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Wednesday, May 15, 2013

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Tuesday, May 14, 2013

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C.V. Raman: The Raman Effect



"I propose this evening to speak to you on a new kind of radiation or light emission from atoms and molecules." With these prophetic words, Professor C. V. Raman of Calcutta University began his lecture to the South Indian Science Association in Bangalore on March 16, 1928. Raman proceeded to describe a discovery that resulted from a deceptively simple experiment. Conducted far from the great centers of scientific research in the Western world, the results would capture the attention of scientists around the world and bring many accolades, including the Nobel Prize, to their discoverer. "

Raman’s Fascination with Light Scattering

Educated entirely in India, C.V. Raman made his first trip to London in 1921, where his reputation in the study of optics and especially acoustics was already known to the English physicists J. J. Thomson and Lord Rutherford, who gave him a warm reception. Raman's specialty had been the study of the vibrations and sounds of stringed instruments such as the violin, the Indian veena and tambura, and two uniquely Indian percussion instruments, the tabla and the mridangam.

But it was the return trip from London to Bombay aboard the SS Narkunda that would change forever the direction of Raman's future. During the fifteen-day voyage, his restless and probing mind became fascinated with the deep blue color of the Mediterranean. Unable to accept Lord Rayleigh's explanation that the color of the sea was just a reflection of the color of the sky, Raman proceeded to outline his thoughts on the matter while still at sea and sent a letter to the editors of the journal Nature when the ship docked in Bombay.

A short time later Raman was able to show conclusively that the color of the sea was the result of the scattering of sunlight by the water molecules. Ironically, it was exactly the same argument that Rayleigh had invoked when explaining the color of the sky—the blue was the result of the scattering of sunlight by the molecules in the air.

Raman was now obsessed with the phenomenon of light scattering. His group in Calcutta began an extensive series of measurements of light scattered primarily by liquids but also by some solids. As a result, Raman was able to explain the blue color observed in the ice of Alpine glaciers.



Raman Measures the Effect


Analysis of light scattered by a liquid is not an easy task, and much of the early work in Calcutta was done by the visual observation of color rather than precise measurements of the light's wavelength as shown in Figure 1 at right. The fundamentals of Raman's crucial experiment are outlined in Figure 2.

The violet light of the solar spectrum is isolated with a violet filter and passed through the liquid sample. Most of the light emerging from the liquid sample is the same color as the incident violet beam: the so-called Rayleigh scattered light. However, Raman and K. S. Krishnan were able to show that some of the scattered light was a different color, which they could isolate by using a green filter placed between the observer and the sample. The advantage of using a visual observation is that several substances can be studied quickly. In his first report to Nature, titled "A New Type of Secondary Radiation," Raman indicated that approximately 60 different liquids had been studied, and all showed the same result—some scattered light had a different color than the incident light. "It is thus," Raman said, "a phenomenon whose universal nature has to be recognized."

The Raman Effect is a very weak effect; only one in a million of the scattered light particles, or photons, actually exhibits the change in wavelength. This explains, in part, why the effect was not discovered earlier. In all of the early light-scattering studies, the excitation source was sunlight, which Raman has described as being plentiful in Calcutta, but it still lacked the desired intensity. The acquisition in 1927 by the IACS of a seven-inch (18 cm) refracting telescope enabled Raman to condense the sunlight and create a more powerful light source for his studies. By early 1928, mercury arc lamps were commercially available, and he switched to this even more intense light source.

Raman knew that visual and qualitative observations alone would not be sufficient information. He methodically set out to measure the exact wavelengths of the incident and Raman scattering by replacing the observer with a pocket spectroscope. He ultimately replaced it with a quartz spectrograph with which he could photograph the spectrum of the scattered light and measure its wavelength. These quantitative results were first published in the Indian Journal of Physics on March 31, 1928.

Raman Effect as the Physicist’s Tool

The significance of the Raman Effect was recognized quickly by other scientists. Professor R. W. Wood of Johns Hopkins cabled Nature to report that he had verified Raman's "brilliant and surprising discovery ... in every particular. It appears to me that this very beautiful discovery which resulted from Raman's long and patient study of the phenomenon of light scattering is one of the most convincing proofs of the quantum theory."

Raman had also recognized that his discovery was important to the debate in physics over the new quantum theory, because an explanation of the new radiation required the use of photons and their change in energy as they interacted with the atoms in a particular molecule. Raman also knew that there was a more important result, remarking in his 1930 Nobel Prize address that "... the character of the scattered radiations enables us to obtain an insight into the ultimate structure of the scattering substance."

In the first seven years after its discovery, the Raman Effect was the subject of more than 700 papers in the scientific literature, mostly by physicists who were using the technique to study the vibration and rotation of molecules and relating those phenomena to the molecular structure. Then, as noted by Raman biographer G. Venkataraman, there was a decline in interest, as "the first bloom of novelty had worn off and physicists were satisfied that they understood the origin of the effect." At the same time, chemists became interested in the Raman Effect as an analytical tool. In James Hibben's words, "The Raman Effect became the adopted child of chemistry."

Raman Effect as a Chemist’s Tool

By the late 1930s the Raman Effect had become the principal method of nondestructive chemical analysis for both organic and inorganic compounds. The unique spectrum of Raman scattered light for any particular substance served as a "fingerprint" that could be used for qualitative analysis, even in a mixture of materials. Further, the intensity of the spectral lines was related to the amount of the substance. Raman spectroscopy could be applied not only to liquids but also to gases and solids. And unlike many other analytical methods, it could be applied easily to the analysis of aqueous solutions. It was a ubiquitous technique, giving information on what and how much was present in a plethora of samples.

The use of Raman spectroscopy as a basic analytical tool changed sharply after World War II. During the war, infrared spectroscopy was enhanced by the development of sensitive detectors and advances in electronics. Infrared measurements quickly became routine operations, while Raman measurements still required skilled operators and darkroom facilities.

Raman spectroscopy could no longer compete with infrared until another development in physics—the laser—revived Raman spectroscopy in a new form beginning in the 1960s.

The Laser and Raman Spectroscopy

Raman understood the need for more intense light sources to amplify the effect and observation of the scattered light. The laser provided an even more intense source of light that not only could serve as a probe exploring the properties of the molecule but could also induce dramatically new effects.
With the development of the Fourier transform (FT) technique and the application of computers for data handling, commercial FT-Raman spectrometers became available in the late 1980s, resulting in resurgence in the use of the original Raman Effect.

The new Raman spectroscopy has been used to monitor manufacturing processes in the petrochemical and pharmaceutical industries. Illegal drugs captured at a crime scene can be analyzed rapidly without breaking the evidence seal on the plastic bag. Chemists can watch paint dry and understand what reactions are occurring as the paint hardens. Using a fiber-optic probe, they can analyze nuclear waste material from a safe distance. Photochemists and photobiologists are using laser Raman techniques to record the spectra of transient chemical species with lifetimes as small as 10-11 seconds. Surface-enhanced Raman spectroscopy is used for studying surfaces and reactions on surfaces. And, according to Kathy Kincade, Raman spectroscopy "has the ability to provide specific biochemical information that may foreshadow the onset of cancer and other life-threatening illnesses."

In his 1928 talk in Bangalore, Raman concluded, "We are obviously only at the fringe of a fascinating new region of experimental research which promises to throw light on diverse problems relating to radiation and wave theory, X-ray optics, atomic and molecular spectra, fluorescence and scattering, thermodynamics, and chemistry. It all remains to be worked out."

Seventy years later scientists are still actively working out the results and practical applications of Raman's deceptively simple experiment.

The Life of Sir C.V. Raman

According to Hindu tradition, Raman was originally named Venkataraman after a Hindu deity, preceded by the initial of his father's first name, Chandrasekhara. In school his name was split to C. Venkata Raman, which later became C.V. Raman. With a father who was a professor of physics and mathematics and a mother who came from a family of Sanskrit scholars, Raman exhibited a precocious nature at an early age. He received a B.A. degree from Presidency College in Madras at the age of 16, placing first in his class and receiving a gold medal in physics.

