Assignment 6

What is the Hubble Space Telescope?

Fig. 5 Hubbles Orbit [5]

Travelling at eight kilometres per second, five hundred and seventy kilometres above sea level [3], the legendary Hubble Space Telescope soars overhead once every hour and a half [1]. This one and a half billion dollar (at launch) scientific marvel was the first of its kind [3], a telescope mounted in the fabric of space, high above the ionosphere [1]. The uniqueness and placement of the Hubble Space Telescope are ultimately due to its base purpose, to see past the light distortions caused by Earth's atmosphere. These distortions consisted of too many variables to manually and individually address, from twinkling lights caused by shifting air pockets to the dampening of ultraviolet, gamma rays and X-rays as they passed through the atmosphere. Naturally, an easy solution to all of these problems was to place a telescope in space beyond Earth's protective veil [7].

The Hubble Space Telescope is a type of telescope known as a Cassegrain reflector [1]. Essentially, this means that it is fundamentally composed of 2 mirrors, a primary and a secondary. Light reflected off the primary mirror is funnelled by the secondary mirror, and focused through a doughnut hole in the primary mirror. This focusing of light causes an incredible increase in light collection and therefore exposure, creating a much clearer, brighter image [8]. Interestingly, the distortions caused by the atmosphere are so significant that even though Hubble's primary mirror was significantly downsized (due to budget issues) to two meters and forty centimetres, the images it produces outclass the competition by far. This is even more surprising in a relative sense, when considering that at its size, Hubble's primary mirror is only about twenty five percent the size of a mirror in a ground telescope [1].

Fig. 4 Hubble Inner Workings [4]

Not only is Hubble an imposing one of a kind telescope, it is also a high functioning space observatory. The hundred and twenty gigabytes of  data collected by Hubble per week [3] is analyzed by the treasure trove of scientific instruments it carries and is then transmitted via antennae to the Goddard Space Flight Centre. There the information is compiled and forwarded to the Space Telescope Science Institute to be consolidated, organized and then stored for safe keeping [1]. The brain of Hubble is controlled by two separate computers, and much like the left and right hemispheres of the human brain, they control separate functions. One computer controls the fundamental systems of the observatory including positioning the telescope; receiving satellite signals with instructions from Md. Engineers, while the other handles all of the scientific instruments [7]. 

Hubble History: 

Fig. 6 Hermann Obeth [6]

The first recorded instance of a proposal for a space telescope occurred over a half century before the launch of Hubble. In 1923,Hermann Obeth suggested in his book titled "Die Rakete Zu Den Planetraumen", that it would be possible to blast a telescope into space on a rocket. Due to technological restrictions this idea would be cast aside, not to be taken seriously again until just over two decades later [4]. Lyman Spitzer Jr. was the one who reignited the torch. He submitted a proposal for a space observatory in 1946, the space observatory that would eventually become known as Hubble. Over the next twenty three years Spitzer Jr. worked tirelessly, trying to convince NASA that the space telescope would be of insurmountable usefulness and finally, in 1969 the Large Space Telescope project was born [6].

Soon the intrigue of the Space Telescope spread to other nations and by 1975 the European Space Association began to collaborate with NASA on the Large Space Telescope. Not surprisingly, with the interest building, less than two years later Congress approved funding for the project [1]. With the project now in full swing there were many important decisions to be made. The Marshall and Goddard Space Flight Centres and Perkin-Elmer Corporation were chosen for their expertise to over see various tasks involved in Hubble's completion. As already mentioned, the Goddard Space Flight Centre was to deal with the transmission of Hubble's valuable data upon completion. Prior to launch they were also responsible for the design of the many scientific instruments aboard the observatory including the Wide Field and Planetary Camera, the High Speed Photometer, the Faint Object Spectrograph, the Faint Object Camera and the Goddard High Resolution Spectrograph. The design for the actual telescope however fell on the shoulders of Marshall Space Flight Centre  and their completed plans were sent to Perkin-Elmer Corporation for construction [6].

With construction underway, efforts were refocused on other preparations that needed to be made and by 1979, six years before the completion of the telescope, they began training astronauts for the upcoming missions [1]. In 1981 the primary mirror had been completed and four years later, Hubble was born [4]. Excitement soaring and tensions rising, Hubble was set to launch early 1986, all eyes were on the sky. Unfortunately, tragedy struck in the form of the Charger shuttle explosion; a space shuttle burst while lifting off causing a panic. All missions were to be grounded and the launch for Hubble was delayed [6]. Thankfully, order returned within just a few months and Hubble was carried into orbit by the shuttle Discovery before the years end [3]. 

Fig. 7 Charge Explosion [7]

The excitement of Hubble's successful launch would be short lived, for once the first photos returned by Hubble were collected they were found to be far too blurry; they were still an improvement over previous images, but were a far cry from expectations [1]. Through various calculations scientists realised that Hubble's primary mirror had a tiny, almost indiscernible flaw that was causing an unintentional bend in light, creating distortions in the images. In essence, the flaw in Hubble's main mirror was that it was too flat by roughly one fiftieth of a hair. Since the flaw in the mirror was so small, and an error in missing volume there was no good way to directly repair the mirror and replacing the entire mirror in space was infeasible. Instead, scientists calculated the placement of several smaller mirrors that would be placed inside Hubble to redirect the distorted light [2]. The next several years were dedicated to preparations for Hubble's first service mission; the parameters of which were extended to include upgrading the High Speed Photometer to the COSTAR as well as the Wide Field and Planetary Camera to the Wide Field and Planetary Camera 2 [1].

On December 2, 1993, after almost a year of harsh training,  an elite team was sent up to perform repairs on Hubble, its first service mission. This was one of the most important space missions of all time, for not only was it a very technical task on an incredibly expensive and fragile piece of equipment, but it was also the first real test of whether or not telescope repairs in space would be viable. The renovations on Hubble took place over the next seven days, over which the repairs and upgrades were completed in addition to some minor maintenance and replacing perishable parts [1]. Luckily, all of the tasks performed by the service team went without a hitch and all of Hubble's images thereafter were clear as a "crisp spring morning".

