Modern Astronomy

Hubble Space Telescope

Birth and Construction:

Galileo, the 17th century astronomer invented the first telescope which he used to look toward the heavens. Using this new invention, astronomers found rings around Saturn, moons around Jupiter and nebulous bands of Milky Way (1). Since then, telescopes have been developed and grown in both complexity and efficiency. The best places for telescopes until mid-20th century were mountain tops away from brightly-lit cities, to minimise the effects of light pollution and atmospheric consequences like clouds, wind and rain. By the last decade of the 20th century, mankind had developed enough to reach the "ultimate" height for a telescope, one in space near Earth, which was named the Hubble Space Telescope. 

In 1946, a professor and researcher at Yale University, Lyman Spitzer proposed the advantages a space telescope over a ground-based telescope (2). He explained that a space telescope will not be affected by the factors of atmospheric effects, and also that it can receive X-rays before it is blocked by our atmosphere (2). This was later put to use into starting to make Hubble Space Telescope a practical reality. The National Academic of Science pushed forward this idea with the support from NASA in mid-1960s (2). After preliminary study of challenges and phased-developments in 1971, George Low, then NASA's Administrator approved the Steering Group of the early Hubble to further develop practical tests (2). The $400 to $ 500 million project needed a lot more support at an international level in 1975 with European Space Research Organisation (ESRO) participating in producing solar panels and helping with research and development after which the cost was brought down by about half with a mirror reduction from 3 to 2.4 meters (2). 

The Hubble Space Telescope was started to build with Perkin-Elmer Corporation constructing the mirror & related optics and the Lockheed Missiles and Space Company engineering the spacecraft and its support systems (2). In 1983, the Space Telescope Science Institute at the John Hopkins University in Maryland was founded which was a great support to the development of the Hubble program which was also when this space telescope was named after Edwin Powell Hubble who first proved the expansion of our Universe at a large scale (2). With such a large scale project, delays were to be expected and the assembling of the optical systems and the spacecraft was delayed until 1985 (2). The Space Shuttle Challenger lifted off from Florida with the Hubble telescope and only a minute into its flight, the vehicle exploded into a ball of smoke on January 28, 1986. Finally on April 24, 1990 NASA's Hubble Space Telescope was successfully launched on the space shuttle rightly named Discovery from the Kennedy Space Station (1).

Figure 1: Space Shuttle Discovery carrying the Hubble Space Telescope (3)  

Precision of Mirrors:

Placing a telescope in space orbit around Earth was a remarkable achievement by the human race. However as with most great inventions, it required improvements; just few weeks into operation, the images taken by Hubble were blurred which prevented it from sending spectacular images of our Universe.  A study was probed into this to reveal spherical aberration in the primary mirror, caused due miscalibration of an instrument that produced the mirror which ground it a bit too flat (2). The curvature in spherical mirrors are produced to focus the light rays to the focal point to produce sharp images, but if the curvature is not calibrated precisely, the rays do not meet at one point which causes blurred images as shown in the figure below (4).

Figure 2: Spherical Aberration caused by a slightly non-spherical concave mirror (4)

Scientists and engineers then quickly found a fix to this problem before Hubble's first scheduled servicing mission in 1993 (2). This fix was called COSTAR, which stood for Corrective Optics Space Telescope Axial Replacement comprising of a set of optics which can work to correct the spherically-aberrated mirror to produce sharp images as originally expected (2). In the December of 1993, the crew of STS-61 was intensively trained in servicing and replacing a number of the Hubble Space Telescope parts along with installation of COSTAR, upgrade of Wide Field/Planetary Camera and new solar arrays (2).

 The start of 1994 was an exciting year not just astronomers who could study our Universe in more detail then ever before, but also the public who was awe-stricken by the spectacular images of the beauty in our Universe. In 1997, the crew of STS-82 installed the Near Infrared Camera and Multi-Object Spectrometer (NICMOS) and the Space Telescope Imaging Spectograph (STIS) which could give us an infrared vision into the Universe (2). This we know hugely helped in studying the objects that hide behind gas clouds and dust which are opaque to visible light. Later service & missions led to the installation of computers, advanced gyroscopes to help target precisely, sensors, new Advanced Camera for Surveys (ACS), all of which gave Hubble a wider field of view and faster gathering of images (2).

