Wednesday, December 24, 2008

Experimental Physics

Experimental Physics

Added & Edited by:

Shahreer Zahan & Friends and Arif Nurahman

Apparatus for making Bose-Einstein Condensate (from cua.mit.edu)


Prof. Michael Romalis romalis@princeton.edu, Office: Jadwin 230, Phone 8-5586
Lectures: Tuesday 12;30-1:20 PM, Room 343
Labs One lab every two weeks, by arrangement with TA's
Office Hours: Tuesday, Thursday 1:30-2:30 PM
TA: Fiona Burnell

fburnell@princeton.edu, Office Jadwin 422

TA: Ben Loer bloer@princeton.edu, Office Jadwin 224, B30, Phone 8-1122

Support: Ray Laue

rlaue@princeton.edu, Office: Jadwin 116, Phone 8-4370

Syllabus

Lecture notes
Statistics and Error Analysis
Introduction to electronic circuits
Introduction to Genplot
Radioactivity
Vacuum Techniques
Detection of high-energy particles
Semiconductors and Optics
Superconductors and Cryogenics

Online course for handling sealed radiation sources - Read the material and take online test. After completing the test you will be issued a monitoring badge which is required for experiments involving radioactive sources (Mossbauer, Beta spectrum and Positron labs)

Labs

Experiment

TA

Description

Manuals

Electronics Lab (required)

Mike

Building a two-way radio

ARRL Handbook

Muon Decay

Ben

Measurement of the lifetime of cosmic muons stopped in a liquid scitillator

Muon_lifetime.pdf

Mössbauer

Ben

Demonstration of the Mössbauer effect : recoilless emission and absorption of gamma rays

Mossbauer.pdf

Holography

Ben

Recording of photographic laser holograms

Holography.pdf

b spectrum

Ben

Measurement of the energy spectrum of beta decay electrons

Beta_spectrum.pdf

Positron decay

Fiona

Measurement of the momentum distribution of gamma rays from positron decay

Positron.pdf

Electron Diffraction

Fiona

Measurement of electron diffraction by metal crystals

Electron_diffraction.pdf

Photoelectric effect

Fiona

Photoelectric effect: study of the photoemission of electrons

Photoelectric.pdf

Coulomb force

Fiona

Test of the 1/r2 nature of the Coulomb force

Coulomb.pdf

NMR

Fiona

Nuclear Magnetic Resonance, Spin echo and measurements of transverse spin relaxation time

Spin_echo.pdf

Optical pumping

Mike

Demonstration of optical pumping of Rb atoms and optical detection of magnetic resonance.

Optical_pumping.pdf
E-coli Ben Study of the motion of E-coli bacteria E_coli.pdf
Two-slit interference Mike Double-slit single photon interference measurements

Experimental Physics Seminar

PHYS 210 – Experimental Physics Seminar

Next offered Spring 2007
Contact Prof. Lyman Page


Past Student Projects:

2006 Microscope interferometery by Emily Kosten and Peter Combs
Laser Microphone by Seth Blumberg, Joel Thompson and David Zaslavsky
Magnetic Leviation by Lenny Shulgin, Eric Berglund, and Howard Yu

2005 Balancing a pencil on its tip with feedback by Caleb Howe, Greg Haislip and Lear Janiv
Wire chamber for muon detection by Martin Niederste-Ostholt, Ariel Kleinerman, Jess Riedel and Corey Ritter
Magnetic properties of superconductors by Shankar Iyer, Giwan Kim, Yijia Eric Lu and Leizhi Sun
Properties of superfluid helium by Yu Gan, Godfrey Miller and Carl Boettiger

2004 Electromagnetic Railgun by Denis Erkal, Ma'ayan Bresler, Paul Nelson, and Aaron Wertheimer
Electron Cyclotron by Austin Akey, Josh Brodie, Lucy Jacobson, and Mike White
Single Bubble Sonoluminescence by Aaron Kleinman, Aly Spencer, Dan Recht, and Nitesh Paryani
Properties of Plasma Discharge by Richard Aspinall, Ying Gao, Scott Schiffres, and Teddy Wieser

2003 Laser Optical Tweezers by Adam Hopkins, James McClave, and Nhan Tran
Ultrasound Ranging by Steven Andrews and Blake Robinson
Temperature of Cosmic Microwave Background Radiation by Srivas Prasad
Superconducting Tunneling Junctions by Ursula Pavlish, Josh Burton, and Cullen Blake

Lab/Lecture 1: LabView Tutorial
Handouts: Syllabus
LabView Tutorial
LabView Quick Guide
LabView Reference