Over then next two decades Hubble would receive three more service missions as well as numerous operations extensions. In 1997 service mission two was launched, installing new instruments on board the observatory [4] as well as extending its life from 2005 to 2010 [2]. Service mission three was split into two trips, one in 1999 to fully overhaul Hubble's systems and one in 2002 simply to install instruments once again [4]. Hubble's fourth service mission was scheduled for 2006, but much like its launch, was delayed by another space shuttle explosion, the Columbia disaster [1] and would not occur for another three years. Finally, in 2009, Hubble was serviced for the last time, adding new instruments and performing final maintenance checkups [4]. This last mission maxed Hubble's lifetime to last until 2014 [1].

After two and a half decades of service, Hubble is reaching the end of its days. Its parts have slowly but surely degraded and aged, making them more difficult to and less worth replacing. Originally, Hubble had been planned to be retrieved, but now it will be left in orbit until it completely loses functionality and plummets back to Earth or is thrown into the dark depths of space [1]. Finally, once Hubble's usefulness is completely expired it will be replaced by the James Webb Space Telescope [9].

Achievements and Importance:

The ultimate power of Hubble's sight is not the images that it takes, but the vast expanse of accessable information it provides. Anyone can request time on the telescope and if approved by a comittee of proffessionals, have a year to collect and organise as much information as possible. Once a year is up the information is published to the public and becomes accessable to anyone [1]. Ironically, but not surprisingly time on the famed Space Telescope is hard to come by and only about twenty percent of proposals and selected [1].

Among the over ten thousand documents published based on Hubble information [1] some note worthy examples are:

• Discovering two moons of Pluto [5]
• discovered that gamma ray bursts were caused by incredibly massive stars collapsing in on themseleves when they no longer have the critical density to remain stable [1]. 
• increased the accuracy of the estimate for the age of the universe by a significant amount by measuring the pulsing of Cepheid variable stars [5]

Below are three of Hubble's most prominant images:

In Fig. 1 below is a massive galaxy, so massive in fact that many astronomers did not believe it could exist. They did not believe a galaxy could have formed so completely in such a short time. Not only is it incredibly massive, it is increidbly old as well, dating back to almost eleven billion years of age, brinking on the dawn of the universe. This "grand-design" spiral galaxy is the oldest galaxy ever discovered and would not have been seen without the Space Telescope. [12] 

Fig. 1 "Grand-Design" spiral galaxy [1]

Fig. 3 Hubble Deep Field Section [3

Fig. 2 Mixing Galaxies [2]

Depicted in Fig. 2 is a glimpse into our far future. Milllions of years from now the Milky Way and the Andromeda Galaxy will collide [10]. The swirling mass in the image below are the galaxies NGC 7714 and NGC7715. Passing close enough to eachother, their respective massive gravities began to affect eachotehr greatly. One day this glorious view will beam across our very own horizions and this may be the only real glimpse of it this generation will ever see [13].

In Fig. 3 is a portion of the famous Hubble Deep Field. This is one of the largest and most important images ever take by Hubble. In it, over a thousand five hundred galaxies can be seen, of densly various types. This has lend to a much greater understanding of the formation of galaxies through camparing the images of galaxies at different ages [14].

Works Cited:

1. http://hubblesite.org/the_telescope/hubble_essentials/ 
2. http://www.aerospaceguide.net/spacehistory/hubble-history.html
3. http://content.time.com/time/photogallery/0,29307,1897016,00.html
4. http://www.spacetelescope.org/about/history/
5. http://www.space.com/15892-hubble-space-telescope.html
6. http://www.nasa.gov/mission_pages/hubble/story/the_story.html
7. http://en.wikipedia.org/wiki/Hubble_Space_Telescope
8. http://www.britannica.com/EBchecked/topic/98119/Cassegrain-reflector
9. http://www.jwst.nasa.gov/
10. http://en.wikipedia.org/wiki/Andromeda%E2%80%93Milky_Way_collision
11. http://www.space.com/15947-milky-andromeda-galaxies-collision-simulated-video.html
12. http://io9.com/5927315/hubble-has-spotted-an-ancient-galaxy-that-shouldnt-exist
13. http://www.space.com/28583-galaxy-merger-hubble-telescope-photo.html
14. http://en.wikipedia.org/wiki/Hubble_Deep_Field#/media/File:HDF_extracts_showing_many_galaxies.jpg

Figures:

1. http://i.kinja-img.com/gawker-media/image/upload/s--n4NKplLg--/c_fit,fl_progressive,q_80,w_636/17tatwtoiu44djpg.jpg
2. https://blogger.googleusercontent.com/img/proxy/AVvXsEgwHTS3JW5Mnp1fveFMkZNqzX8tAcnrXHODC1tSKQmjMcCI5Xe6iJ49hfMmFQzlDYcAhdB2FUFtYkkhIwFqDPZnlTa_d2858iPu-xe4Z7wcL1Km1kvoVJx0b0C_BOoP9BCgRa8fN28dZFtTI-BEA3G4GlJbU7Hos9-1bd8b2gRCiXd5Ag=
3. http://upload.wikimedia.org/wikipedia/commons/0/03/HDF_extracts_showing_many_galaxies.jpg
4. https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEig-CZ89MpdLpXs43w5_pkcEPTG5QVoxMujMnqGEjnczuWPIUoZXkEgVQ7jDHs29b0WthWlZzK30KQBS9S4tInhl6zAoLi2UBA9iWQbaALZEY5fh-0s7TMEhZFtTSEv0B5NYi48BW0UBO1n/?imgmax=800
5. http://amazing-space.stsci.edu/news/archive/2008/03/graphics/hst_orbitposition.jpg
6. http://upload.wikimedia.org/wikipedia/commons/c/cc/Photo_of_Hermann_Oberth_-_GPN-2003-00099.jpg
7. http://vignette3.wikia.nocookie.net/ethics/images/f/fe/Challenger-disaster-myths-explosion_31734_600x450.jpg/revision/latest?cb=20130129201106

Assignment 5

Biography:

Fig.1 Alexander Friedmann

Alexander Alexandrovich Friedmann of Saint Petersburg, Russia   was born in the year 1888 [1]. Interestingly, Friedmann's date of birth, the 16th of June is often misstated as the 29th. This is due in part to Friedmann's incorrect conversion from an old Russian numbering style to a newer one, listing his birthday as the 17th. Furthermore, not knowing it had already been converted once, it was once again converted to the 29th [2]. Regardless of day, Friedmann was born to a family of performers; his father Alexander was a ballet dancer and his mother, Ludmila, a musician [1] He did not stay with them long however, as they divorced when Friedmann was only 9 years old and was taken into the custody of his soon to be remarried father [2].   