T-plus Hubble

The Hubble Space Telescope has been providing such valuable data that till date, obtaining telescope time for a particular research is highly competitive for researchers. While all this exciting observations were made, on February 1, 2003, a very tragic event occurred in which all seven astronauts aboard Columbia were killed as it disintegrated during its reentry into the Earth's atmosphere (2). Following this tragedy, investigations were made and the NASA Administrator Sean O'Keefe decided that any future shuttle missions would be to only the International Space Station (2).  He also took extended efforts with the Goddard Space Flight Center before sending another servicing mission to the Hubble Space Telescope (2). 

Figure 3: Comparison of the Primary mirrors in Hubble & other Space Telescopes (5)

The Hubble Space Telescope has been a big success and a huge advancement in the field of observational astronomy. However, it will last only a few more years before it becomes too old to be serviced. This has led to the development of our next-generation of Space telescopes, which will be led by the James Webb Space Telescope (JWST of Webb) named after former NASA Administrator, James Webb which will be a large infrared telescope with a 6.5-meter primary mirror compared to the 2.4 meters in Hubble Space Telescope (6). This will be launched on an Ariane 5 rocket from French Guiana in October of 2018 (6). The primary observatory for the next decade will be JWST which will aid in developing our knowledge in the history of our Universe to the formation of extra-terrestrial planets (6). 

Great Hubble moments

Oceans on Ganymede

Ganymede is the biggest and the only moon that creates its own magnetic field around it (7). Observations made by the Hubble Space Telescope show us the oscillation of auroral belts near this moon's north and south poles which astronomers believe must imply a big reservoir of salty liquid ocean below the icy crust of Ganymede (7). Reflecting on a decade back, I feel this is an awesome achievement that we are able to make observations of auroras in a moon around Jupiter without having to go that far! 

Figure 4: Oscillation belt of auroral belts on Ganymede as seen by STIS in Hubble Space Telescope (7)

 Collision with Jupiter

In July 1994, the Comet Shoemaker-Levy (SL9) went on an impact collision against Jupiter (8). This spectacular event was the first of its kind observed in our solar system. The power of Hubble Space Telescope was used to capture this striking event in high-resolution and collect spectral data of Jupiter before, during and after the comet collision (8). The Hubble Space Telescope also looked for changes in Jupiter's atmosphere, evolution of the comet material, effects on Jupiter's magnetosphere and if this collision caused any development of the rings of Jupiter (8). This event, with the Hubble Space Telescope helps not us not only study the planetary dynamics and evolution, but reveals spectacular extra-terrestrial collision events in high resolution as shown in the figure below.

Figure 5: Comet SL9 collision with Jupiter captured by the Hubble Space Telescope (8)

 Millions and more

On Monday, July 4, 2011, Hubble made a landmark by making its millionth observation which was a gas giant planet larger than Jupiter at about 1000 light-years away (9). This planet was named HAT-P-7b, also known as Kepler 2b discovered by ground based telescopes (9). Even though Hubble Space Telescope did not discover this planet, it is a huge landmark in the amount of observations it has made in the 21 years (until 2011) (9). Since then, this planet has been of interest in studying the planet's temperature and the composition of its atmosphere using "high-precision" photometry by astronomers in University of Toronto (10)

References

(1) http://www.nasa.gov/mission_pages/hubble/story/#.VRrFnvnF-jk

(2) http://history.nasa.gov/hubble/
(3) http://www.spacetelescope.org/images/10063561/

(4) http://farside.ph.utexas.edu/teaching/302l/lectures/node136.html
(5) http://www.asc-csa.gc.ca/eng/satellites/jwst/webb-hubble.asp
(6) http://jwst.nasa.gov/about.html
(7) http://spaceflightnow.com/2015/03/13/hubble-observations-reveal-ocean-on-ganymede/
(8) http://www2.jpl.nasa.gov/sl9/hst.html
(9) http://www.cbsnews.com/news/hubbles-yowza-moment-its-millionth-science-observation/
(10) R. Jayawardhana., et al. 2014, arXiv:1407.2245, "Changing Phases of Alien Worlds"