While studying for his M.A. degree, he published his first research paper in Philosophical Magazine at the age of 18. It was the first research paper ever published from Presidency College.

Because of poor health, he was unable to go to England for further education. With nothing else available in
India, in 1907 he passed the Financial Civil Service exam, married, and was posted to Calcutta as assistant accountant general.

Shortly after arriving in Calcutta, Raman began after-hours research at the Indian Association for the Cultivation of Science (IACS). In the first 10 years, working almost alone, he published 27 research papers and led the way for the IACS to become recognized as a vibrant research institute. Much of this early work was on the theory of vibrations as it related to musical instruments. After brief postings in Rangoon and Nagpur, he returned to Calcutta, took up residence next door to the IACS, and constructed a door that led directly into the institute, giving him access at any time. He received research prizes in 1912 and 1913 while he was still a full-time civil servant. He also increased the IACS reputation with his extensive lectures in popular science, holding the audience spellbound with his booming voice, lively demonstrations, superb diction and rich humor.

At the age of 29 he resigned from his lucrative civil service job when Sir Ashutosh Mukherjee, vice-chancellor, Calcutta University, offered him the Palit Chair Professorship. He continued to lecture even though it was not required, and he used the IACS as the research arm of the university. By the time of his first visit to England in 1921, his reputation in physics was well known. Three years later he was elected a Fellow of the Royal Society—only the fourth Indian so honored. That same year he toured the United States, spending four months at the California Institute of Technology through the invitation of Nobel Laureate Robert Millikan.

After discovering the Raman Effect in 1928, he was knighted by the British government in India and received the Nobel Prize in physics in 1930. Three years later, Raman left Calcutta for Bangalore, where he served as head of the Indian Institute of Science. There he continued his work on the Raman Effect and became interested in the structure of crystals, especially diamond. In 1934 he founded the Indian Academy of Science and began the publication of its Proceedings.

In 1948 he became director of the newly constructed Raman Research Institute, where he remained continually active, delivering his last lecture just two weeks before his death. His research interests changed in later years when he primarily investigated the perception of color.

Jagdish Mehra, a biographer, states, "Educated entirely in India, Raman did outstanding work at a time when the small Indian community worked almost entirely in isolation and few made science a career. In fostering Indian science, Raman emerged as one of the heroes of the Indian political and cultural renaissance, along with ... Mahatma Gandhi and Jawaharlal Nehru." But as Raman himself once said, outstanding investigators "are claimed as nationals by one or another of many different countries. Yet in the truest sense they belong to the whole world."

Landmark Dedication and Acknowledgments

Landmark Dedication

The American Chemical Society and the Indian Association for the Cultivation of Science dedicated The Raman Effect an International Historic Chemical Landmark on December 15, 1998 at the Indian Association for the Cultivation of Science in Jadavpur, Calcutta, India. The plaque commemorating the event reads:
At this institute, Sir C. V. Raman discovered in 1928 that when a beam of coloured light entered a liquid, a fraction of the light scattered by that liquid was of a different color. Raman showed that the nature of this scattered light was dependent on the type of sample present. Other scientists quickly understood the significance of this phenomenon as an analytical and research tool and called it the Raman Effect. This method became even more valuable with the advent of modern computers and lasers. Its current uses range from the non-destructive identification of minerals to the early detection of life-threatening diseases. For his discovery Raman was awarded the Nobel Prize in physics in 1930.

Acknowledgments:

Produced by the American Chemical Society in 1998.
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Sunday, May 12, 2013

What Is Astronomy?

AStronomy

Astronomy, derived from the Greek words for star law, is the scientific study of all objects beyond our world. It is also the process by which we seek to understand the physical laws and origins of our universe.

Pioneers of Astronomy

Over the centuries there have been countless innovators that have contributed to the development and advancement of astronomy. Some of these key individuals include:

Nicolaus Copernicus (1473 - 1543): He was a Polish physician and lawyer by trade, but is now regarded as the father of the current heliocentric model of the solar system.

Tycho Brahe (1546 - 1601): A Danish nobleman, Tycho designed and built instruments of greater power and resolution than anything that had been developed previously. He used these instruments to chart the positions of planets and other celestial objects with such great precision, that it debunked many of the commonly held notions of planetary and stellar motion.


Johannes Kepler (1571 - 1630): A student of Tycho’s, Kepler continued his work, and from that discovered three laws of planetary motion:
  1. Planets move in elliptical orbits with the Sun at one focus of the ellipse.
  2. The orbital speed of a planet varies so that a line joining the Sun and the planet will sweep over equal areas in equal time intervals.
  3. The amount of time a planet takes to orbit the Sun is related to its orbit’s size, such that he period, P, squared is proportional to the semi-major axis, a, cubed.
Galileo Galilei (1564 - 1642): While Galileo is sometimes credited (incorrectly) with being the creator of the telescope, he was the first to use the telescope to make detailed studies of heavenly bodies. He was the first to conclude that the Moon was likely similar in composition to the Earth, and that the Sun’s surface changed (i.e., the motion of sunspots on the Sun’s surface). He was also the first to see four of Jupiter’s moons, and the phases of Venus. Ultimately it was his observations of the Milky Way, specifically the detection of countless stars, that shook the scientific community.

Isaac Newton (1642 - 1727): Considered one of the greatest scientific minds of all time, Newton not only deduced the law of gravity, but realized the need for a new type of mathematics (calculus) to describe it. His discoveries and theories dictated the direction of science for more than 200 years, and truly ushered in the era of modern astronomy.

Albert Einstein (1879 - 1955): Einstein is famous for his development of general relativity, a correction to Newton’s law of gravity. But, his relation of energy to mass (E=mc2) is also important to astronomy, as it is the basis for which we understand how the Sun, and other stars, fuse hydrogen into Helium for energy.

Edwin Hubble (1889 - 1953): During his career, Hubble answered two of the biggest questions plaguing astronomers at the time. He determined that so-called spiral nebulae were, in fact, other galaxies, proving that the Universe extends well beyond our own galaxy. Hubble then followed up that discovery by showing that these other galaxies were receding at speeds proportional to their distances away form us.

Stephen Hawking (1942 - ): Very few scientists alive today have contributed more to the advancement of their fields than Stephen Hawking. His work has significantly increased our knowledge of black holes and other exotic celestial objects. Also, and perhaps more importantly, Hawking has made significant strides in advancing our understanding of the Universe and its creation.

 Branches of Astronomy

There are really two main branches of astronomy: optical astronomy (the study of celestial objects in the visible band) and non-optical astronomy (the use of instruments to study objects in the radio through gamma-ray wavelengths).

Optical Astronomy: Today, when we think about optical astronomy, we most instantly visualize the amazing images from the Hubble Space Telescope (HST), or close up images of the planets taken by various space probes. What most people don’t realize though, is that these images also yield volumes of information about the structure, nature and evolution of objects in our Universe.

Non-optical Astronomy: While optical telescopes are sometimes considered the only pure instruments for doing astronomy research, there are other types of observatories that make significant contributions to our understanding of the Universe. These instruments have allowed us to create a picture of our universe that spans the entire electromagnetic spectrum, from low energy radio signals, to ultra high energy gamma-rays. They give us information about the evolution and physics of some of the Universe’s most dynamic treasures, such as neutron stars and black holes. And it is because of these endeavors that we have learned about the structure of galaxies including our Milky Way.

Subfields of Astronomy

There are so many types of objects that astronomers study, that it is convenient to break astronomy up into subfields of study.

Planetary Astronomy: Researchers in this subfield focus their studies on planets, both within and outside our solar system, as well as objects like asteroids and comets.

Solar Astronomy: While the sun has been studied for centuries, there is still a significant amount of active research conducted. Particularly, scientists are interested in learning how the Sun changes, and trying to understand how these changes affect the Earth.

Stellar Astronomy: Simply, stellar astronomy is the study of stars, including their creation, evolution and death. Astronomers use instruments to study different objects across all wavelengths, and use the information to create physical models of the stars.