Following a relatively ordinary childhood, Friedmann enrolled in highschool at the Second St. Petersburg Gymnasium in 1897. There his brilliance would become apparent as he quickly blossomed from his shell of normality and it was not long before Friedmann was gunning for the top spot against his soon-to-be best friend Yakov Tamarkin. Then in 1905, astonishingly Friedmann and Tamarkin submitted a paper on Bernoulli numbers for publication. A year later the paper was published and  Friedmann and Tamarkin both began college life at the University of St. Petersburg [2]. By this point in time, Friedmann and Tamarkin were inseparable, working, studying and even striking together and eventually, upon meeting Paul Ehrenfest, they became the only two mathematicians to join Ehrenfest's Modern Physics Seminar group. There they discussed relativity, quantum theory and statistical analysis with Ehrenfest and a number of other younger physicists [1]. Throughout the course of his undergraduate studies in mathematics, Friedmann was heavily influenced by physicists such as Vladimir Steklov and Ehrenfest; this pushed him towards an interest in applied mathematics, particularly aeronautics. 

Fig. 2 Yakov Tamarkin, Vladimir Steklov and Paul Ehrenfest

After graduating in 1911, Friedmann immediately went on to attend graduate school for a masters in mathematics. This would prove to be a productive year for Friedmann; not only did he publish an article on the aeronautic contributions of Zhukovsky and Chaplygin, but he also joined an academic group, with Tamarkin, that studied the applied mathematics and analysis of mechanics [2]. Throughout the course of his masters degree, Friedmann continued to expand his areas of research, spreading from mathematics to aeronautics to the mechanics of fluids and meteorology [1] and as if he was not busy enough, he also lectured at the Mining Institute and Railway Engineering Institute [2]. Even with his varied research and massive workload, Friedmann concluded his masters degree in under two years and after graduating, was assigned a position with the Aerological Observatory in Pavlovsk. Surprisingly, given his more mathematical background, out of the topics he had researched at the university he was at the Observatory to study meteorology.

Fig. 3 Russian WWI Bomber

Later that same year, Friedmann joined the Russian air force predominantly for his mathematical prowess and physics knowledge, however he was also trained to be a bomber pilot [1]. Unfortunately war broke out all over Europe the following year, the first World War. Initially, Friedmann continued his efforts in meteorology, and sought out its most prominant mind, Vilhelm Bjerknes, but as the war stretched on with no end in sight, Friedmann decided to contribute directly to the war effort. Friedmann worked in the field, putting his mathematical skills and physics knowledge to the test. As a bomber, his goal was to mathematically model the trajectory a bomb would taken under variable conditions. He worked on his model furiously, writing letters to his cohort Steklov, from his days at the University of Saint Petersburg and was eventually successful in accurately modeling the bomber attack on the city of Przemysl [2]. At the end of 1915, Friedmann left field work and began instructing, he taught pilots about aerodynamics along with his discoveries in trajectory modeling. He was so successful with this that less than a year later he was promoted to head of the Central Aeronautical Station. Friedmann's time in this position was not to last though, for the Central Aeronautical Station was shutdown in 1917 post Russian Revolution [1].

After the end of the war in 1918, Friedmann accepted a professorship at Perm University, where he studied theoretical mechanics, but left abruptly two years later when civil war broke out [1]. He ended up taking a position at the Main Geophysical Observatory [2]. While working at the observatory, Friedmann crossed paths with Einstein's General Theory of Relativity and was instantly enthralled; another two years later he produced a solution to Einstein's equations that supported a dynamic universe [1]. This was groundbreaking, but also incredibly controversial, up to this point the vast majority of the physics community believed in the static unchanging universe. Einstein himself, even altered his equations in 1917 with a cosmological constant to force them to work with a static universe model [3]. Friedmann eagerly shared his finding with Einstein, who was naturally skeptical. At the first sight of Friedmann's idea, Einstein was off put, describing the work as "suspicious" and replied to Friedmann with his criticisms. Friedmann however, was not to be discouraged, he immediately sent Einstein a copy of all of his work on the matter urging him to look through it. After a careful half year long review Einstein admitted that the results were all correct, but was still an adamant believer in the static universe, stating that Friedmann's results were not descriptive of reality, similar to how Copernicus' model of the solar system was stated to be a tool [2]. Due to Einsteins critique as well as the fact that Friedmann only published in Russian, he received minimal recognition for his idea [3].

Friedmann completed his Master's dissertation on compressable fluids in 1922 and in 1924 he published a paper on his three Friedmann Models of the Universe, expanding models that fell in line with his solution to Einsteins equations [2]. He was unable to finish his work, for a year later Friedmann died from typhoid fever at the young age of 37 [1].

 Friedmann's Solutions to Einsteins Equations and the Friedmann Models of the Universe:

One of Friedmann's specialisations, and the topic of his Master's degree was the mechanics of fluids. As a natural extension to this, Friedmann viewed the whole universe much like a vast expansive fluid. He envisioned the universe as an even distribution of "universe-ness", that any two random pieces of the universe (at a large enough scale) should be basically indistinguishable. Under this belief and applying his mathematical knowledge of fluids, in conjunction with Einsteins equations, Friedmann was able to create the general form of a dynamic universe as a solution to said equations. Unfortunately, he was missing some vital information involving the properties of this so called "universe-ness", he could envision the universe as a fluid, but there was no way to determine the pressure or density of this mystery fluid [4]. With this lack of information, his general solution proposed three possible types of dynamic universe that fit the model. 

