Assignment 6: Modern Astronomy

Sourced From: http://www.phys-astro.sonoma.edu/brucemedalists/hubble/

History of the Hubble Telescope

Since the beginning of time mankind has been attempting to investigate the cosmos but has always been limited by the capability of human vision and thus giving humans the inability to understand the universe. Classical astronomers such as Copernicus , Galileo, and Kepler from the 16th and 17th century had the advantage to use the telescope, enhancing their vision also giving them the ability to observe and understand the universe. Telescopes have evolved over the years being bigger and better allowing us to collect data about planets, stars, galaxies. With spectroscopy and photography make great strides, telescopes have become more versatile, sensitive, and given more power for discovery.



In 1924, an american astronomer Edwin Hubble was able to prove to the rest of the world how much we really didn't know about the universe. At the time during the 20th century, most of world had their heads wrapped around the idea that universe consisted of only one galaxy, our milky way galaxy. Edwin Hubble set out on an expedition to Los Angeles, California atop Mount Wilson and using a 100 inch hooker telescope, he was able to observe billions of other galaxies and forever changing our perception of the universe. He also noticed that almost all the galaxies he had observed were moving away from each other. The supported the Big Bang theory as it suggested that the universe was indeed expanding.

Many astronomers like Edwin Hubble were able to make amazing observations through telescopes and observatories but they all faced similar critical issues disabling them from obtaining a clear view of the universe, which was the earth's atmosphere. Due to the physical make up of earth's atmosphere visible light was often blurred and it absorbed
many other wavelengths of lights making the observations of ultraviolet, gamma rays, x-rays, etc virtually impossible. [1]

In 1923, a German astronomer by the name Hermann Oberth wrote about the benefits of a telescope in space. Hermann Oberth was a founding father in space travel and he was able explain how it was possible for a telescope to be propelled into the earth's orbit using a rocket. In the late 1940's and early 1960 when NASA went on expeditions into space they decided to send scientific instruments to collect data such as balloons, smaller rockets, satellites. These additions to the space crafts provided enough evidence of how much was still to be discovered. In 1968 and 1972 NASA was able to launch two successful satellites which were designed to observe stars. These satellites produced a heap of information and the support for a space telescope grew. NASA began to organize a team of scientists to begin designing this telescope and the instruments needed in 1973 and in 1977 Congress finally authorize the funding for the project.

Many other organizations suddenly offered to be apart of the project. Marshall Space Flight Center located in Huntsville, Alabama was assigned the duty of designing, developing, and constructing the the telescope. A Maryland based flight center by name Goddard Space was responsible for the development of the scientific instruments and ground control center. Perkin Elmer Corporation was chosen to develop the optical system and guidance sensors. The European Space Agency agreed that they would furnish the solar arrays and one of the scientific instruments.

In 1985 the ground control center for the the telescope was established and its purpose was to compute computer commands and relay it to the telescope and in turn the observation data received is formatted into common data which is usable. The actual construction and assembly of the telescope was very difficult and dragged out for almost a decade. The precision ground mirror was completed in 1981 and the remaining of the optics was delivered for integration into the satellite in 1984. The assembly of the actual space shuttle that was going to the launch the telescope in space was an entirely different process that took a lot of time in it self. The assembly of the space shuttle was completed in 1985.



Sourced From :http://www.spacetelescope.org/about/

In 1986 the original launch for the telescope was scheduled but disaster stuck due to the Challenger accident. NASA's space shuttle, the challenger, broke about 73 seconds in to it's flight causing the death of several NASA astronauts. Due to the incident, the launch for the telescope was postponed but this gave engineers a chance to re evaluate and conduct intensive testing on the telescope. In 1989 the telescope was shipped to the Kennedy Space Center in Florida. In April 24, 1990 the telescope was finally launched aboard the STS-31 mission of the Space Shuttle Discovery.