Galactic Astronomy: The Milky Way Galaxy is a very complex system of stars, nebulae, and dust. Astronomers study the motion and evolution of the Milky Way in order to learn how galaxies are formed.

Extragalactic Astronomy: Astronomers study other galaxies in the Universe to learn how galaxies are grouped and interact on a large scale.

Cosmology: Cosmologists study the structure of the Universe in order to understand its creation. They typically focus on the big picture, and attempt to model what the Universe would have looked like only moments after the Big Bang.
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Black Holes


Often the subject of science fiction novels, black holes are mysterious objects that, while very real, have a certain mythology that surrounds them. Some of these myths actually arise out of scientific truth, while others are the result of wild imagination. So what is fact and what is fiction? And where do black holes come from anyway?

What Is a Black Hole?

Simply put, a black hole is a region of space that is so incredibly dense that not even light can escape from the surface. However, it is this fact that often leads to miss-understanding. Black holes, strictly speaking, don't have any greater gravitational reach than any other star of the same mass. If our Sun suddenly became a black hole of the same mass the rest of the objects, including Earth, would be unaffected gravitationally. The Earth would remain in its current orbit, as would the rest of the planets. (Of course other things would be affected, such as the amount of light and heat that Earth received. So we would still be in trouble, but we wouldn't get sucked into the black hole.)

There is a region of space surrounding the black hole from where light can not escape, hence the name. The boundary of this region is known as the event horizon, and it is defined as the point where the escape velocity from the gravitational field is equal to the speed of light. The calculation of the radial distance to this boundary can become quite complicated when the black hole is rotating and/or is charged.

For the simplest case (a non-rotating, charge neutral black hole), the entire mass of the black hole would be contained within the event horizon (a necessary requirement for all black holes). The event horizon radius (Rs) would then be defined as Rs = 2GM/c2.

 How Do Black Holes Form?

This is actually somewhat of a complex question, namely because there are different types of black holes. The most common type of black holes are known as stellar mass black holes as they are roughly up to a few times the mass of our Sun. These types of black holes are formed when large main sequence stars (10 - 15 times the mass of our Sun) run out of nuclear fuel in their cores. The result is a massive supernova
explosion, leaving a black hole core behind where the star once existed.

The two other types of black holes are supermassive black holes -- black holes with masses millions or billions times the mass of the Sun -- and micro black holes -- black holes with extremely small masses, perhaps as small as 20 micrograms. In both cases the mechanisms for their creation is not entirely clear. Micro black holes exist in theory, but have not been directly detected. While supermassive black holes are found to exist in the cores of most galaxies.

While it is possible that supermassive black holes result from the merger of smaller, stellar mass black holes and other matter, it is possible that they form from the collapse of a single, extremely high mass star. However, no such star has ever been observed.

Meanwhile, micro black holes would be created during the collision of two very high energy particles. It is thought that this happens continuously in the upper atmosphere of Earth, and is likely to happen in particle physics experiments such as CERN. But no need to worry, we are not in danger.

How Do We Know Black Holes Exist If We Can't "See" Them?

Since light can not escape from the region around a black hole bound by the event horizon, it is not possible to directly "see" a black hole. However, it is possible to observe these objects by their effect on their surroundings.

Black holes that are near other objects will have a gravitational effect on them. Going back to the earlier example, suppose that our Sun became a black hole of one solar mass. An alien observer somewhere else in the galaxy studying our solar system would see the planets, comets and asteroids orbiting a central point. They would deduce that the planets and other objects were bound in their orbits by a one solar mass object. Since they would see no such star, the object would correctly be identified as a black hole.

Another way that we observe black holes is by utilizing another property of black holes, specifically that they, like all massive objects, will cause light to bend -- due to the intense gravity -- as it passes by. As stars behind the black hole move relative to it, the light emitted by them will appear distorted, or the stars will appear to move in an unusual way. From this information the position and mass of the black hole can be determined.

There is another type of black hole system, known as a microquasar. These dynamic objects consist of a stellar mass black hole in a binary system with another star, usually a large main sequence star. Due to the immense gravity of the black hole, matter from the companion star is funneled off onto a disk surrounding the black hole. This material then heats up as it begins to fall into the black hole through a process called accretion. The result is the creation of X-rays that we can detect using telescopes orbiting the Earth.

Hawking Radiation

The final way that we could possibly detect a black hole is through a mechanism known as Hawking radiation. Named for the famed theoretical physicist and cosmologist Stephen Hawking, Hawking radiation is a consequence of thermodynamics that requires that energy escape from a black hole.

The basic (perhaps oversimplified) idea is that, due to natural interactions and fluctuations in the vacuum (the very fabric of space time if you will), matter will be created in the form of an electron and anti-electron (called a positron). When this occurs near the event horizon, one particle will be ejected away from the black hole, while the other will fall into the gravitational well.

To an observer, all that is "seen" is a particle being emitted from the black hole. The particle would be seen as having positive energy. Meaning, by symmetry, that the particle that fell into the black hole would have negative energy. The result is that as a black hole ages it looses energy, and therefore loses mass (by Einstein's famous equation, E=Mc2).

Ultimately, it is found that black holes will eventually completely decay unless more mass is accreted. And it is this same phenomenon that is responsible for the short lifetimes expected by micro black holes.
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Some facts about Hubble Space Telescope

The Hubble Space Telescope was the world's first space-based optical telescope. It received its name from American astronomer Edwin Hubble (1889–1953). Dr. Hubble confirmed an "expanding" universe, which provided the foundation for the Big Bang theory.  

Cool Fact:

Scientists believe our universe began with a “big bang” some 13.7 billion years ago. If all the events in the history of the universe until now were squeezed into 24 hours, Earth wouldn’t form until late afternoon and humans would have existed for only 2 seconds.

Hubbles Space Telescope Mission:

  • Launch: April 24, 1990 from space shuttle Discovery (STS-31)
  • Deployment: April 25, 1990
  • Mission Duration: Up to 20 years
  • Servicing Mission 1: December 1993
  • Servicing Mission 2: February 1997
  • Servicing Mission 3A: December 1999
  • Servicing Mission 3B: February 2002

Hubbles Space Telescope Size:

  • Length: 43.5 ft (13.2 m)
  • Weight: 24,500 lb (11,110 kg)
  • Maximum Diameter: 14 ft (4.2 m)
Hubble is nearly the size of a large school bus—but it can fit inside a space shuttle cargo bay.

Cost at Launch:


$1.5 billion Spaceflight Statistics:
  • The Hubble Space Telescope whirls around Earth at a speed of 5 miles per second.
  • Orbit: At an altitude of 307 nautical miles (569 km, or 353 miles), inclined 28.5 degrees to the equator (low-Earth orbit)
  • Time to Complete One Orbit: 97 minutes
  • Speed: 17,500 mph (28,000 kph)

Optical Capabilities:

Hubble can’t observe the Sun or Mercury.
  • Sensitivity to Light: Ultraviolet through infrared (115–2500 nanometers)
  • First Image: May 20, 1990: Star Cluster NGC 3532
The most frequently observed celestial object is Earth. Earth is observed regularly for calibration—to make sure that all the charge-coupled detectors (CCDs) are working properly. The images from these "test" observations show no detail.

Data Stats:


Hubble transmits about 120 gigabytes of science data every week. That's equal to about 3,600 feet (1,097 meters) of books on a shelf. The rapidly growing collection of pictures and data is stored on magneto-optical disks. Power Needs:
  • Energy source: the Sun
  • Mechanism: two 25-foot solar panels
  • Power usage: 2,800 watts
In an average orbit, Hubble uses about the same amount of energy as 28 100-watt light bulbs.

Pointing Accuracy:

In order to take images of distant, faint objects, Hubble must be extremely steady and accurate. The telescope is able to lock onto a target without deviating more than 7/1000th of an arcsecond, or about the width of a human hair seen at a distance of 1 mile. Aiming Hubble is like holding a laser light steady on a dime that is 200 miles away.