Fig. 4 Geometry of the Universe

1.  A Flat Universe: this is the most intuitive type of universe, and the type that most people probably envision when thinking about the universe. In this model, the curvature of space is nonexistent and its maximum expansion is infinite, however it's rate of expansion tends to zero [5]. In other words, this is a sheet-like universe that experiences constant, decelerating expansion. Eventually this model would be debunked, as it is known that the expansion is accelerating.
2.  A Closed Universe: this type of universe is akin to blowing up and deflating a balloon repeatedly. It has spherical (positive) curvature and expands out to a maximum and then shrinks back down to an infinitesimally small point [5]. This is also one of the current theories of the end of the universe, a cyclical universe that is continually destroyed and recreated. 
3. An Open Universe: this type of universe has hyperbolic (negative) curvature and is the hardest to imagines. It can be thought of as the shape of a hyperbolic saddle furthermore, all that is known about the expansion of this kind of universe if that it is always nonzero and will converge to some unknown constant [5]. 

George Gamow, Student of Friedmann:


George Gamow was a Russian physicist and cosmologist who was born in 1904. He was a student to Friedmann and would go on to help continue Friedmann's legacy by contributing to George Lemaitres Big Bang Theory, which was one of two competing theories spawned from Friedmann's ideas. He specialized in radioactive decay and would eventually defect from Russia to move to America [6].

His work with the Big Bang Theory was truly exceptional, beginning with his assumption of the "hot universe", that the universe in its youth was incredibly hot. From there, he applied Friedmann and Lemaitres theories of the expanding universe as well as his speciality in radiation to make groundbreaking discoveries in the formation of the universe [6]. 


Works Cited:

1. http://www.physicsoftheuniverse.com/scientists_friedmann.html
2. http://www-history.mcs.st-and.ac.uk/Biographies/Friedmann.html
3. http://www.decodedscience.com/alexander-friedmann-unsung-hero-of-modern-cosmology/19423
4. http://www.brighthub.com/science/space/articles/79590.aspx
5. http://www.einsteins-theory-of-relativity-4engineers.com/friedmann-equation.html
6. http://en.wikipedia.org/wiki/George_Gamow

Figures:

1. http://upload.wikimedia.org/wikipedia/commons/c/ca/Alexander_Friedman.png
2. http://apprendre-math.info/history/photos/Tamarkin.jpeg and http://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Steklov.jpg/220px-Steklov.jpg and http://upload.wikimedia.org/wikipedia/commons/8/8a/Paul_Ehrenfest.jpg
3. http://www.wio.ru/ww1a/gal/im_e.jpg
4. http://map.gsfc.nasa.gov/media/030639/030639_2_320.jpg

Assignment 4: The Changing Pluto

Pluto is a small celestial body known as a dwarf planet. Its diameter is roughly 20 percent of Earth's and its mass only 2 one thousandths [4]. Not only is Pluto small compared to the Earth, but it is also smaller than a number of moons in our Solar System, including Ganymede and Europa [8]. Given that its orbital distance is quite far relative to the solar system, at 39.3 AU and its general lack of atmosphere, Pluto is also incredibly cold. At minus 230 degrees Celsius, Pluto's surface temperature is only about 40 Kelvin above absolute zero, the coldest possible temperature [4].

Fig. 3: Interior of Pluto

Although Pluto usually does not have much of an atmosphere, it grows much more substantial as Pluto moves towards its perihelion [5], and across its path, it experiences changes in apparent brightness ranging from about 15-13.5 on the magnitude scale [6]. As far as composition goes, spectroscopy reveals that Pluto's icy surface is comprised predominantly of nitrogen, which freezes under the immense cold [7]. Underneath Pluto's frozen skin, lies its core of solid rock [5], furthermore, estimates involving Pluto's density place the ratio of rock to ice between 1:1 and 3:7. In other words the rocky components of Pluto contribute to over half of its mass; under the [reasonable] assumption that the majority of the rock is contained in the core. This suggests that Pluto has a substantially large rocky core, with a thinner icy surface [7]. Though it is the only dwarf planet to have ever been considered a planet, Pluto may not be the largest celestial object of its kind in our Solar System, Eris is a close contender, so close in fact that our current technologies cannot determine which is larger [4]. It is known however, that Eris is more massive than Pluto by almost 30 percent [9].

Fig. 4: Percival Lowell

The discovery of Pluto began with the discovery of Neptune. By observing the perturbations in the orbit of Uranus, an astronomer by the name of Urbain Le Verrier was able to mathematically predict the existence of Neptune; his prediction was incredibly accurate, placing Neptune within one degree of its exact location. Using his prediction, astronomers managed to finally observe the planet less than a year after Le Verrier's final prediction [10]. This idea of using perturbations to find a planet sparked a sudden interest in the astronomical community. Many individuals began searching for another planet who's gravity was acting on Neptune and Uranus, at the time, this mystery planet was dubbed "Planet-X" [11]. It was not until 1906 that any significant progress in this idea would be made, at which point a man named Percival Lowell initiated the search for "Planet-X" that would eventually lead to its discovery. Using a 23 cm telescope, Lowell managed to plot several probable locations for Pluto. Though he never managed to successfully identify it, a photograph containing Pluto was taken at his observatory nearly 15 years before it was observed by the man credited with its discovery [12]. 