Sourced From: http://blogs.sacbee.com/photos/2011/03/space-shuttle-discoverys-final.html

The Hubble Space Telescope was designed to be in space for 15 years it was said to be approximately 10 times better than any telescope on earth. However, within a few months a major defect was detected aboard the telescope. The Hubble's main mirror had an optical distortion which was due to an incorrect shape in the mirror.  The edge of the mirror was to flat by 1/50th the width of a human hair and this caused a blur in the images of all celestial objects. Although the camera equipped on the Hubble telescope could produce pictures better than telescopes on ground.

The huge advantage to Hubble telescope was that the parts were serviceable and interchangeable making it easy to change failed parts or update the telescope. The problem NASA faced was that the lens could not be removed but optics could be fixed by placing a corrective lens. NASA had also planned to service the telescope so this wasn't a problem.

NASA had to properly train 7 selected astronauts and had to practice the procedure for close to year and a half. Their duty was to install the Wide Field/Planetary Camera and the Corrective Optics Space Telescope Axial Replacement. On December 2, 1993 the crew of astronauts launched into space with the challenge of installing and fixing the Hubble Telescope lens. The was successfully able to install the Wide Field/ Planetary Camera and replaced the high speed photo meter with the Corrective Optics Space Telescope Axial. They also installed a new computer co-processor which allowed the telescopes computer memory and processor to process information much faster.


Sourced From: http://forum.xcitefun.net/unbeatable-pics-of-repairing-of-hubble-telescope-t31770.html

The Hubble Telescope has allowed scientist to understand the universe far more and the technology that was produced from it has also had its impact. Non surgical breast biopsy techniques developed using imagining Charge Couple Devices which were originally supposed to be used for the Hubble Telescope. The technology allows doctors to detect lumps in women's breast.

The Hubble Telescope was designed and expected to last for 15 years to come and 3 additional servicing missions are planned to keep the Telescope running without compromises. Already due to these service trips the Hubble Telescope has been able to add on The Near Infrared Camera and Multi-Object Spectrometer, The Space Telescope Imaging Spectrograph, and an Advanced Camera. [2]

At the current day NASA's Hubble Telescope is 23 years old and is expected to last until 2018. NASA has been able to preserve the iconic Telescope and prolong its expected life dramatically. NASA now has plans for the Hubble Telescope's successor and it's reported to be on track with production. It is known as the as the JWST Telescope set to be launched in 2018. [3]

Great Discoveries of the Hubble Telescope 

1. Dark Matter
]
sourced from: http://en.wikipedia.org/wiki/Dark_matter

Dark matter makes up roughly 23% of the universe and Hubble Telescope has helped construct the largest 3D map. Scientists have a good idea now how the dark matter is distributed around the universe. This has helped show the clumps and growing clumps of dark matter over time and the normal gravity caused by it. By better understanding how dark matter behaves, scientist can understand further what is actually is.

2. Alien Worlds

sourced from:http://newt.phys.unsw.edu.au/~cgt/planet/AAPS_Home.html
The Hubble Telescope has been used to find many extra solar planets and there has been close to 400 extra solar planets discovered. The Hubble Telescope has also allowed scientist to figure out the chemical composition of the atmospheres on exo-planets and imaging of visible light. This is important because having knowledge about other planet that possibly in habitable can lead to us knowing if other life forms exist.

3. Age of the Universe

Sourced From: http://www.karlremarks.com/2013/04/study-confirms-that-lebanon-is-indeed.html

The age of the universe has always been a mystery and it was impossible to know how long ago the beginning of time actually was. The Bubble Telescope has been able to narrow down the rate of expansion in the universe. With the Hubble's calculations, the age of the Universe has now been estimated to roughly 13.75 billion years old. This is important because it allows scientists to model our universe and understand how it has evolved over this time frame. Also it helps with understanding other seemingly unrelated cosmic parameters such as the mass of neutrinos. [4]


Sources
1. http://www.nasa.gov/mission_pages/hubble/story/the_story.html
2. http://quest.nasa.gov/hst/about/history.html
3. http://www.extremetech.com/extreme/202282-nasa-confirms-hubble-telescope-successor-is-on-time-on-budget-for-2018
4. http://www.space.com/17-amazing-hubble-discoveries.html

Discovery of the Expanding Universe

For many centuries, scientists and astronomers have been battling over the question of how old and big the universe is? The ancient Greek civilizations came to the realization of how difficult it was to vision a infinite universe and what it would look like.