Lab/Lecture 2: Signal Recovery Techniques
Electronic circuits
Handouts:Signal Recovery
Electronic Circuits and Feedback

Lab/Lecture 3: Cosmic ray detection
High Energy Physics
Cosmic microwave background radiation
Cosmology
Solar cell fabrication
Semiconductors
Vacuum Technology
Semiconductor applets
PN Junction
Conduction through PN diode
Conduction through bipolar transisor
Other semiconductor applets

Lab/Lecture 4: Superconductivity
Condensed Matter Physics Part I: Superconductivity
Condensed Matter Physics Part II: Superconductive Quantum Interference Devices
Atomic Spin Magnetometer
Atomic Physics

Lab/Lecture 5: Optics and Microscopy
Microscopy

Class handouts:
LabView Tutorial
LabView Quick Guide
LabView Reference
Signal Recovery
Electronic Circuits and Feedback
High Energy Physics
Cosmology
Semiconductors
Vacuum Technology
Condensed Matter Physics Part I: Superconductivity
Condensed Matter Physics Part II: Superconductive Quantum Interference Devices
Optics

Additional information on advanced topics:
Semiconductors and electronic devices links
Overview of Semiconductors
p-n junction
Manufacturing of intergrated circuits
Steps in manufacturing process
P-N junction
Conduction of P-N junction
More Semiconductor Applets
Cosmic Microwave background
Introduction to Cosmic Microwave Background
Discussion of Cosmic Microwave Background
High Energy Physics
Cosmic ray showers
Professional-strength particle physics review
LEP Z-decay Java simulator
Pictures from high-energy detectors
CDF Detector (Fermilab),
D0 event, top quark (Fermilab),
L3 event, Higgs candidate (CERN),
STAR event (BNL),
Super-Kamiokande Neutrino Detector

Useful links
Free Evaluation copy of LabView (Need to register with National Instruments)

Literature Search Databases
Web of Science
INSPEC

Superconductivity Links
A Guide to Superconductivity,
Superconductuvity Cocepts,
SQUIDs: A popular account,
SQUIDs: A technical Report
High Temperature Superconductors

Other Topics
Laser operation

Major high-energy physics laboratories
FermiLab, near Chicago, home to the highest energy proton-anti-proton collider.
SLAC, near San Francisco, the largest linear electron accelerator and B meson factory for testing CP violation.
BNL, Long Island, home to Relativistic Heavy Ion Collider, colliding gold nuclei
CERN, Geneva, Switzerland, home to the largest e+-e- circular collider and future Large Hadron Collider.
KEK, Japan, home to a B-meson factory for study of CP violation.

Other Links
American Physical Society
Society of Physics Students


Add & Edited by:

Shareer Zahan & Friends and Arif Nurahman

What is classical mechanics

What is classical mechanics?



By:

Arif Nurahman & Shahreer Zahan and Friends

Classical mechanics
is the study of the motion of bodies (including the special case in which bodies remain at rest) in accordance with the general principles first enunciated by Sir Isaac Newton in his Philosophiae Naturalis Principia Mathematica (1687), commonly known as the Principia. Classical mechanics was the first branch of Physics to be discovered, and is the foundation upon which all other branches of Physics are built. Moreover, classical mechanics has many important applications in other areas of science, such as Astronomy (e.g., celestial mechanics), Chemistry (e.g., the dynamics of molecular collisions), Geology (e.g., the propagation of seismic waves, generated by earthquakes, through the Earth's crust), and Engineering (e.g., the equilibrium and stability of structures). Classical mechanics is also of great significance outside the realm of science. After all, the sequence of events leading to the discovery of classical mechanics--starting with the ground-breaking work of Copernicus, continuing with the researches of Galileo, Kepler, and Descartes, and culminating in the monumental achievements of Newton--involved the complete overthrow of the Aristotelian picture of the Universe, which had previously prevailed for more than a millennium, and its replacement by a recognizably modern picture in which humankind no longer played a privileged role.

In our investigation of classical mechanics we shall study many different types of motion, including:


Translational motion--motion by which a body shifts from one point in space to another (e.g., the motion of a bullet fired from a gun).

Rotational motion--motion by which an extended body changes orientation, with respect to other bodies in space, without changing position (e.g., the motion of a spinning top).

Oscillatory motion--motion which continually repeats in time with a fixed period (e.g., the motion of a pendulum in a grandfather clock).