Fig. 5: Tracking Perturbations in Orbits

Fig. 1: Clyde Tombaugh

The actual discovery of Pluto is credited to an avid stargazer by the name of Clyde Tombaugh. Born to a family of farmers in 1906, Illinois, Tombaugh grew up in relative poverty. Though unable to afford a formal higher education, Tombaugh studied rigorously on his own and used his finely honed knowledge of geometry to build his first telescope at the age of 20 [1]. Dissatisfied with his own initial handiwork, as well as the available telescopes on the market, Tombaugh continued to improve his designs. Eventually, his work with telescopes would bear him much fruit; notably, the 23 cm reflector telescope he built in 1928 got him his job at the Lowell Observatory [2]. He had based his design for the telescope on the details listed in an issue of Popular Astronomy, that

Fig. 2: Tombaugh's 1928 Telescope

being said, Tombaugh was not just hired for his design, he was hired for his observations with his telescopes. While working at the observatory, Tombaugh would accomplish much, his first major breakthrough being the discovery of Pluto. Using a telescope almost 50% larger than his design in 1928, he tracked the motion of celestial bodies [3], and in 1930, discovered the ex-ninth planet near one of the locations predicted by Lowell [12].  The next 5 years would be eventful for Tombaugh, during that time he began his formal university education in astronomy at the University of Kansas and married his wife Patricia Edson. By 1939, Tombaugh had graduated with both his bachelors and masters degrees in astronomy from UofK and had two children with Patricia, all the while working on and off with the observatory [2]. Tombaugh spent  nearly the next entire decade after his graduation noting down the motions of over 30,000 celestial bodies as his last contribution to the Lowell Observatory, after which he decided to travel to New Mexico [3]. Tombaugh spent the rest of his working days at the State University there, teaching lectures and raising funding for students, he died in the comfort of his own home after 9 decades of life [1].

At the time of its discovery, Pluto was believed to be a planet with mass approximately equivalent to that of Earth, however, this belief was founded solely on the perturbations of Neptune's and Uranus' orbit [13]. Once Charon, a moon of Pluto, was discovered by James Christy in 1978 [upon noticing a bulge towards one side of a photo of Pluto] [17], more precise measurements of Pluto's mass could be made by observing Charon's orbit [18].

Fig. 6: Discovery of Charon

Fig. 7: Orbit of Charon

These new calculations yielded a surprising result, that Pluto's mass was over 500 times smaller than astronomers initially believed [4]. This new discovery began to instigate doubt among many, as to whether Pluto should be considered a planet at all, and ensured that Pluto could not be the cause of the perturbations in Uranus' orbit [13]. Then, in 2006 Pluto was officially demoted from the rank of planet due to the fact that it failed to possess one of the three defining properties of planets as proposed by the International Astronomical Union; that every planet must orbit the sun, have enough mass to gain a spherical shape and have enough gravitational influence to absorb all competitive bodies in its vicinity. It is clear that Pluto satisfies the first two of these requirements, earning it the title of dwarf planet, as it is spherical and orbits the sun, however Pluto is not massive enough to gravitationally overpower its similarly sized neighbors and as such, cannot be considered a planet [14].


Among these similarly sized neighbors to Pluto, are the Plutinos, objects belonging to the Kuiper belt at a very specific location in space. All Plutinos have an orbital distance roughly equivalent to Pluto's, in addition to a whole number

Fig. 5: Kuiper Belt

resonance with Neptune [15], and are named as such because Pluto was the first Plutino. Some other notable Plutinos are Orcus and Ixion, as they rank among the brightest of currently known Plutinos [16]. Ultimately, Plutnios differ from Pluto and other Plutoids, bodies similar to Pluto, in orbital motion and size, with Pluto having a 3:2 resonance with Neptune while other Plutinos  have resonances ranging from 3:2 to 2:1 [19]. Furthermore, Plutoids (other than Pluto) tend to be smaller than Pluto by quite a bit and are even occasionally thrown out of resonance under the influence of Pluto's gravity [15].



Works Cited:

1. http://www.achievement.org/autodoc/page/tom0bio-1 
2. http://www.space.com/19824-clyde-tombaugh.html
3. http://www.britannica.com/EBchecked/topic/598927/Clyde-W-Tombaugh
4. http://space-facts.com/pluto/
5. http://solarsystem.nasa.gov/planets/profile.cfm?Object=Pluto
6. http://nssdc.gsfc.nasa.gov/planetary/factsheet/plutofact.html
7. http://www.space.com/43-pluto-the-ninth-planet-that-was-a-dwarf.html
8. http://www.mikebrownsplanets.com/2010/11/how-big-is-pluto-anyway.html 
9. http://en.wikipedia.org/wiki/Eris_%28dwarf_planet%29 
10. http://www.universetoday.com/21621/who-discovered-neptune/
11. http://en.wikipedia.org/wiki/Pluto#cite_note-Tombaugh1946-40 
12. http://en.wikipedia.org/wiki/Percival_Lowell#Pluto
13. http://en.wikipedia.org/wiki/Pluto#Demise_of_Planet_X
14. http://www.loc.gov/rr/scitech/mysteries/pluto.html
15. http://scienceworld.wolfram.com/astronomy/Plutino.html
16. http://en.wikipedia.org/wiki/Plutino
17. http://jameschristy.weebly.com/james-w-christy.html
18. http://lasp.colorado.edu/~bagenal/1010/SESSIONS/17.PlutoCharon.html
19. http://cseligman.com/text/planets/plutoid.htm

Figures: 

1. http://www.achievement.org/achievers/tom0/photos/tom0-006a.gif
2. http://upload.wikimedia.org/wikipedia/commons/4/43/ClydeTombaugh2.gif 
3. http://www2.astro.psu.edu/users/niel/astro1/slideshows/class39/035-pluto-interior.jpg 
4. http://media.web.britannica.com/eb-media/63/133163-004-13A32A74.jpg 
5. http://i.space.com/images/i/000/018/506/i02/kuiper-belt.jpg?1339696229
6. https://solarsystem.nasa.gov/multimedia/gallery/Charon_Disc.jpg
7. http://spaceplace.nasa.gov/review/ice-dwarf/pluto_orbit.en.gif

Assignment 3

Sir Isaac Newton was the first man to prove mathematically that Kepler's Laws of nature follow from the square inverse force of universal gravitation [1]. Many astronomers and physicists at the time had the intuition that such an force may well exist, with most believing the force to be one of gravity, while some thought it was due to magnetism. When a Dr. Edmond Halley visited Newton for the first time, his purpose was to inquire about this exact problem. Much to his elated shock, Newton had solved the problem many years before. Amazingly, he had invented a fundamental form of calculus, necessary to prove the relation between universal gravitation and Kepler's Laws [2]. This was exciting news for Halley, for not only was it the solution to an incredibly difficult problem [in some sense an impossible one], but it was also an incredible breakthrough for all of physics and astronomy.