Hubble Space Telescope's mirrors:
  • Primary Mirror
    • Diameter: 94.5 in (2.4 m)
    • Weight: 1,825 lb (828 kg)
  • Secondary Mirror
    • Diameter: 12 in (0.3 m)
    • Weight: 27.4 lb (12.3 kg)
Both of Hubble's mirrors were ground in such a way that they do not deviate from a perfect curve by more than 1/800,000ths of an inch. Power Storage:
  • Batteries: 6 nickel-hydrogen (NiH)
  • Storage capacity: equal to 20 car batteries 

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The History of Astronomy



Early Astronomers
The history of astronomy goes back several thousand years ago. Almost all ancient cultures had stories about how the universe was created, what it was like, who created it, and how the earth and humans got here, but those stories are usually not very believable. The early Egyptians believed that the universe was a large rectangular box with Egypt at the center of the bottom and with huge lamps which hung down from the top for stars. The ideas of the other cultures which were near Egypt usually had the same concept of an enclosed space with that culture’s part of the world at the center. One major factor holding the ancient cultures back from developing the technology to look farther into the cosmos was their belief in many unpredictable gods who controlled the universe. If the universe was unpredictable because of gods, why try to understand it if what you learned could become obsolete at the whim of the next god. The only culture that worshipped one God who made a predictable universe at that time were the Jews. The Bible, which came from that culture, later had a profound positive impact on science.

Some of the astronomers in the ancient cultures kept records of their observations. The Chinese have records going back to about the 1300s B.C. By about 700 B.C., the Babylonians could predict certain heavenly events. By about 600 B.C., the Greeks started to get interested in astronomy.

The Greeks

The first ancient culture that usually comes to mind as being more aware of the truth of their surroundings than other cultures of that time period are the Greeks. In fact, our word astronomy comes from the Greek words meaning "law and order". The Greeks were not the first culture to try their hand at astronomy but the work of their philosophers was widely distributed by the Romans and was the accepted authority on that subject for hundreds of years. The Greeks discovered that the earth was a sphere by several methods and the philosopher Eratosthenes measured the circumference of the earth to within about 300 kilometers of today’s generally accepted value. In about 200 BC Aristarchus first stated that the earth revolves around the sun but most philosophers argued that everything revolves around earth.

There were apparently also some cultures about which we know little who were interested in astronomy. Stonehenge and the various other similar structures which appear to be ancient calendars are some examples of monuments built by those groups.

Ptolemy
Around 150 A.D. Ptolemy (100?-165? A.D.), an Alexandrian astronomer, invented the concentric system to explain the motions of the planets around the earth. His work was the accepted authority on astronomy until 1543.

To fully understand why some of the early modern astronomer’s ideas were not accepted and why some of those ideas led the astronomers to be ridiculed, it is helpful to have a background on what was happening to the culture at that time.

For a time under the Romans, from about 300 BC to 476 AD, there was a decline in the study of astronomy in favor of astrology and some of the works of the Greek philosophers were destroyed.

Modern Astronomy

The modern history of astronomy starts in Europe in about 1300 AD. Before that time, the Roman Catholic Church had been the dominant religion in Europe and at times had more control over countries than did the kings of those countries. The Roman Catholic Church started in about 300 AD under the Roman emperor Constantine. Over time, the popes started getting more powerful because of the fact they were the heads of a religion followed by most of Europe and gradually replaced the empire as the center of power. During that time, some of the popes introduced some controversial beliefs to increase their power and the popes and most of the clergy became corrupt. By the 1200s, it was obvious that most of the clergy were more interested in gaining political power than in helping the people spiritually.

In 324 AD, the Roman emperor Constantine moved the capital of the Roman empire from Rome to the city of Byzantium, present day Istanbul, and renamed it Constantinople. As he built up his new capital, he collected and stored many of the ancient writings of the Greek philosophers in libraries in the city. In 395 AD, the empire split up into two parts. The eastern half had its capital in Constantinople and was called the Byzantine empire. The western half had its capital in Rome. The church also split into two parts; the eastern half was called the Eastern Orthodox Church and the western part was called the Roman Catholic Church. Each church also had its own pope and very different ideas. In about 476 AD the western half of the empire was destroyed by the Visigoths, Vandals, and other Germanic tribes. Southern Europe was then plunged into what is now called the Dark and Middle Ages, which was marked by frequent wars and a lack of strong governments. During that time, not much learning at all occurred and most of the population lived under lords as serfs. The priests of the Roman Catholic Church, however, kept education from dying out completely during that time. The eastern empire stayed together for another thousand years until 1453 when the Ottoman Turks captured Constantinople. Before the Turks could capture Constantinople and make it into Istanbul, however, most of the population fled the city, taking with them the works of the ancient Greek philosophers. As the knowledge from the city spread throughout Europe, it helped start what is now called the Renaissance.

The Renaissance

The Renaissance, which took place from the early 1300s to about 1600, was a time in which people in southern Europe began to learn, which had not taken place there much since the western empire fell. As the people started to learn, they saw the corruption of the Roman Catholic Church which led them to turn away from it altogether and to start pursuing the improvement of themselves with knowledge. They got much of that knowledge from the monasteries of Catholic Church which had preserved most of the books written before that time.

Starting in the 1500s, the learning from southern Europe began to enlighten the people in the north. In northern Europe, however, when they saw the corruption of the church, instead of turning away from the church, they tried to reform it. This period is called the Reformation. During the Reformation, people began to read the Bible for themselves, which the Roman Catholic Church was supposed to be based on, and found beliefs in the Bible which they thought were contrary to the beliefs of the church. Some of these people started the Protestant movement. Many thousands of people were killed, usually being burned as heretics, because of their belief in things which were contrary to what the pope, who set the beliefs of the Catholic Church, said. The Catholic Church was still very powerful and one of the beliefs that the pope set is that the earth itself is the center of the universe and that all other heavenly bodies revolve around it. This is the reason that the church persecuted those who believed Copernicus’s ideas about the sun being the center of the solar system.

The printing press was invented in the year 1430 which helped spread information about all of the sciences. This made the common man able to afford a book, which before then had to be handwritten and thus were very expensive. By this time, most educated people were aware that the earth was a sphere.

Copernicus

About that time a Polish canon of ecclesiastic law and astronomer named Copernicus (1473-1543) began to wonder if there could be a more aesthetically pleasing and reasonable arrangement for the planets than the concentric system. He studies Aristarchus’s heliocentric ideas and built a new system out of it. He developed a system where all of the planets, including earth, orbit the sun and where each one of these orbits was in the shape of a circle with the sun at its center. After almost forty years of study, he published his monumental book On the Revolutions of the Heavenly Orbs in 1543, the year he died. He was never able to prove his ideas but later advances in physics would make it possible to prove a version of those ideas.

Copernicus’s book caused an amazing amount of controversy. Martin Luther attacked his book by saying that Copernicus was "the fool who would overthrow the whole science of astronomy." Religious leaders attacked the heliocentric system by saying that they were contrary to scriptural revelations. The publisher of his book even inserted an anonymous apologetic note the readers of his book implying that his ideas were far fetched. Since the heliocentric cosmology was contrary to church ideas, advocating Copernicus’s ideas was punishable as heresy so the scientific community at that time was extremely reluctant to have anything to do with it. Philosopher Giordano Bruno committed this "crime" and was burned at the stake.

Copernicus’s ideas were not perfect because, since he believed that the planets move in perfect circles, he had to insert some epicycles and other mathematical structures into his theory which made it about as inaccurate as Ptolemy’s system. However, Copernicus’s theory was a tremendous leap in astronomy.

The next person to make an advance in astronomy was Tyco Brahe (1546-1601). With help from King Frederick II, he built an observatory on the Island of Hveen that was equipped with the most accurate pre-telescopic instruments for observing space ever built. He was able to determine positions of objects to within one minute of an arc, far more accurate than any previous attempt. Brahe constructed an uninterrupted record of the positions of many planets and other bodies for several years, but he did not accept Copernicus’s ideas. His idea of the universe was a compromise, he believed that the five planets orbited the sun, but the sun orbited the earth. He reasoned that the motion of the earth would be felt and he thought that Copernicus’s ideas were unscriptural.