Georges Lemaitre

Sourced From: http://www.physicsoftheuniverse.com/scientists_lemaitre.html

Georges Lemaitre was a catholic priest and a Belgium cosmologist. He was born in 1894 in Charleroi, Belgium and even as a young boy he had a passion for science[1]. He completed his primary education at College du Sacre-Coeur which was located in Charleroi and later wen on to study at the catholic university of Louvain focusing on civil engineering at the age of 17[2]. As World War 1 began it unfortunately interrupted his education as he served as a artillery officer and witnessed the first poison gas attack in history. After the war he returned back to school and decided to focus his studies theoretical physics[1]. During the same time of his schooling he also worked on becoming a priest and by the year 1923 he was ordained a catholic priest. After being ordained he continued on in school to graduate studies in Astronomy at University of Cambridge which is located in England[2]. In 1924 he migrated to America and studied at the Massachusetts Institute of Technology. In the 1925, at the age of 31[1], Georges Lemaitre became a professor at the University of Louvian where he originally completed his studies at. Due to an injury he sustained in war, he was able secure his position as a teacher and he had a strong passion to teach[2]. Lemaitre had very strong religious beliefs but his love for science was that much stronger[3]. Einstein had already theorized about General Relativity and in 1927 Georges Lemaitre published a research paper that went unheard of but it went in depth in a solution to the equations of General Relativity specifically the case of an expanding universe.

Unfortunately, a Russian scientist by the name Alexander Friedmann had already derived he solution prior in 1922 which is 5 years earlier. Although Friedmann had a higher interest in the physics and mathematics of the solutions and possible expanding and contracting universes theoretically. Friedmann did not apply his solution to the physical universe. However, Lemaitre produced his solution with the sole purpose of explaining the cosmos and he realized that his solutions predicted the expansion of the real universe.

Edwin Hubble, another famous astronomer, in 1929 published his official report after discovering a redshift in the light emitted from distant galaxies further proving Lemaitres expanding universe theory. Lemaitre published his research in 1927 but it wasn't until astronomer Arthur Eddington who widely publicized the theory on again in 1931 by translating it and republishing it in English.

Later that year, Lemaitre further explored into our expanding universe and came to bold proposal that the universe originated at one point as a single particle. This theory came to be known as " The Big Bang Theory"

This is theory had some friction with other scientist when it was initial proposed. Einstein did not approve of the theory initially because he didn't agree with the physics but he did accept the argument that the static model that he proposed could explain indefinitely into the past. Although the theory caught on in later years by the media and Lemaitre obtained much praise for it.

Lemaitre eventually gave up his teaching career and retired but still continued to work on his calculations and developed an interest in computer language and sciences. He passed away on June 20, 1966 after the discovery of cosmic radio microwaves which further proved his theory[2].


Friedmann

Sourced From: http://www.physicsoftheuniverse.com/scientists_friedmann.html

Alexander Friedmann was born on June 16, 1888 in Russia and he known as a cosmologist and mathematician. Through out his career he developed many model that explained the universe and its development. He is also widely known in the scientific communtiy for his solutions to Albert Einstein's general relativity equations which provided early evidence of the Big Bang Theory and steady state model of the universe.