                                              Fig. 1 [9]

Newton's proof was groundbreaking. It demonstrated beyond a shadow of a doubt that the force of gravity was not only a very real thing, but also one that is universal, a force that applies to everything. In this way, Newton was able to cast into the fire, all the old notions of heavenly and earthly bodies being separate, as Earth must experience gravity in the same way as all the other planets [1]. Another more subtle reason for the significance of this proof, is that it was the spark to the great flame that was Newton's Principia. Formalizing the proof caused Newton to become borderline obsessed with the material and though Halley was only expecting a write up of the proof, he instead received a veritable goldmine of brilliant new discoveries [3]. These discoveries would eventually lead to the creation of Principia Newton's book containing all of his work on the laws of gravity. In other words, it was a book containing an entire field of physics that Newton birthed from this one idea [2]. In this way the initial spark of the square inverse force proof was far more important than just its direct corollaries. 

The creation of Principia was not exactly smooth sailing and very nearly never occurred. Interestingly, the  publication of the book  had far more to do with the personalities of two odd men [and one not-so odd] than any mathematical proof. Newton was a surly, sulky recluse, with far more angst built up than your average teenager; he immaturely held grudges and would not take criticism. Robert Hooke however, was the Joker to Newton's Batman; brash, brazen and with an ego to boot, Hooke was a jock of academia if there ever was one [4].  However, unlike the relationship between the Joker and his masked vigilante, Hooke had very little interest in Newton, though the latter had quite the grudge against the former. Years before he had begun working on Principia Newton had sent a paper to the Royal Philosophical Society about his thoughts on color and light. He received a reply containing nothing but scathing criticism from none other than Robert Hooke, who at the time was a member of the Society [2]. 

After a time, Hooke forgot all about his words to Newton, then one fateful day he and two other members at the Royal Philosophical Society would start a conversation that would set up Newton for a permanent place in history. Robert Hooke, Edmond Halley and Christopher Wren sat discussing the inverse square force and how it may relate to universal gravitation, they all agreed that it would be incredible to prove that one induces the other and/or visa versa [1]. With his ego bursting at the seams, Hooke adamantly proclaimed that he would formalize a proof of the relation within two months. Amused and intrigued Wren proposed a gambit, a battle of wits between Hooke and Halley. Two months time they were give, to produce a proof of the square inverse force relation and the winner was to receive 40 shillings [2]. 

As Newton was the first to prove the relation, naturally Halley and Hooke failed. Hooke, embarrassed by his inability to create a proof levied excuse after excuse, claimed his occupation with other more pressing endeavors; Halley however, was truly intrigued. He was an accomplished mathematician himself and though blunt, Hooke was no slouch either. Halley wondered who could solve a problem that he and Hooke could not [2]. Here we return to the beginning of the story, Halley, bested by the problem, sought aid in the form of Isaac Newton. Halley had heard that Newton was an incredibly brilliant mathematician working at Cambridge and upon his arrival, Halley was not disappointed. He did however, leave empty handed, as Newton had not yet formally written up his proof [3].

When Halley finally received word from Newton, after many months of waiting, he got much more than he asked. Newton had sent Halley the groundwork for Principia, something Halley immediately recognized as an incredible breakthrough [3]. He fervently urged Newton to publish his work. Being the hermit that he was, Newton was hesitant to publish for fear of criticism, though he pressed on in the continuation of his work. This trend repeated countless times, Halley would plea Newton to publish, but Newton would refuse yet strangely keep on working [2]. As word of Newton's work began to spread within the circle of Halley's associates, Hooke was naturally one who caught wind. Perhaps jealous of the fact that he himself was unable to solve the problem, he began putting down Newton's work, inventing mistakes and eventually even claiming that the proof idea was his to begin with. Infuriated with his claims in addition to the age old grudge, Newton decided to give Hooke a well deserved back hand to the face, in the form of Principia, the completed publication of all his work on the laws of gravity [1].

It is also possible that Hooke may have had more to do with the proof of the inverse-square law than it may seem initially. It is acknowledged that Hooke sent a letter to Newton about the possible inverse square relation of gravity, though it is unclear whether Newton came up with the idea first. Furthermore, in his Principia, Newton notes that the idea of the inverse square relation was independently discovered by Hooke, Wren and Halley, but this was little comfort to Hooke. [5]

His rivalry with Hooke was not the greatest and most earthshaking conflict that Newton had been a part of. Indeed his infamous controversy against Leibniz would result in Continental mathematics speeding ahead of their once close rival Britain [7]. Ultimately, the conflict arose when Newton and Leibniz both independently discovered Calculus. At first they coexisted happily, as Newton was not one to seek credit, however eventually, accusations from third parties spurred the two men into a furious debate. Leibniz desired the credit for his powerful notation, notation that is still for the most part used today, while Newton simply wanted to defend his honor as an honest man. Naturally, Britain sided with Newton, not only because it was his homeland, but also because all of the studies of calculus in Britain were Newtonian, many British mathematicians could not even decipher work done using Leibniz superior notation [6]. Unfortunately for the Brits, Leibniz notation would prove to be so far ahead of Newton's, that Continental mathematics grew exponentially, leaving Britain in the dust [7].

        Fig. 2 [12]                                                          Fig. 3 [11]                                                             

The events involving Newton, Leibniz, Hooke, Halley and Wren dig up some interesting topics for discussion. Who should receive more credit(?), someone who happens upon and sets up the ground work for a new idea or someone who fully realises that same idea; additionally, can it really be considered a discovery if said discover-er refuses to release the information to the public. I personally believe that the initial spark, the one who starts a new idea and sets the foundation for it should receive far more praise than one who simply fleshes out the details. I find it analogous to the general proof method of popular unsolved equations in the mathematics community. Often times, a well known mathematician will provide a road map of sorts to the solution of a difficult problem; they give a list of simpler ideas that if proven, give rise to the one in question. This can be thought of as the first realization of the idea. From there the rest is in some sense grunt work. Once the plans have been laid out, hundreds of mathematicians can now tackle these simpler problems, this being akin to the fleshing out of a theory. Without the initial intuition, the fleshing out could never occur, making it far more necessary, once the idea is out there, eventually there will be those who will flesh it out. Furthermore, with regards to who should claim credit for the discovery or generation of a theory or idea, I believe the glory should go only to those who share the knowledge. Glory, fame, credit and praise should be given to those deserving and how can one who hides his knowledge from all be deserving? They have not given anything, therein by the property of reciprocation, they deserve nothing. The first individual to publicly disclose the information should be credited, for they are the ones who actually contribute to the general knowledge of the public. 