Kepler

As the Renaissance was coming to and end, a German man named Johannes Kepler (1571-1630), who
believed Copernicus, started looking at the records of Brahe’s observations. He discovered that none of the ideas presented thus far about the motions of heavenly bodies lined up to the evidence in Brahe’s records so he formulated his own ideas. After seventeen years of work, he finally came up with the true motions of the planets and published them in two books in 1609 and 1619. He discovered that the planets move around the sun in ellipses with one focus of the ellipse at the center of the sun and the other focus at a usually unoccupied point in space. He also came up with rules for their movements called Kepler’s laws.

Because of Kepler and Brahe, astronomers now had a model for the solar system that actually fit the evidence and that could be used to predict future events or reconstruct past ones. This was a giant leap for astronomy but the work still remained to give reasons for what Kepler observed.

Galileo

Living at the same time as Kepler, an Italian named Galileo Galilei (1564-1642) made the next breakthrough for astronomy. Galileo is probably best known for some experiments with falling objects from the leaning tower in Pisa, his home town, but he also made some exciting discoveries with his homemade telescopes and experimented with pendulums. Galileo was also a believer in the Copernican theory. Since Ptolemy first made up his concentric model, many people argued that Ptolemy’s theory must be true because they reasoned that the earth would leave the moon behind if it traveled around the sun. In 1610, Galileo made the discovery with his telescope, which was the most advanced at that time, that Jupiter had at least four moons orbiting it. This was proof against the concentric system because Jupiter’s moons were orbiting Jupiter and not the Earth, which everything orbited according to Ptolemy’s concentric model. If Jupiter could retain its satellites, then the Earth could retain the moon as it went around the sun. He published a paper about his findings and got in trouble twice with the Roman Catholic Church which placed him under house arrest until his death for advocating the Copernican theory.

Newton

The science of astronomy still needed one more piece in its foundation for others to build upon. This piece was contributed by an English man named Sir Isaac Newton (1642-1727). Newton was an astronomer, scientist, and mathematician who investigated the laws of gravity and made spectacular discoveries about light. He formulated laws which explained how objects move and how gravity operates. He also laid the ground work for the study of spectrum analysis. He also made the first reflecting telescope which made possible the huge observatory telescopes of today.

The laws provided by Kepler, Galileo, and Newton were not perfect but they had a good degree of reliability and were used for many years. There have been revisions of their laws by Albert Einstein and others but the original laws are still used by many for calculations that do not need an extremely high degree of precision.

Einstein

One of the most profound impacts on science were two theories proposed by Albert Einstein. Albert Einstein (1879-1955) realized that all motion was relative, that is, coordinates and the descriptions of movements meant nothing unless the reference body was defined. He also had evidence that the speed of light was a constant, being the same speed no matter how fast an observer is moving, which violates the Newtonian laws of motions but was later demonstrated experimentally. In creating his theory, he made the requirements that all defined laws must work with respect to all bodies of reference and that the speed of light with respect to all bodies was the same. To bring the requirements into one theory, he used a set of mathematical formulas called the Lorentz transformation. The Lorentz transformation defined the formulas to use when converting coordinates from one reference body to another when the first body is moving at a constant speed with respect to the second. With these formulas, he discovered that time and mass cannot be constant for the speed of light to be constant; thus, time can not be separated from space so the two must exist together in a four dimensional space-time continuum. For instance, if two trains are moving on two parallel tracks in the same direction at different speeds toward a light source, and the speed of light from the light source is the same for both of them, then time for the faster train must be slightly slowed. In 1905, Einstein published his findings in his Special Theory of Relativity. The Special Theory of Relativity could only be used in the absence of gravitational fields so he published his General Theory of Relativity in 1916. The General Theory of Relativity basically says that all matter curves space, and in turn, how space is curved affects the movement of matter, which explains gravitational fields. This theory is constantly being validated by modern scientific experiments.

Space Exploration

The history of space exploration starts at about this time. In 1926, an American scientist named Robert H. Goddard built and flew the first successful liquid propelled rocket. By 1930, groups were being formed which experimented with rockets and by the early 1940s, the United States and the Soviet Union were both researching high altitude rockets.

The Space Race

During the cold war in the 1950s, both the United States and the Soviet Union announced plans to launch earth-orbiting satellites. This began what is called the "space race". At first, Dwight Eisenhower, the president of the U.S. at the time, was reluctant to get involved in the race because he thought that an American satellite orbiting the earth above the Soviet Union’s territory would be seen as a threat and start a war.

At this time, the U.S. military had a high altitude rocket called the Jupiter. On a missile test flight on September 20, 1956, the Jupiter rocket was flying over the South Atlantic when its nose cone briefly went into space before arching down to the ocean. The Jupiter’s designer and a few others knew that the nose cone, if detached, could have gone fast enough to orbit the earth. The Pentagon suspected that the Army might try to "accidentally" put another Jupiter nose cone into orbit so they ordered the Army to fill the nose cones with sand and to disable the Jupiter’s fourth stage.

Sputnik 1 and Explorer

One year and 14 days later, on October 4, 1957, the Russians put a small sphere with a radio transmitter into orbit, which was the first manmade satellite to orbit the earth. They named this small satellite Sputnik 1 and it prompted the Americans to put their own satellite into orbit. On January 31, 1958, the American satellite Explorer, which had some scientific equipment, was put into orbit with a Jupiter C rocket. Explorer had been fitted with a special Geiger counter from physicist James Van Allen which recorded the previously unknown Van Allen belts of radiation around earth.

Human Exploration

On January 20, 1961, John F. Kennedy became president and on May 25 of that same year announced the goal of sending an American to moon and bringing him back safely. To reach this goal, he executed the Apollo program. Before humans could go to the moon, however, humans needed to at least get into orbit. Before humans went into orbit, each country used animals to test the technology.

The Soviets were the first ones to send an animal into space. In 1957, they sent a dog named Laika into orbit in a capsule named Sputnik 2. She survived for a week before running out of oxygen.

The Americans were next, on January 31, 1961, they shot a chimpanzee named Ham in a Mercury capsule to an altitude of 157 miles. The chimp was recovered in good health.

That year, on April 12, the Soviet Yuri Gagarin was the first person in space. The Americans followed on May 5 with Alan Shepard being the first American in space. Gagarin’s flight lasted 1 hour and 48 minutes and he was in orbit 89 minutes. His highest altitude was 203 miles above the earth. Shepard’s flight lasted 15 minutes and he rocketed to 117 miles above the earth but did not make it to orbit.

On February 20 1962, John Glen became the first American to orbit the earth. His trip lasted 4 hours and 55 minutes and he orbited the earth three times. His highest altitude was 162.5 miles.

For years after that, the space race between the Soviets and the Americans continued and many more people orbited the earth as the technology progressed. The race finally ended on July 20, 1969 when Apollo 11 successfully landed on the moon and Americans Neil Armstrong and Edwin Aldrin became the first humans to walk on the moon. The United States sent a total of 12 men to the moon, the last being Eugene Cernan on the Apollo 17 mission on December 14, 1972. No human has walked on the moon since. The Soviets never made it to the moon.

Since then, many scientists have made discoveries and developed the technology to look farther into the cosmos, but not much could have happened without those first astronomers, philosophers, and scientists taking time to look at our universe for what it really was.
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Monday, May 6, 2013

What if you traveled faster than the speed of light?


When we were kids, we were amazed that Superman could travel faster than a speeding bullet. We could even picture him, chasing down a projectile fired from a weapon, his right arm outstretched, his cape rippling behind him. If he traveled at half the bullet's speed, the rate at which the bullet moved away from him would halve. If he did indeed travel faster than the bullet, he would overtake it and lead the way. Go, Superman! In other words, Superman's aerial antics obeyed Newton's views of space and time: that the positions and motions of objects in space should all be measurable relative to an absolute, nonmoving frame of reference.
In the early 1900s, scientists held firm to the Newtonian view of the world. Then a German-born mathematician and physicist by the name of Albert Einstein came along and changed everything. In 1905, Einstein published his theory of special relativity, which put forth a startling idea: There is no preferred frame of reference. Everything, even time, is relative. Two important principles underpinned his theory. The first stated that the same laws of physics apply equally in all constantly moving frames of reference. The second said that the speed of light -- about 186,000 miles per second (300,000 kilometers per second) -- is constant and independent of the observer's motion or the source of light. According to Einstein, if Superman were to chase a light beam at half the speed of light, the beam would continue to move away from him at exactly the same speed.