Alexander excelled in his studies both in highschool and at Saint Petersburg State University. Friendmann studied mathematics in university from 1906 to 1910 as well as attending Paul Ehrenfest's modern physics seminars. These seminars discussed in great detail about quantum theory, relativity, and statistical mechanics. In 1914 he graduated and received his master's degree in applied and pure mathematics.

While completing his graduate studies in 1913 he was given a position at the Aerological Observatory in Saint Petersberg, which was known for meteorology. At this observatory he studied theoretical meteorology and took part in many expeditions around the earth skies making meteorological observations. As Friedmann graduated, that same year the world war 1 had began and Alexander Friedmann decided to volunteer for the Russian army, specifically in the air force as a bomber pilot. After 1915 he decided to lecture pilots on the topic of aerodynamics and later taught mathematics and mechanics at Petrograd University. Once a professor he became very aware with Einsteins Theory of Relativity and in 1922 he discovered the solutions to the field equations of the expanding universe[4]. Einstein did not approve of the calculations that Friedmann made and sent a letter to the German Physics Journal saying that Friedmann's work was suspicious. Afterwords Friend sent Einstein proof of his work in a detailed letter and six months later Einstein wrote in the journal and apology saying that he himself made mistakes in his calculations.[5]

Friedmann published papers in 1924 which demonstrated 3 models of the universe with positive, zero, and negative space time curvature. These cosmological models helped explain general relativity and the big bang theory. In 1924 he also became a director of Main Geophysical Observatory in Leningrad where he met George Gamow who was a Russian physicist and cosmologist and he stuided under Friedmann for a number of years. Unfortunately for Alexander Friedmann on September 16, 1925 he was diagnosed with typhoid fever and suffered a tragic death[4].

George Gamow

Sourced From: http://www.physicsoftheuniverse.com/scientists_gamow.html

Geogre Gamow, born on March 4, 1904, was theoretical physicist who studied under Alexander Friedmann. He had many predictions about the cosmic microwave background radiation and he explained about the levels of hydrogen and helium in the universe. The explanations provided important evidence and support to the Big Bang Theory.

In 1948, George Gamow published a research paper that was very important in the world of theoretic physics. His paper about the universe was entitled "The Origin of Chemical Elements" and in it he explains the present levels of the element hydrogen and helium saying that they made up 99% of all matter in the universe. He also mentioned that this make up of the universe was due to the reactions that occured in the initial stages of the Big Bang. In the same paper he published a prediction of the cosmic microwave background radiation saying that after billions of years the radiation filling the universe would have cooled down to about 5 degrees above absolute zero. Surprisingly, in 1965 when cosmic microwave background radiation was accidentally discovered, that they were 2.7 degrees above absolute zero which was very accurate to the predictions.[6]


3 models of the Universe

Soured from: http://abyss.uoregon.edu/~js/cosmo/lectures/lec15.html

Positive Curvature - Spherical

Negative Curvature - Hyperbolic or saddled shape

Zero curvature - flat

According to the Friedmann Equations the shape of the universe depended on the overall mass / energy in relation to critical density [5]

Sources:

1. http://www.amnh.org/education/resources/rfl/web/essaybooks/cosmic/p_lemaitre.html
2. http://www.pbs.org/wgbh/aso/databank/entries/dp27bi.html
3. http://www.physicsoftheuniverse.com/scientists_lemaitre.html
4. http://www.physicsoftheuniverse.com/scientists_friedmann.html
5. http://www.decodedscience.com/alexander-friedmann-unsung-hero-of-modern-cosmology/19423
6. http://www.physicsoftheuniverse.com/scientists_gamow.html
7. http://abyss.uoregon.edu/~js/cosmo/lectures/lec15.html

The Changing Pluto

History of Pluto



sourced from: http://interviewly.com/i/nasas-new-horizons-oct-2014-reddit

Pluto was once recognized as one of nine major planets orbiting the sun but is now only considered as a dwarf planet. In modern day astronomy, Pluto is seen as one of the largest members of the Kuiper Belt [1]. The Kuiper belt is a disc shaped ring and its a region of icy objects located billions of kilometers away from the sun [2].