Discoverer of Expanding Universe

Life of Alexander Friedmann

Figure 1: A picture of Alexander Friedmann (1)

Alexander Friedmann (1888 - 1925) was a scientist born on June 16, 1888 in Saint Petersburg, Russia (1). He wasan excellent scholar in his high school at Second Saint Petersburg Gymnasium and at Saint Petersburg State University where he pursed his study in Mathematics from 1906 to 1910 (1). He learnt about quantum theory, relativity and statistical mechanics from seminars by Vienna- born Paul Ehrenfest in the same university (1). 

Like most scientists in the early modern physics era, Friedmann also researched on different topics like fluid dynamics, meteorology and electro-magnetism. In 1913, He started studying meteorology in the Aerological Observatory in a suburb of Saint Petersburg (1).  Following that year, he got in to aeronautics in Leipzig where he started taking part in flights in airships to make meteorological observations, and later volunteered to partake with the Russian Air Force as a technical expert and pilot  in the First World War (1). During this period, he taught aerodynamics to pilots and in 1916, the became the head of the Central Aeronautical Station in Kiev (1). In 1920, Friedmann returned to Saint Petersburg due to political conditions in Moscow, to the Main Geophysical Observatory (1). As a professor in Petrograd University, he taught mechanics, physics and mathematics while researching in Railway Engineering, Naval Academy and Optical Institute (1). Few weeks before his death from typhus in September 1925, Friedmann made a risky record-breaking balloon flight to collect data in high altitude (2).

Contributions to Cosmology

Alexander Friedmann studied Albert Einstein's papers on General Theory of Relativity and in 1922, he discovered a solution to Einstein's equations describing the expanding universe (1).  It was the birth of the theory of the formation of our universe, Big Bang. His solutions that describe the evolution of our Universe was initially strongly resisted. His equations named, the "Friedmann equations" set a framework for describing Cosmology using General Relativity, the evolution of a perfect-fluid cosmon of uniform mass density (2).  Friedmann and Frederiks put together a mathematical introduction to tensor calculus and General Relativity and Friedmann himself introduced the fundamental idea of modern cosmology, and the possibility that our Universe could have originated from a singularity in two Zeitschrift fur Physik papers (2). 

Figure 2: Three Possible Scenarios described by Friedmann on the evolution of our universe with t0 referring to the current time (2) 

Alexander Friedmann came up three possible scenarios for the fate of our Cosmological Universe as shown by the three curves on the plot in Figure 2. The curve M1 is the scenario where our Universe started with a singularity, with a short decelerating rate of expansion followed by the current accelerated expansion; the curve M2 shows a scenario where our Universe started with a finite radius and since then has been expanding at an accelerated pace. The curve referred to as P shows a scenario where our Universe will in the future stop expanding and contract back to a point of singularity and he found the period of this universe to be 100 billion years (2).

Einstein and Friedmann

Friedmann used papers written by Einstein and de Sitter (Two people who had given solutions the General Relativity equation) to give a wider perspective than either of them on the interpretation of General Relativity with Riemannian geometry (2). At present, we use Friedmann's first order differential equation  to describe the dynamics of the "3-D hypersphere" Universe of ours (2). However, in 1922 when Friedmann published his papers on these ideas, Einstein was not welcoming about his main ideas (2). Einstein had believed in a static Universe that always existed while Friedmann's theory was the idea of singularity and the expanding Universe. Einstein showed his reaction by suggesting a mathematical error in Friedmann's derivation of his equations and that the equations were approximations (2). Responding to Einstein, Friedmann wrote a long letter explaining his derivation and Einstein had published another note on the correctness of Friedmann's derivation and eight years later Einstein accepted the idea of the expanding Universe by looking at the observations made by Edwin Hubble of distant galaxies (2). 