These concepts seem deceptively simple, but they have some mind-bending implications. One of the biggest is represented by Einstein's famous equation, E = mc², where E is energy, m is mass and c is the speed of light. According to this equation, mass and energy are the same physical entity and can be changed into each other. Because of this equivalence, the energy an object has due to its motion will increase its mass. In other words, the faster an object moves, the greater its mass. This only becomes noticeable when an object moves really quickly. If it moves at 10 percent the speed of light, for example, its mass will only be 0.5 percent more than normal. But if it moves at 90 percent the speed of light, its mass will double.

As an object approaches the speed of light, its mass rises precipitously. If an object tries to travel 186,000 miles per second, its mass becomes infinite, and so does the energy required to move it. For this reason, no normal object can travel as fast or faster than the speed of light.

That answers our question, but let's have a little fun on the next page and modify the question slightly.

Almost As Fast As the Speed of Light?

We covered the original question, but what if we tweaked it to say, "What if you traveled almost as fast as the speed of light?" In that case, you would experience some interesting effects. One famous result is something physicists call time dilation, which describes how time runs more slowly for objects moving very rapidly. If you flew on a rocket traveling 90 percent of light-speed, the passage of time for you would be halved. Your watch would advance only 10 minutes, while more than 20 minutes would pass for an Earthbound observer.

You would also experience some strange visual consequences. One such consequence is called aberration, and it refers to how your whole field of view would shrink down to a tiny, tunnel-shaped "window" out in front of your spacecraft. This happens because photons (those exceedingly tiny packets of light) -- even photons behind you -- appear to come in from the forward direction. In addition, you would notice an extreme Doppler effect, which would cause light waves from stars in front of you to crowd together, making the objects appear blue. Light waves from stars behind you would spread apart and appear red. The faster you go, the more extreme this phenomenon becomes until all visible light from stars in front of the spacecraft and stars to the rear become completely shifted out of the known visible spectrum (the colors humans can see). When these stars move out of your perceptible wavelength, they simply appear to fade to black or vanish against the background.

Of course, if you want to travel faster than a speeding photon, you'll need more than the same rocket technology we've been using for decades. Perhaps pulling on blue tights and a red cape isn't such a far-fetched idea.
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Sunday, May 5, 2013

What is Dark Matter?

The Dark Matter

The story of dark matter is best divided into two parts.  First we have the reasons that we know that it exists.  Second is the collection of possible explanations as to what it is.

Why the Universe Needs Dark Matter

We believe that that the Universe is critically balanced between being open and closed.  We derive this fact from the observation of the large scale structure of the Universe.  It requires a certain amount of matter to accomplish this result.  Call it M.
We can estimate the total baryonic matter of the universe by studying Big Bang nucleosynthesis.  This is done by connecting the observed He/H ratio of the Universe today to the amount of baryonic matter present during the early hot phase when most of the helium was produced.  Once the temperature of the Universe dropped below the neutron-proton mass difference, neutrons began decaying into protons.  If the early baryon density was low, then it was hard for a proton to find a neutron with which to make helium before too many of the neutrons decayed away to account for the amount of helium we see today.  So by measuring the He/H ratio today, we can estimate the necessary baryon density shortly after the Big Bang, and, consequently, the total number of baryons today.  It turns out that you need about 0.05 M total baryonic matter to account for the known ratio of light isotopes.  So only 1/20 of the total mass of the Universe is baryonic matter.
Unfortunately, the best estimates of the total mass of everything that we can see with our telescopes is roughly 0.01 M.  Where is the other 99% of the stuff of the Universe?  Dark Matter!
So there are two conclusions.  We only see 0.01 M out of 0.05 M baryonic matter in the Universe.  The rest must be in baryonic dark matter halos surrounding galaxies.  And there must be some non-baryonic dark matter to account for the remaining 95% of the matter required to give Ω, the mass of the Universe, in units of critical mass, equal to unity.
For those who distrust the conventional Big Bang models, and don't want to rely upon fancy cosmology to derive the presence of dark matter, there are other more direct means.  It has been observed in clusters of galaxies that the motion of galaxies within a cluster suggests that they are bound by a total gravitational force due to about 5-10 times as much matter as can be accounted for from luminous matter in said galaxies.  And within an individual galaxy, you can measure the rate of rotation of the stars about the galactic center of rotation.  The resultant "rotation curve" is simply related to the distribution of matter in the galaxy.  The outer stars in galaxies seem to rotate too fast for the amount of matter that we see in the galaxy.  Again, we need about 5 times more matter than we can see via electromagnetic radiation.  These results can be explained by assuming that there is a "dark matter halo" surrounding every galaxy.

What is Dark Matter?

This is the open question.  There are many possibilities, and nobody really knows much about this yet.  Here are a few of the many published suggestions, which are being currently hunted for by experimentalists all over the world.  Remember, you need at least one baryonic candidate and one non-baryonic candidate to make everything work out, so there there may be more than one correct choice among the possibilities given here.
  • Normal matter which has so far eluded our gaze, such as:
    • dark galaxies
    • brown dwarfs
    • planetary material (rock, dust, etc.)
  • Massive Standard Model neutrinos.  If any of the neutrinos are massive, then this could be the missing mass.  On the other hand, if they are too heavy, as the purported 17 keV neutrino would have been, massive neutrinos create almost as many problems as they solve in this regard.
  • Exotica (See the Particle Zoo FAQ entry for some details.)
Massive exotica would provide the missing mass.  For our purposes, these fall into two classes: those which have been proposed for other reasons but happen to solve the dark matter problem, and those which have been proposed specifically to provide the missing dark matter.
Examples of objects in the first class are axions, additional neutrinos, supersymmetric particles, and a host of others.  Their properties are constrained by the theory which predicts them, but by virtue of their mass, they solve the dark matter problem if they exist in the correct abundance.
Particles in the second class are generally classed in loose groups.  Their properties are not specified, but they are merely required to be massive and have other properties such that they would so far have eluded discovery in the many experiments which have looked for new particles.  These include WIMPS (Weakly Interacting Massive Particles), CHAMPS, and a host of others.
References: Dark Matter in the Universe  (Jerusalem Winter School for Theoretical Physics, 1986-7), J.N. Bahcall, T. Piran, & S. Weinberg editors.
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Saturday, April 6, 2013

How To Improve Your Basketball Game and Be Your Best - Work at Your Game

Basket

Over the years I have met many players who had dreams of going on to be successful in basketball. What success means is a major question in itself. Let's just say, in a basketball sense, it means being the best player you can be. That could mean playing on the junior high school team, playing on the high school team, going beyond that level, or just being a good player in the summer league. It's all relative. How can you improve your game so you can be the best player possible?

First, you have to have a passion for the game. Maybe that is an overused word, but it is true. Why? Because basketball is a highly skilled game and takes a lot of work. Most people have to do more than just "shoot around." You have to love the game to put in the necessary work. Basketball for many people is a year round sport.

What is required to be a good player? First, play as much as you can, wherever you can (within reason). It's a great game. Have fun. Learn from the players around you. Watch what they do well. What can you do to practice and become as good as your opponents? Do other players have moves that would be effective for you? Learn from others.

Also, be aware of what you do well. Practice those things more. Take a strength that you have and make it stronger. If you are a fair shooter, shoot more and become a good shooter. If you are a good shooter, shoot even more and become a great shooter. Play as much as you can and improve the things you do best.
I am telling you to practice alot, but do so in moderation. Balance in life is important so don't misunderstand.
My point is to love the game, play and practice alot, and try to improve.