Pluto was once classified as the ninth planet in our solar system therefore being extremely far away from our earth. Due to the enormous distance, there's is little information about the planets size or surface condition. According to the article in www.space.com, Pluto is estimated to have a diameter equivalent to less than one fifth of the Earth. It guesses that Pluto's surface probably contains ices of various composition such as methane and nitrogen at the surface, a mantle of water ice under the surface, and a rocky core at the center. NASA's hubble space telescope has been able to provide observations and evidence of the different compositions of gas.

This Hubble Space telescope from NASA has shown that Pluto has a very eccentric orbits therefore creating huge variance in distance from the sun as well as penetrating the planet Neptune's orbit. As Pluto orbits closer to the sun, the ice on the surface of the planets temporarily melts and forms a thin atmosphere around the planet containing mostly nitrogen and methane. Due to Pluto's extremely low gravity causes the temporary atmosphere to extend higher than earths atmosphere. While Pluto has its atmosphere, it can apparently experience strong winds. Once Pluto orbits further away from the sun, it's atmosphere beings to freeze and eventually disappears. Pluto apparently has one of the most cold surfaces in the entire solar systems with approximately 375 degrees Fahrenheit below zero. Astronomers also discovered that Pluto had a very large moon and they have a very short distance between each other in terms of other planets and their moons.[1]

Discovery of Pluto


Sourced by: http://sciencefiction.com/2014/10/12/pluto-may-just-fact-planet/

Pluto was discovered less than 100 years ago, which is very recent in terms our known existence. An astronomer at the Lowell Observatory in Flagstaff, Arizona by the name, Clyde W. Tombaugh, discovered the planet on February 18, 1930. Originally, it was an American Astronomer by the name Percival Lowell who proposed that there was another planetary body somewhere in the range of Neptune and Uranus because he had observed something affecting the orbits of the two planets have been the gravitational pull of something large. Lowell referred to the large body as "Planet X" in 1905 and unfortunately died in 1916, sadly never being able to discover the planet.[3]

More than a decade later the Lowell Observatory decided to continue on with research of "Planet X" done by Percival Lowell, the founder of the observatory. Clyde W. Tombaugh was hired to discover the existence of this unfounded planet using a 13-inch telescope that the Observatory had built just for the purpose of it's discovery. Tombaugh had to contribute an immense number hours and hard work before discovering the planet Pluto. On February 18, 1930 Tombaugh was able to examine the photographic plates that were outputted by the telescope. The Lowell Observatory was not ready to announce the discovery until more research took place and on March 13,1930, which would have been Percival Lowell;s 75th birthday, they confirmed the discovery.[3]

The "Planet X" eventually needed a name and was chosen by an  11 year old girl, Venetia Burney. The name "Pluto" often refers to the roman god of the underworld which fit due to the similar surface conditions of the planet. The name also hon ours Percival Lowell because the first two letters in "Pluto" and his initials. [3]

Sourced From :http://www.icollector.com/Clyde-W-Tombaugh_i11385124

Clyde W Tombaugh also discovered many galaxies and clusters of stars with this improved telescope. He also made various observations of the surfaces on Mars, Venus, Saturn, Jupiter, and the moon. After the discovery of Pluto, Tombaugh attended the University of Kansas and going on to receive his M.A. in astronomy. After graduation he returned back to the observatory to continue his astronomical work and he cataloged over 30,000 objects in the universe. He also went on to teaching at a few colleges and university. Even when he decided to retire he still continued to observe the sky and advise the university. [4]

As mentioned before the telescope used in the discovery of Pluto at the Lowell Observatory was very advanced and it was equipped with photography. This camera within the telescope was used to take two pictures of the sky on various days. They also used a device known as a blink comparator which switch views between pictures rapidly. In these pictures, the stars and galaxies were stationary but orbiting objects could be identified due to the motion across the sky. Apparently, Clyde W. Tombaugh close to 7000 hours analyzing each pair of photos which contained 150000 to 1 million stars in a single photo. After precise measurements and study, Tombaugh was able to identify the movement of one particular object[5].