Figure 3: Scientists who worked on expansion theory of Universe and also convinced Einstein of a  non-static evolution of our Universe (3)

George Gamow (1904 - 1968) born in Ukraine was a US-based physicist (4). He attended Leningrad University at Saint Petersburg where he was a student of Alexander Friedmann (5). He helped Friedmann with calculations in his theories, however he himself worked on developing quantum theory of radioactivity and successfully first explained the theory behind the decay of radioactive elements (5). He later continued his work on theoretical nuclear physics at the Copenhagen Institute of Theoretical Physics as a fellow (5). 

Friedmann's 1923 book about the theory behind the size of our cosmos has been largely unknown, and it sad that some of his misquoted papers are his "established" work (2). In a bigger perspective, his contributions to our little understanding of the dynamics of our universe has been outstanding. Research in 1998 by teams led by laureates - Saul Perlmutter, Adam Riess and Brian Schmidt revealed the accelerated expanding universe was worthy of the 2011 Nobel Prize (2).

Interesting Fact: "Friedmann and Tamarkin were student leaders of strikes at the school in protest at the government's repressive measures against schools." (6)

References

(1) http://www.physicsoftheuniverse.com/scientists_friedmann.html

(2) Phys. Today 65(10), 38 (2012), A. Belenkiy; doi: 10.1063/PT.3.1750
(3) http://legrandunivers.blogspot.ca/2014/03/le-destin-de-lunivers.html
(4) http://www.atnf.csiro.au/outreach/education/senior/cosmicengine/hubble.html
(5) http://www.britannica.com/EBchecked/topic/225123/George-Gamow
(6) http://www-history.mcs.st-and.ac.uk/Biographies/Friedmann.html

Assignment 4

The changing Pluto

Introduction:

Pluto was once considered a major planet of the solar system mainly made up of ice, orbiting the Sun beyond Neptune. However, it was classified as a dwarf planet in 2006 [1], considered to be a large member of the Kuiper belt of objects. The surface temperature of Pluto is 375 to 400 degrees [2] below zero. It is on average more than 5.8 billion kilometers away from the Sun (about 40 times as far from the Sun as the Earth). It is only 2300 kilometers [2] wide and is slightly smaller than our moon. The period of Pluto's revolution is about 248 years. Pluto has three noticeable moons, the largest being Charon, and the other two, Nix and Hydra (discovered in 2005 by NASA's Hubble Space Telescope). The mass of Pluto is very low so that its gravity is about one-fifteenth [2] that of Earth. This means that a person who weighs 100 pounds on Earth would weigh only 7 pounds on Pluto.  

Figure 1: Artistic Rendering of Pluto's surface with the view of its big moon, Charon (1)

The atmosphere in Pluto is mainly composed on nitrogen [3] , carbon monoxide and methane. The perihelion (nearest point to Sun) and aphelion (farthest point to Sun) vary quite a lot for Pluto, 30 to 50 AU, because of its highly eccentric orbit. This affects the dwarf planet's atmosphere largely. At perihelion, thin layers of gases/ices are formed in the atmosphere, and near its aphelion, these gas molecules solidify. The atmosphere also is thought to have clouds and winds, but the confirmation has to wait until we have more detailed observations from space crafts.

Discovery, an "accident":

Percival Lowell [1] , an American astronomer observed deviations from the predicted orbits of Neptune and Uranus which led him to think there could be the gravity of another object that could be causing it. In 1915, he predicted such an object, but didn't find it. However, Clyde Tombaugh used these predictions, to discover Pluto in 1930 at the Lowell Observatory in Flagstaff of Arizona. The discovery was an accident as the calculations later turned out to predict a much more massive planet X [4] beyond Neptune and Uranus to account for the observed motions of the two gas giants, Neptune and Uranus. We now know there is no such planet X but there are a large number of small asteroid-type objects (Kuiper belt) beyond the orbit of Neptune.

Figure 2: Clyde Tombaugh, the discoverer of Pluto, looking through a telescope at the Lowell Observatory (2)

Clyde William Tombaugh discovered the first objects of Kuiper belt.  He was born in Streator, Illinois. A hailstorm destroyed his family's farms which hindered his college start. So in 1926 [5], he started making telescopes and started a job at Lowell Observatory in Arizona where he worked until 1945. He graduated from the University of Kansas in 1938 with a master's degree. After working in the observatory, he was part of the World War II working at the White Sands Missile Range after which from 1955 until his retirement in 1973, he was an instructor of astronomy at New Mexico State University. 