In addition, learn what you need to improve in. Practice to become competent in skills that you have been weaker in. Work on developing a good, all-around game. I know these things seem obvious, but how many people do them?

There are camps, leagues, clinics, intramural sports, and other places you can play. These are all opportunities. Join these types of programs and have fun, but always try to learn. Listen to people who are successful and find out what made them successful. Try to model those behaviors.

Now, comes the hardest part-"practice, practice, practice." The more you practice, the better you'll play. When you practice, practice with a purpose. Break the game down into skills you need to improve on and the skills you are good at. As I said, work on improving your weaknesses and work at really making those skills you are good at greater.

Make a practice schedule and follow it. Time each drill and stay on schedule. Have goals for each practice session and work toward achieving those goals. Work out with a friend so you can help each other and reinforce each other. Learn from each other.

This sounds a bit like school or work! They are very similar. That's why it's important. The work habits you develop as a player will also help you to become a better student, better worker, good team mate, and a great person. If you work hard at basketball, you should improve and have fun, and you'll learn to be an even better person.

What does it take to become a better player?
• Set Goals
• Work on your strengths
• Improve your weaknesses
• Play as much as you can
• Make use of clinics, leagues, camps, and programs
• Learn from others
• And most importantly, love the game! You can't turn this on at a moments notice, but passion is what makes greatness.

Here are some skills oyu can work on:
  • Work on dribbling with your head up using both hands
  • Shoot as much as you can from inside the key and the periemeter
  • Work on offensive moves off the dribble and before dribbling
  • Work on passing skills-practice with a friend
  • Work on defensive techniques, stance, sliding, and footwork
  • Practice ball fakes, jam steps, and up and under moves
  • Always display a great attitude-listen, learn, and be the best team mate you can

Again, I want to make the point that life is about balance. You have to balance your skills in basketball to become a well-rounded player. I am telling you to play a lot, practice hard, and let your love of basketball grow. But you must be a balanced person and have other interests. Be a good student and study hard. Work hard. Develop other interests. But let basketball teach you how to be the best you can be in everything and Be Great!
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21 Easy Ways to Improve Your Basketball Shooting Percentage


Tip #1 – Locate Your Target (the Rim) Earlier
Getting in the habit of locating your target (the rim) earlier will improve your shooting percentage.  Why?
Locating the rim just a split second earlier gives your brain more time to subconsciously calculate distance and focus on your objective. Your eyes should be on the rim as early as possible. To make this little trick work, you need to develop this habit in practice, which carries over into games.

Tip #2 – Always Hold Your Follow Through
You’ve probably heard this a hundred times but there’s good reason for it.  Holding your follow through solves a multitude of shooting problems.  This simple movement helps you maintain good basketball shooting technique without even thinking about it.


Tip #3 – Finish with a Floppy Wrist
A common mistake is for players to follow-through with a tense wrist.  Your wrist should be as relaxed as possible.  Your hand should finish on line and often bouncing during follow-through.

Tip #4 – Use a Colored Ball to Improve Rotation
To improve the straightness of your shot, try a colored basketball during practice.   This makes it easy to see the rotation and direction of the ball.  The immediate feedback makes it quick and easy for you to adjust and improve your shot.

Tip #5 – Don’t Shoot like Kobe
TOO many kids try to copy Kobe and end up with bad shots for the REST OF THEIR LIVES!
Youngsters have no business trying to hang like Kobe and shoot.  Kobe is a freak of nature!  You should shoot as you’re going up (at least 1 inch before you reach the top of your jump).  Trying to mimic Kobe’s shot will just earn you a place on the bench and lots of frustration.
Tip #6 – Stop Thinking about Your Shot During Games
One of the worst things you can do is think about your shooting mechanics during a game.
Thinking about your shot is for practice, NOT for games!  In fact, you should only think during certain parts of your practice.  It’s ok to think during a form shooting session or when learning a new skill, but once you start developing rhythm and get further into practice, don’t think!
During games, train yourself to think about other things or nothing at all.
You’re going to miss a few.  So what!  Don’t think, just shoot the damn ball!!!
If you adopt this mentality, your shooting percentage will go UP.

Tip # 7 – Eliminate Negative Thoughts with this Simple Trick
Eliminating negative thoughts can dramatically improve your basketball shooting percentage.
To stop thinking and eliminate bad thoughts, you can try this little trick…
Before each game, practice, and shooting session, tell yourself that you don’t care if you make any baskets.   Say it out loud or in your head several times.
THEN, when you go to shoot (right as you’re catching the ball), say something to yourself like, “Nice shot. I can do better.”  In other words, try not to care if it goes in or not.
This simple little trick helps you to relax into the process and not think about the result. Using this technique will be enough to break you out of mini slumps and restore your confidence.

Tip #8 – Develop Optimal Arc
DID YOU KNOW that a shot with a flat 35 degree arc only has .6 inches of margin for the ball to clear without hitting the rim?  The shot has to be almost perfect to get a swish.
BUT a shot with a 45 degree medium height arc has a 3 inch margin of error!
That’s right.  Just by increasing the arc of your shot, your margin of error could increase as much as 500%!
How many shots bounce OUT of the basket because you missed by just a fraction?
As a general rule of thumb, finish your follow through with the rim clearly visible beneath the fingers of your shooting hand.  That way you will ensure that you have a decent arc on the shot.  Shots with proper arch have a much better chance of going in.
Just don’t go too high.  Because if your arc gets too high, you’ll loose your distance control.

Tip #9 – Watch DVDs
Simply by watching great shooters groove their shots over and over, you can improve your confidence and form.
The good habits and examples can be contagious.  As you watch, the good form becomes ingrained in your mind.
Not to mention, you should never stop learning.  There are lots of good shooting DVDs and books for you to learn from.

Tip #10 – Use a Partner to Tune your Shot Alignment
Spend a little time during each practice lined up along a court line about 20 feet from a partner, shooting back and forth and trying to have the ball bounce as close to the line as possible. This simple practice technique will help you to fine tune your control of the precision of your shot.

Tip #11 – Land in the Same Spot
Balance is a very important aspect of shooting.  You achieve balance primarily through a proper stance and footwork.  After your shot, you should land pretty much exactly where you started.  This means you have established good balance from your stance.

Tip #12 – Film Your Shot
You’d be amazed at how filming your shot in both games and practices can help you.
The most common response from players is… “That’s how I shoot!!??”
That’s right.  Most players haven’t seen their own shot before. Seeing your shot on film can help you to detect poor mechanics and motivate you to make commitments for improvement.  Bottom line– it’s a great way to refine your shot.

Tip #13 – Get a Partner
When possible, try to shoot with a partner.  Because when you’re alone, you end up chasing the rebound before following through properly.
This is important.  Think about how you practice…
You shoot and then you start following the shot immediately so you can get lots of reps.  Guess what?  This can mess up your follow-through.  You need to FINISH each shot and hold your follow-through.  That’s why we recommend getting a partner to rebound for you.  Now just because you can’t find a partner you can (and should) still practice by yourself.  Just be aware of holding your follow through.

Tip #14 – Fix Bad Habits by Immediately Correcting Your Shot
This is one of the easiest ways to break bad shooting habits.  For example, let’s say you forgot to hold your follow-through.  Well, immediately after you shoot, raise your hand back up and put your hand in the correct follow-through position.  This simple technique will help you quickly correct the bad habit

Tip #15 – Use a Return Device
Using basketball rebounding and return devices can literally double the number of shots you can take in practice.  Just think how much time you spend chasing the ball when you practice.  A return device solves that problem and lets you take more shots in less time.

Tip #16 – Keep the Ball Above Your Waist
When you catch the ball, always keep the ball above your waist and in the shot pocket.  There’s NO need to dip the ball.  This is wasted movement.

Tip #17 – Don’t Fall for Gimmicks
Too many players spend their hard earned money on shooting gloves and gimmicks, thinking this will make them great shooters.
You can’t use these devices during a game so it really doesn’t do you much good.  You need to learn how to shoot effectively without these devices.  There is NO magic pill.