Of course, as with every opinion, there are the extreme cases where credit should go to one who hides the information out of necessity. A simple example of this is how Alan Turing cracked the Enigma machine during WWII, but could not release said information at the time without jeopardizing the war effort [8].

References:

1.  http://en.wikipedia.org/wiki/Isaac_Newton
2.  http://faculty.wcas.northwestern.edu/~infocom/Ideas/newton.html
3.  http://www.pbs.org/wgbh/nova/newton/principia.html
4.  http://www.physics.org/interact/physics-evolution/text-only/03.html
5.  http://en.wikipedia.org/wiki/Inverse-square_law
6.  http://en.wikipedia.org/wiki/Leibniz%E2%80%93Newton_calculus_controversy
7.  Hyman, Anthony. Charles Babbage, Pioneer of the Computer. Princeton, NJ: Princeton UP, 1982. Print.
8.  http://en.wikipedia.org/wiki/Alan_Turing

Images:

     9.   http://hydrogen.physik.uni-wuppertal.de/hyperphysics/hyperphysics/hbase/forces/imgfor/isqg.gif
    10.  http://upload.wikimedia.org/wikipedia/commons/f/ff/Newton_-                                                                      _Principia_%281687%29,_title,_p._5,_color.jpg 
    11.  https://whatsnewwithnewton.files.wordpress.com/2008/10/dsc01537.jpg
    12. https://classconnection.s3.amazonaws.com/33333/flashcards/644875/jpg/ftc1-leibniz-a.jpg

Assignment 2

Nicholaus Copernicus was a polish mathematician and astronomer who was also a man of the church. Though he was not the first, Copernicus proposed an idea that would, eventually, revolutionize the entire field of astronomy as well as our understanding the solar system; he proposed a heliocentric model of the solar system. Dissatisfied with the geocentric model proposed by Pytolemy, Copernicus yearned for a model of the solar system that would please him, not with respect to accuracy, but with respect to simplicity and beauty. Copernicus ventured to create a system that he could intuitively feel was correct, a system where he could see the beauty of God's work.

Copernicus' model relies on several key ideas:

The planets revolve around the Sun, with Earth making a complete cycle in one year:

The most jarring and perhaps most important change that Copernicus made to the model of the solar system was making it heliocentric, that is he believed that it was Sun centered not Earth centered. As if only to add salt to the metaphorical wound, not only did Copernicus proclaim that the Earth was not special enough to be the center of the system, but that it was just like all the other planets and that they all revolved around the Sun.   

The Earth has a daily rotation around its tilted axis:

As opposed to the common belief at the time, that the starry sky revolved around the Earth to create night and day, Copernicus asserted that the actual cause was the rotation of the Earth around its axis with the stars as a fixed background. Furthermore he believed that the axis of the Earth was not parallel to a tangent of the Sun, but rather that it was tilted towards or away from the Sun and that the axis tilt would also make one full revolution per year.

The motions of the heavenly bodies are circular:

Copernicus believed that all the orbits of the heavenly bodies had to be circular. Circles are in some sense a perfect shape, circles have no beginning nor end and in this way they are eternal. As a man of God, Copernicus would not have himself believe that God would create anything less than such eternal perfection. Ironically, this belief would become one of the root causes for the inaccuracies in Copernicus' calculations and would make the acceptance of his ideas much more difficult. This is not to look down on Copernicus of course, in some sense it may have been necessary to accept this assumption; for it would have been unlikely for the Church to allow blasphemy in the form of elliptical orbits.

Ultimately, Copernicus lived in an age where proving his ideas would prove to be impossible. Not only were the tools and technology lacking, the philosophical implications of his work were so outrageous that he was heavily reluctant to share what work he had. The geocentric model of the solar system was so ingrained in the minds of the educated public that even suggesting otherwise was almost surely a one way ticket to ridicule.

    This of course, is not to say that there was no evidence to support Copernicus' claims. In fact, from the modern perspective, there is much more good in Copernicus' heliocentric model than the bad, however the physics at the time was not sophisticated enough to register relative correctness of his assertions.

    Copernicus' belief in the Sun centered system with an orbiting Earth had the very enticing benefit of easily explaining the retrograde motion of the planets, a mysterious phenomenon that was torturously worked into the Pytolemic model using complex and very specific epicycles. Retrograde motion is simply when another heavenly body, from the perspective of a viewer on Earth, reverses the direction of its orbit. In the heliocentric system if the planets orbit at different speeds, then whenever one passes another, the slower one would appear to experience retrograde motion from the perspective of the faster one. Furthermore, the tilt of Earth's axis while revolving around the Sun would explain the seasons, since the area of the Earth tilted towards the Sun experiences more sunlight during the day, it is warmer producing summer and visa versa for winter. 

    In the end, Copernicus decided that these benefits alone were not enough to warrant a publication of his ideas, and it was not until a student of his named Rheticus insistently urged him to release his work that it would finally be seen by the eyes of the public. Unfortunately, this most important piece of knowledge that Copernicus imparted upon the world [in the form of the book De Revolutionibus] would fly so far below the radar it was practically a resident of the Marianas Trench. This may in part be due to the fact that Copernicus' model did not provide significantly improved results in terms of accuracy over the Pytolemic model, as he stubbornly held onto the idea of epicycles. This led to many academics passing off Copernicus' system as a mathematical tool as opposed to a physical reality. It would not be until hundreds of years later that the heliocentric model would come to be accepted.