The discovery of Pluto was not a true theoretical predication based on celestial mechanics. The Titus Bode law explained the approximate distance from planet to planet going away from the sun. Using Newtonian physics and the Titus Bode law, the planets and their distances from each other made sense. Astronomers noticed that there was a supposed "missing planet" between mars and Jupiter that should be in place rather than a gap. Guiseppe  Piazzi in  1801 discovered Ceres, a large asteroid/ minor planet, and many other minor planets forming and asteroid belt. Mathematical astronomers used the Titus bode law to explain the gap between mars and Jupiter. The law also pointed out that there should another planet after Jupiter and due to this theory astronomers later found Uranus.[6]

Le Verrier, another famous astronomers noticed that the orbit of Uranus didn't match its theorized paths as well as Neptune which was found due to this reason very reason. At the time Le verrier used Titus Bode Law to predict the paths of Neptune and Uranus and published his predictions. However with modern day science we figure out that Uranus, Neptune, and Pluto do not follow the Titus Bode law, therefore proving that Le Verrier and other astronomer's findings completely luck. Even the discovery of Pluto was due to luck.[7]

Changes to Plutos Discovery

Originally, Pluto was thought to be a similar size as the earth and therefore there was no question about it being a ninth planet. It was considered as the ninth planet in our solar system for 70 years. In 1978 astronomers discovered Pluto's largest moon, Charon. With this discovery they were able to approximate Pluto size at around 2400 km, which would make it the smallest planet in our solar system but the largest object past the orbit of Neptune. With advances in technology and observatories, astronomers were able to find many other celestial objects similar to Pluto and its moon in the Kuiper belt. There are approximately 70000 icy object with the same composition as Pluto within this Kuiper belt that extends out from the orbit of Neptune to 55 AU.

Astronomers had to decide on what exactly was the definition of a planet. There are three criteria that a celestial object has to meet to be considered a planet:
1. It needs to be in orbit around the sun
2. It has to have a strong enough gravitational pull to form itself into a sphere
3. It needs to have a clear dominant gravitational orbit

Unfortunately, Pluto did not meet the third criteria because it is in orbit along with tens of thousands of other objects in the kuiper belt. Astronomers decided that any celestial objects that also dont meet the third requirement is considered a dwarf planet. [9]


Plutinos

"Pluto and Eris were the first worlds to be classified as Plutoids, a special class of dwarf planets that orbit our sun in the icy region beyond the orbit of Neptune"[10]. Terrestrial planets are small rock and metallic objects orbiting close to the sun and Jovian planets are large objects with low density mainly made up of liquid composition, gases, and ices. Pluto is definitely not Terrestrial and is similar to a Jovian planet but because of its size cannot be classified as Jovian either. Due to this problem, astronomers have decided to create a new classification known as "Plutoids" to classify other objects like Pluto. Plutinos is a sub category of Plutoids but they are distinguished by the distinct way they orbit the sun. Pluto orbits in a perfect whole number ratio of 3 to 2 for the length of its orbital period compared to that of Neptune. Plutinos all share a similar ratio in orbital period either 3 to 2 or 4 to 3 or 2 to 1 but in any case it's a ratio of whole number.[10]




Sources (footnotes)