As the sub-heading suggests, Pluto wasn't the predicted planet and there were systematic differences [6] between the observations and predictions of the planet X. The predictions of these planets can be tied back to the "law" of Titius-Bode which had reasonably good predictions for the planets close to the Sun which was the motivation to extend it beyond Jupiter and other gas giants as time progressed. It was probably not a clear prediction from the laws of celestial mechanics which would have not caused the systematic differences between observations and the theoretical predictions.

The sliding "status" of Pluto:

On the episode named "The Pluto Flies" [7] in the series NOVA, Dr. Neil Degrasse Tyson provides an interesting story of the status of Pluto, how it was considered to be one of the planets in solar system and how it was sharply demoted into one of the many objects in solar system. He narrates that for more than 75 years, our solar system was considered to contain nine planets (including Pluto), but at the start of this 21st century, a visitor to the Hayden Planetarium (where Neil worked), could take a look at all the then planets of solar system, except for Pluto.  This turned out onto the front page of newspapers, one headline read, "Pluto's Not a Planet? Only in New York" [7]. Following this, Neil had received unhappy responses on this subject, "The Pluto Flies". The scientific responses to it were that Pluto is shaped close to a sphere unlike other bodies comparable to its size. The arguments for the demotion of Pluto consisted of (i) Pluto's orbit crossed that of Neptune due to its highly ecliptic orbit, (ii)Charon, one of Pluto's moon is as big as Pluto itself, so it would be equally reasonable to call Charon a planet and Pluto its moon. (iii) There are many other bodies (some moons and asteroids) as massive as Pluto that would need to be considered a planet.

IAU, the International Astronomical Union is the official group which has the power to decide on the names of the extra terrestrial objects based on the regulations set by the union. The union agreed that the Solar system would consist of only eight planets and that Pluto was classified into a new class of objects, "dwarf planets" which are different from planets. Ceres and Eris were also grouped with Pluto. In spite of the demotion, the dwarf planet Pluto was considered to be an important object in the category of Trans-Neptunian objects (those that cross the orbit of Neptune) perhaps one of the factors could have been the history and controversy of the status of Pluto. In light of this, the union also named these Trans-Neptunian objects as plutoids [8].  In the present, Pluto is still considered as a dwarf planet.

Plutinos:

Figure 3: Some objects that fall under the class of plutinos (3)

Plutinos are a sub-class (largest) of Trans-Neptunian objects that are in 2:3 orbital mean-motion resonance with Neptune of which Pluto itself is one of them. This class refers only to this resonance [9] and in no way relates to the physical characteristics of the object with Pluto or Neptune. Some of the Kuiper belt objects also fall under this category. The first plutino, other than Pluto itself, was discovered on September 16, 1993 [9] was named (385185) 1993 RO. Some of the other objects that are classified as Plutinos are: 2005 TV 189 , 2007 JH 43 and 2002 VX 130 . These three objects are unusual for their ecliptic and highly inclined orbits unlike most other plutinos which have Pluto-like orbital inclination and eccentricities. The unusual plutinos because of their close approaches to Pluto resonate with Pluto which puts off the plutino's long term stability.

Interesting Fact [10] : 2015 is the year of Pluto, as NASA's New Horizons spacecraft is approaching the edge of our Solar system to Pluto.

References:

Text:

[1] http://www.space.com/43-pluto-the-ninth-planet-that-was-a-dwarf.html

[2] http://www.nasa.gov/audience/forstudents/k-4/stories/what-is-pluto-k4.html#.VP0nUPnF-jk

[3] http://www.space.com/18564-pluto-atmosphere.html

[4] http://nineplanets.org/pluto.html

[5] http://en.wikipedia.org/wiki/Clyde_Tombaugh

[6] Celestial Mechanics 43 (1988), 55-68, Kluwer Academics Publishers. 