    Though Copernicus started the revolution towards heliocentrism by being the first individual to combine both the mathematics and the physics of such a system, the ideas he incorporated into his model were actually much older. The idea that the Earth was not stationary in the universe was first hatched by Philolaus of Magna Graecia, though he did not specifically believe in a heliocentric system. Before Philolaus the was  Aristarchus of Samos, the earliest recorded individual to propose a heliocentric system, back in the days of Aristotle who naturally and promptly stomped the idea back into the supposedly stationary Earth. Furthermore, Aristarchus had a surprisingly significant following so it is probable that at least a few of them worked on the heliocentric system; unfortunately, if such work ever existed, it has long been lost. Beyond the ancient astronomers, a number of Medieval astronomers also toyed with similar ideas as Copernicus including Nicholas of Cusa, who queried whether or not the Sun was the center of the universe. Another was Nicole Oresme, who was also a man of the Church. He believed that the Earth had an axial rotation to cause night and day prior to Copernicus. Even more generally, outside of Europe, there were quite a few astronomers in Indian and Islamic regions who worked on results involving the motion of the Earth and position of the planets. Given the surprisingly large number of individuals who worked on heliocentrism before Copernicus, it is almost miraculous that it took so long for the idea to catch on. Such is the power of the inertia of belief.

    In the end, what is likely the most important belief held by Copernicus was his belief in the Sun being the unmoving center of the Solar System. This fundamental idea was the main concept of Copernicus' system, and without a solid foundation he could not have put his entire model together. It was his precise fusion of mathematics and physics that really pushed the idea of heliocentrism, giving it the initial jolt of energy needed to eventually overtake geocentrism. The spinning of Earth around its axis, though interesting in itself, is not fundamentally a key part of heliocentrism, furthermore, the Earth orbiting the Sun like the other planets is not a hard leap to make, once you assume that the Sun is the center. Ultimately, it is the foundational idea that should be most important, the other two points are interesting and related but are not as vital. Fundamentally the importance is in the name of system itself, helio meaning Sun and centric meaning centered at.

Resources:
-http://en.wikipedia.org/wiki/Philolaus
-http://en.wikipedia.org/wiki/Georg_Joachim_Rheticus
-http://en.wikipedia.org/wiki/Copernican_heliocentrism
-http://starchild.gsfc.nasa.gov/docs/StarChild/whos_who_level2/copernicus.html
-http://en.wikipedia.org/wiki/Heliocentrism
-http://www.space.com/15684-nicolaus-copernicus.html
-http://astronomy.nju.edu.cn/~lixd/GA/AT4/AT402/HTML/AT40203.htm
-http://csep10.phys.utk.edu/astr161/lect/retrograde/copernican.html

Images:
-http://www.splung.com/cosmology/images/retro.gif
-http://www.icr.org/i/articles/imp/imp-261.gif
-http://www.mhhe.com/physsci/astronomy/fix/student/images/04f08.jpg
http://www.sussexvt.k12.de.us/science/The%20History%20of%20the%20World%201500-1899/Copernicus%20and%20the%20heliocentric%20solar%20system_files/image005.jpg
 

   

    

Assignment 1

Eratosthenes was a Greek astronomer, mathematician and geographer among other things; his jack-of-all-trades abilities earned him the title of Pentathlos, the "All-Rounder". And rightly so, he made significant contributions to all of the above fields, from his estimation of the size of the Earth, to his solution for Doubling the Cube to his writing of Geographika.

    As an astronomer and scientist in general, Eratosthenes made quite a few important measurements and calculations. Not only did he calculate the circumference of the Earth, but also the tilt of its axis, as well as the diameter of the Sun (though this last measurement was significantly less accurate than the former).

    Eratosthenes also furthered mathematics by creating a method to look for prime numbers, which is still one of the most important area's of Number Theory even today. His most touted mathematical accomplishment however, is his solution to the Doubling of the Cube: attempting to construct the edge of a cube whose volume is double that of a given cube.

    To call Eratosthenes a geographer is a little vacuous, in that he was the father of geography. He wrote a vast trilogy of encyclopedias called Geographika, which encompassed many details of the known world at the time, including climate zones as well as the division of the earth via meridian and parallel lines.

                                                       Meridians and Parallels

    Despite his many contributions to the scientific and mathematical community, Eratosthene's greatest success was probably his estimation of the circumference of the Earth. To accomplish this astounding feat, he used the power of shadows. Eratosthene was told that looking down a well in Syene at noon during the summer solstice would result in one's shadow blocking out the reflection of the Sun at the bottom of the well. Upon hearing this, he deduced that, the Sun must be directly overhead. Then by using a gnomon, the part of a sundial that casts the shadow, at noon in Alexandria he observed the length of the shadow. Using this information, and some trigonometry, Eratosthene deduced that Alexandria must be roughly 7.2 degrees from Syene. Since 360/7.2 = 50, and Alexandria is roughly 800 km from Syene, Eratosthene estimated the circumference of Earth by multiplying 50 x 800 km = 40000 km (of course he did not use km as his unit of measure).

    The accuracy of this method is truly astonishing, with the true circumference of Earth being 40008 km (meaning the relative error of his calculation is only 8/40008 = 0.00019996 or 0.02% approx, although depending on the exact value of his unit the stade).

    This is an incredible accomplishment and a great success, given the number of variables, estimates and assumptions that he had to make, such as the distance from Syene to Alexandria and the assumption that the Earth was spherical.

References:
- http://www.famousscientists.org/eratosthenes/
- http://www-history.mcs.st-and.ac.uk/Biographies/Eratosthenes.html
- http://www.britannica.com/EBchecked/topic/191064/Eratosthenes-of-Cyrene
- http://astrosun2.astro.cornell.edu/academics/courses//astro201/eratosthenes.htm
- http://www.encyclopediaofmath.org/index.php/Duplication_of_the_cube

Images:
-https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfnpxj1PaCL_DEPDvYWdLRGThOAgov3xb1yVc3ee-HKbrAlvupaANWaiDU5nNdzgLFCrGVPU_kayGPacrtvjnUS3SAm_aHNAEDYUkcs6p7hyphenhyphenpylT8GQvz5i5NpdW5QMC_raizPznfHt_SE/
 600/Doubling%2Bthe%2BCube.png
-https://regardingmeasurement.files.wordpress.com/2010/10/eratosthenesmap.png
-http://astrosun2.astro.cornell.edu/academics/courses//astro201/eratosthenes.htm