Tip # 18 – Keep Your Shot Motion Balanced, Fluid, and Consistent
A fluid motion means that there are no jerky movements or stopping points, just one constant flow from start to finish.
Consistency can’t be stressed enough.  Your feet, arms, shot pocket, and jump height should use a consistent motion every time you shoot.  All the greatest shooters in the world have amazingly consistent movements.

Tip #19 – Groove 50 Shots Before Every Game
Before every practice and game, face the basket and shoot 50 EASY shots about four to ten feet from the basket.
Not only does this improve your shooting form, but it helps to develop phenomenal confidence.
You’ll quickly become very good at grooving these shots over and over.  You’ll see the ball going in the basket over and over.  You’ll swish the ball repeatedly and probably shoot 60%, 70%, 80%, or more, which is great for your psyche.
Why do you think that NBA players do this before games?  Why do you think that Tiger Woods starts all of his practice sessions by making 100 three-foot putts?
Because it works!  Don’t overlook this powerful strategy.

Tip #20 – Quickly Chart Your Shot to Determine Tendencies
Head to the gym and shoot a bare minimum of 50 shots.  Ask your partner to chart your shots.  The KEY is to chart the detailed results of each shot.  You will track how many shots fell short, too long, to the left, and to the right.  This information will help you to determine what you need to work on.
For example, if you consistently miss short (like many players do), you’ll need to work on your power and distance control.  If you consistently miss to the right and the left, you need to fix the mechanics of your foot and/or arm alignment.

Tip #21 – Work Game-Like Movement into Your Practice
To make game shots, you need to practice game shots.  You should use good shooting drills and practice movement off screens, cuts, chairs, and pivoting in both directions.

Get to the Gym and Apply What You’ve Learned

There ya go… 21 simple ways for you to improve your basketball shooting percentage.  Now get to the gym, apply what you’ve learned, and knock down more shots!!
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Saturday, March 30, 2013

The Balmer Formula

Leading up to the Formula: 1869 - 1882


In the years after the work of Kirchhoff and Bunsen, the major goal in spectroscopy was to determine the quantitative relationships between the lines in the spectrum of a given element as well as relationships between lines of different substances.
For example, George Johnstone Stoney in 1869 speculated that spectra arose from the internal motions of molecules. However, his mathematical theory was rejected and in 1881, Arthur Schuster concluded:
"Most probably some law hitherto undiscovered exists . . . . "
One year later, Schuster added:
"It is the ambitious object of spectroscopy to study the vibrations of atoms and molecules in order to obtain what information we can about the nature of forces which bind them together . . . But we must not too soon expect the discovery of any grand or very general law, for the constitution of what we call a molecule is no doubt a very complicated one, and the difficulty of the problem is so great that were it not for the primary importance of the result which we may finally hope to obtain, all but the most sanguine might well be discouraged to engage in an inquiry which, even after many years of work, may turn out to have been fruitless. . . . In the meantime, we must welcome with delight even the smallest step in the desired direction."
The Balmer Formula: 1885
On June 25, 1884, Johann Jacob Balmer took a fairly large step forward when he delivered a lecture to the Naturforschende Gesellschaft in Basel. He first represented the wavelengths of the four visible lines of the hydrogen spectrum in terms of a "basic number" h:
Balmer recognized the numerators as the sequence 32, 42, 52, 62 and the denominators as the sequence 32 - 22, 42 - 22, 52 - 22, 62 - 22.
So he wound up with a simple formula which expressed the known wavelengths (l) of the hydrogen spectrum in terms of two integers m and n:
For hydrogen, n = 2. Now allow m to take on the values 3, 4, 5, . . . . Each calculation in turn will yield a wavelength of the visible hydrogen spectrum. He predicted the existence of a fifth line at 3969.65 x 10¯7 mm. He was soon informed that this line, as well as additional lines, had already been discovered.

Here are some calculations using Balmer's formula.

At the time, Balmer was nearly 60 years old and taught mathematics and calligraphy at a high school for girls as well as giving classes at the University of Basle. Balmer was very interested in mathematical and physical ratios and was probably thrilled he could express the wavelengths of the hydrogen spectrum using integers.
Balmer was devoted to numerology and was interested in things like how many sheep were in a flock or the number of steps of a Pyramid. He had reconstructed the design of the Temple given in Chapters 40-43 of the Book of Ezekiel in the Bible. How then, you may ask, did he come to select the hydrogen spectrum as a problem to solve?

One day, as it happened, Balmer complained to a friend he had "run out of things to do." The friend replied: "Well, you are interested in numbers, why don't you see what you can make of this set of numbers that come from the spectrum of hydrogen?" (In 1871 Ångström had measured the wavelengths of the four lines in the visible spectrum of the hydrogen atom.)

Balmer published his work in two papers, both published in 1885. The first, titled 'Notiz über die Spektrallinien des Wasserstoff,' is the source of the equation above. He also gives the value of the constant (3645.6 x 10¯7 mm.) and discusses its significance:
"One might call this number the fundamental number of hydrogen; and if one should succeed in finding the corresponding fundamental numbers for other chemical elements as well, then one could speculate that there exist between these fundamental numbers and the atomic weights [of the substances] in question certain relations, which could be expressed as some function."
He goes on to discuss how the constant determined the limiting wavelength of the lines described by the Balmer Formula:
"If the formula for n = 2 is correct for all the main lines of the hydrogen spectrum, then it implies that towards the utraviolet end these spectral lines approach the wavelength 3645.6 in closer and closer sequence, but cannot cross this limit; while at the red end [of the spectrum] the C-line [today called Ha] represents the line of longest possible [wavelength]. Only if in addition lines of higher order existed, would further lines arise in the infrared region."
In this second paper, Balmer shows that his formula applies to all 12 of the known lines in the hydrogen spectrum. Many of the experimentally measured values were very, very close to Balmer's values, within 0.1 Å or less. There was at least one line, however, that was about 4 Å off. Balmer expressed doubt about the experimentally measured value, NOT his formula! He also correctly predicted that no lines longer than the 6562 x 10¯7 mm. line would be discovered in this series and that the lines converge at 3645.6 x 10¯7 mm.
with m = 2, 3, 4, . . . and n = 1, 2, 3, . . . ; but the two constants change in a particular pattern.
By higher order, he means allow n to take on higher values, such as 3, 4, 5, and so on in this manner:
n m
3 4, 5, 6, 7, . . .
4 5, 6, 7, 8, . . .
5 6, 7, 8, 9, . . .
There is also this one, but I'm not sure if Balmer discussed it:
n m
1 2, 3, 4, 5, . . .
Before leaving Balmer, several points:
1) Balmer's Formula is entirely empirical. By this I mean that it is not derived from theory. The equation works, but no one knew why. That is, until a certain person.
2) That certain person was born October 7, 1885 in Copenhagen. His name? Niels Henrik David Bohr.
3) Be careful when you read about Balmer's Formula in other books. Often, a form of the formula using frequency rather than wavelength is used.
At first Balmer's formula produced nothing but puzzlement, since no theoretical explanation seemed possible. In 1890 Johannes Robert Rydberg generalized Balmer's formula and showed that it had a wider applicability. He introduced the concept of the wave number v, the reciprocal of the wavelength l, and wrote his formula as
v = 1/l = R (1/n12 - 1/n22)
where n1 and n2 are integers and R is now known as the Rydberg constant (value = 10973731.534 m¯1). Later many other atomic spectral lines were found to be consistent with this formula.
For the lines in the hydrogen spectrum (today called the Balmer series), n1 = 2 and n2 takes on the values 3, 4, 5, 6, . . . . If you try the calculations (I don't mind if you do, I can wait.), remember to do one over the answer, so as to recover the wavelength.

In 1885, Balmer wrote these prophetic words:
"It appeared to me that hydrogen . . . more than any other substance is destined to open new paths to the knowledge of the structure of matter and its properties. In this respect the numerical relations among the wavelengths of the first four hydrogen spectral lines should attract our attention particularly."
In 1913, Niels Bohr will announce what is now call the Bohr Model of the Atom. He will offer the correct mechanism for the lines in the hydrogen spectrum.
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