[7] http://www.pbs.org/wgbh/nova/space/pluto-files.html

[8] https://www.iau.org/public/themes/pluto/

[9] http://en.wikipedia.org/wiki/Plutino

[10] http://lowell.edu/in-depth/pluto/

Figures:

(1) http://solarsystem.nasa.gov/multimedia/display.cfm?Category=Planets&IM_ID=16383

(2) http://www.space.com/19824-clyde-tombaugh.html

(3) http://en.wikipedia.org/wiki/Plutino#mediaviewer/File:ThePlutinos_Size_Albedo_Color2.svg

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

Assignment 1

Contributions of Erastosthenes to Ancient Science

Early Life:

Erastosthenes was born in Cyrene (present Libya), an ancient Greek city in 276 BC [1]. He was very involved in learning which took him to being the chief librarian at the Library of Alexandria. He learnt about Geography, Mathematics, Astronomy, Philosophy and History. He was known to be second among the people with similar work which some people who disliked him nicknamed him as Beta which later on he proved wrong with producing accurate results better than others at that time. He discussed about lot of ideas with his friend, Archimedes and these discussions were part of Eratosthenes' inspiration to work on experimental methods [2]. This is an iteration of experimental science which in ancient times was a tool to derive theoretical results where conversely in modern science theories are used to explain experimental results. 

Science work:
Erastosthenes' contributions to science was mainly in Geography and History. He build Chronographia, which lists the dates of major events around the Greeks in his time, like the date of the "seige of Troy at 1184 BCE" with the help of the methods of Hecateus, a Historian & Geographer himself [3].  He also collected data from explorers and voyagers to describe some of the activities of the Earth tectonics activities like fire , earthquakes and volcanism which are very important even in today's geography. He also contributed with his writings in philosophy, chronology,  literary criticism, poetry and most of his work was destroyed in the Destruction of the Library of Alexandria[4]. His work in astronomy is also much notable, he "presumably" knew the correct value of distance to Sun from Earth and also that the rays from the Sun can be practically parallel at the Earth as can be observed in Figure 1 below [5].

[6] Figure 1: Parallel Rays from Sun and the distance to the Sun.

Size of Earth:
[7] Eratosthenes used his knowledge about the shadows Sun's rays of light would produce at Egypt, on the Tropic of Cancer during summer solstice.  He measured the angle between this zenith line and the line of the rays of sunlight to be 1/50th of a circle using a gnomon, which measures angle using the shadows that fall on its sundial. He used this to find the angle the vertical line from Earth's surface at Alexandria made with a line of sunlight to Alexandria. He knew that in similar time interval, at Syene (now Aswan), the Sun's rays appeared directly on top of the head, or at zenith. He assumed the Earth being perfectly spherical (360 degrees), he calculated from his measurements of angles the arc distance between Syene and Alexandria to be 7 degrees and 2 arc minutes of the entire sphere angle and it is great that his measurements precise up to degrees. He then used the data available to him, the distance between Syene and Alexandria which was about 5000 stadia (ancient Greek unit for distance) and hence interpreted the entire circumference of the Earth to be 252000 stadia which is about 46620 km and this is precise to 16.3% to the current accepted value. Some argue that with the conversion he used for stadia and meters, his value is precise to 1.6% to the current accepted value. Nevertheless, such a precision given the tools available to him at that time is indeed something remarkable. He produced his precise results in a essay named, "On the Measurement of the Earth" combining theory with experiment to maximise the accuracy of the results of measurements at that time.

[8] Figure 1: Measuring the size of the Earth

Conclusion:
Eratosthenes contributed in various disciplines of study in his time which can be considered remarkable especially the precision of his measurements. In honour of him, a crater on the moon is named after him, we have the Eratosthenian period in the lunar geologic timescale highlighting his contributions to ancient Astronomy and Geography [9]. One surviving work of his is Catasterisms, text which describes constellations in the form of stories with a count of the number of stars contained in them. Eratosthenes' old age was attributed with blindness and he is said to have "committed suicide by voluntary starvation." [10]

References:
[1] [4] [7] [8] [9] http://en.wikipedia.org/wiki/Eratosthenes

[2] [3] Eratosthenes, http://www.ancient.eu/Eratosthenes/, Cristian Volatti, April 2013

[5] [6] [10] http://www.britannica.com/EBchecked/topic/191064/Eratosthenes-of-Cyrene