1. http://www.space.com/43-pluto-the-ninth-planet-that-was-a-dwarf.html
2. http://solarsystem.nasa.gov/planets/profile.cfm?Object=KBOs
3. http://history1900s.about.com/od/1930s/qt/Pluto.htm
4. http://www.britannica.com/EBchecked/topic/598927/Clyde-W-Tombaugh
5. http://ircamera.as.arizona.edu/NatSci102/NatSci102/lectures/pluto.htm
6. http://www.space.com/19824-clyde-tombaugh.html
7. http://www.fromquarkstoquasars.com/that-pluto-controversy/
8. http://www.splung.com/content/sid/7/page/solarsystem
9. http://www.universetoday.com/13573/why-pluto-is-no-longer-a-planet/
10. https://solarsystem.nasa.gov/multimedia/display.cfm?IM_ID=6823

Assignment 3: Universal gravitation. Discovery disputes

According to the The Biography.com, Sir Issac Newton was born on January 4, 1643, in Woolsthorpe, England and was a very established physicist and mathematician, also credited as one of the great minds of the 17th century Scientific Revolution. He published "Philosophiae Naturalis Principia Mathematica", a book that has been referred to as the single most impacting book on physics. Unfortunately, on March 31, 1727 Newton passed away in London.[1]

Sourced From: http://www.heisnear.com/SirIsaacNewtonPIC400.jpg

In earthobservatory.nasa.gov it explains that Kepler was charged with the task of defining the orbit of mars. Kepler was able to figure out three laws that explained the motion of planet's orbits using a lot of Tycho Brahe's research and observations. Kepler noted that there is a precise mathematical relationship between the distance from the sun and a planet and also the amount of time it takes to revolve around the sun, as defined in his third law. Kepler's third law inspired Newton who also discovered three laws that explains motion.[2]



In the online article "Sir Isaac Newton: The Universal Law of Gravitation'', there is a mathematical proof of Newtons modification of Kepler's Laws. It explains that Newton realized that the both sun and planets orbited around the common center of mass.[3]

The article, Newtonian Gravitation and the Laws of Kepler, further explains how Newton's Laws corrected Kepler's Laws. It explains the Kepler's and Newtons Laws together imply that planets travelling in an ellipitcal orbit around the sun are:
1. heading countinously around the sun
2. proportional to the product for the mass of the planets and mass of the sun
3. inversely proportional to the square of the distance between the planets and sun[4]

Newton goes on to precisely form the Universal Gravitational Law.

Sourced from: http://csep10.phys.utk.edu/astr161/lect/
history/newtongrav.html#universal

An article online, "Imagining the Universe", show what Kepler's third law look like when applied with Newtons Laws. It states the Kepler's third law expresses:


 Sourced From: http://astro.physics.uiowa.edu/ITU/glossary/keplers-third-law/

The period (P, measured in years) squared is approximately equal to the size of the orbit (a, measured in astronomical units) cubed.

Newton then modifies Kepler's 3rd law by applying his laws of motion and law of gravity so that it takes the form:

Sourced From: http://astro.physics.uiowa.edu/ITU/glossary/keplers-third-law/

Newton figures out the precise mathematical relationship where, M1 and M2 are the masses of the two orbiting objects.[5]

This discovery by Newton was an enormous contribution to the Scientific community and an huge scientific breakthrough. Prior to this Newton had already discovered his three laws of motion on earth and by applying his laws with Kepler's Laws, he was able to unify his laws of motion to not only terrestrial applications but also celestial application. He came to the conclusion that the laws of motion and gravity not only apply to the objects on earth but also to the planets. This was also important because he further proved Copernicus's heliocentric theory as well, with the sun in the center and other planets including earth revolved around it.[4] 

Assignment 1: Eratosthenes

Eratosthenes

Eratosthenes, born in 276 BC out of the town Syene, was an ancient Greek scholar who was educated in philosophy and mathematics. He is most well known for his discovery on the measurement of the circumference around the earth with great accuracy. Some of his other achievements include producing the first map of the world which included meridian line and parallel lines. He was able to mark the equator and the size of the polar zones. He also invented geography which we use today. He invented an efficient method to discover prime numbers. Overall Eratosthenes was a well rounded scientist and contributed a lot to our civilization.