, 2010). It is here where he came up with both prime numbers and composite numbers. Prime numbers are those that cannot be divisible by any number except 1 and itself. Composite numbers are those that are multiples of prime numbers. This set foot many mathematical properties that we learn today. 

Measurement of the Earth`s Circumference 

Distance between Alexandira & Syene

     It was not until Eratosthenes` time that the public knew it was possible to measure the Earth`s circumference (Freedman et al, 2010). He was the first person to do this and received incredible recognition, as he is still remembered today. Using his knowledge in mathematics, he calculated the circumference of he Earth by measuring the angles between two shadow castes in two different cities, Alexandria and Syene, while also measuring the distance between those two cities (Freedman et al, 2010). He recorded his findings in the last volume of his book Geographika (Freedman et al, 2010).

     In order to precisely determine the circumference, after careful observation Eratosthenes noted that in his home city (Alexandria) in Egypt, the sun was never directly overhead while in a city further south (Syene), there was a certain day where the shadow never castes at the bottom of the well. During the summer solstice, at noon Eratosthenes realized that the Sun's rays reflected straight above the town of Syene (Freedman et al, 2010). This is because there was no shadow when the Sun's rays hit the zenith vertically - a zenith is the spot that is directly above a specific location (abstract) (Abreu, 2012). On the other hand, in Alexandria, a shadow can be seen (Abreu, 2012). According to his calculations, this shadow was 1/50 of the entire circle and was below the zenith.

     Using mathematical reasoning, the intelligent scholar realized that the shadow`s angle would be the same as the angle between the 2 different cities (Freedman et al, 2010). Since he had exceptional geographical knowledge, he used his knowledge of knowing that Alexandria was located North of Syene (Freedman et al, 2010). He assumed that the Earth was 360 degrees and so the distance between the two locations are 7.2 degrees apart (Freedman et al, 2010). Therefore, he stated that if he could find the distance between the two cities, he would have to multiply that distance by 50 in order to get the Earth`s circumference (Freedman et al, 2010). It is here where he also noted that the Earth was in fact curved and not Earth, and was able to estimate that it was 360 degrees due to its spherical structure. This is because if the Earth were to be flat, the Sun's rays would directly shine overhead both cities (Alexandria and Syene). If this were to occur, there would be no shadows at both locations (Freedman et al, 2010). However according to Eratosthenes there was a shadow at Alexandria indicating that the Earth was in fact curved and flat (Ast, 2014).

     After finding this remarkable discovery, Eratosthenes used this to contribute to science in many other aspects. For example, he created a system for the Earth`s latitude and longitude as well as a device that was able to view the motions of the stars by astronomers, while creating a 12 month calendar that included a leap year.


References

Abreu, A. (2012, June 3). Retrived from http://www.astro.cornell.edu/academics/courses/astro201/eratosthenes.htm

Ast, C., Eratosthenes 276-195 B.C.E. Retrieved from http://www.math.witchita.edu/history/men/ertosthenes. html

Freedman, R., Geller, R., & Kaufmann, W.J. (2010) Universe (8th ed). New York, NY: W.H. Freeman.



All pictures are from public domain.