Circular motion--motion by which a body executes a circular orbit about another fixed body [e.g., the (approximate) motion of the Earth about the Sun].
Of course, these different types of motion can be combined: for instance, the motion of a properly bowled bowling ball consists of a combination of translational and rotational motion, whereas wave propagation is a combination of translational and oscillatory motion. Furthermore, the above mentioned types of motion are not entirely distinct: e.g., circular motion contains elements of both rotational and oscillatory motion. We shall also study statics: i.e., the subdivision of mechanics which is concerned with the forces that act on bodies at rest and in equilibrium. Statics is obviously of great importance in civil engineering: for instance, the principles of statics were used to design the building in which this lecture is taking place, so as to ensure that it does not collapse.

Prof. Michael Romalis

Physics Department, Princeton University, Phone: 609-258-5586, E-mail: romalis@princeton.edu

Teaching: Mechanics, PHYS 203
Experimental Physics Seminar, PHYS 210
Experimental Physics (Junior lab), PHYS 312

Atomic Physics, PHYS 551

Research Webpage



Prof. Michael Romalis romalis@princeton.edu, Office: Jadwin 230, Phone 8-5586
Lectures: Tuesday, Thursday, 11:00 – 12:20, Room: Jadwin A07
Homework Session (optional) : Monday, 7:30-9:30, Room: Jadwin 475
Office Hours: Monday, Tuesday, Thursday, 1:00-2:30 PM, Jadwin 230
TA: Marcus Benna mbenna@Princeton.edu, Office: Jadwin 404
TA office hours: Thursday 3-5 PM, Jadwin 404

Class Description and Syllabus


Homework

Reading assignment
Problems to hand in
Due Date
Solutions
1
Chapter 2, 3.1-3.8, Appendix C
Homework 1
September 27th
Solution 1
2
Chapter 6
Homework 2
October 4th
Solution 2
3
Chapter 7:1-7:9
T&M 7.7, 7.9, 7.13, 7.20, 7.34
October 11th
Solution 3
4
Chapter 7:10,7:13
Homework 4
October 18th
Solution 4
5
Chapter 5,8
Homework 5
October 25th
Solution 5
6
Chapter 9:9-9:10, Chapter 12:1-12:8
Homework 6
November 15th
Solution 6
7
Chapter 12:9, 13:1-13:4,13:6,13:7
Homework 7
November 27th
Solution 7
8
Chapter 3:5,3:6,3:8,3:9
Homework 8
November 29th
Solution 8
9
Chapter 10
Homework 9
December 6th
Solution 9
10
Chapter 11
Homework 10
December 13th
Solution 10

Saturday, December 20, 2008

Let's Move On

-Friendship Like Water, Fresh Every Time-

-The Best of You, is Someone Who Can Contribute for All People-

-H2O-

We Are The Next Champions

We Will Become Champions
Wait World
-We Coming-


Friendship Make World Wonderful
-H2O-




Astrophysics

From Wikipedia, the free encyclopedia


NGC 4414, a typical spiral galaxy in the constellation Coma Berenices, is about 56,000 light-years in diameter and approximately 60 million light-years distant

Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties (luminosity, density, temperature, and chemical composition) of celestial objects such as galaxies, stars, planets, exoplanets, and the interstellar medium, as well as their interactions. The study of cosmology is theoretical astrophysics at scales much larger than the size of particular gravitationally-bound objects in the universe.

Because astrophysics is a very broad subject, astrophysicists typically apply many disciplines of physics, including mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear and particle physics, and atomic and molecular physics. In practice, modern astronomical research involves a substantial amount of physics. The name of a university's department ("astrophysics" or "astronomy") often has to do more with the department's history than with the contents of the programs. Astrophysics can be studied at the bachelors, masters, and Ph.D. levels in aerospace engineering, physics, or astronomy departments at many universities.

Contents


History

Although astronomy is as ancient as recorded history itself, it was long separated from the study of physics. In the Aristotelian worldview, the celestial world tended towards perfection—bodies in the sky seemed to be perfect spheres moving in perfectly circular orbits—while the earthly world seemed destined to imperfection; these two realms were not seen as related.

Aristarchus of Samos (c. 310–250 BC) first put forward the notion that the motions of the celestial bodies could be explained by assuming that the Earth and all the other planets in the Solar System orbited the Sun. Unfortunately, in the geocentric world of the time, Aristarchus' heliocentric theory was deemed outlandish and heretical, and for centuries, the apparently common-sense view that the Sun and other planets went round the Earth nearly went unquestioned until the development of Copernican heliocentrism in the 16th century AD. This was due to the dominance of the geocentric model developed by Ptolemy (c. 83-161 AD), an Hellenized astronomer from Roman Egypt, in his Almagest treatise.

The only known supporter of Aristarchus was Seleucus of Seleucia, a Babylonian astronomer who is said to have proved heliocentrism through reasoning in the 2nd century BC. This may have involved the phenomenon of tides,[1] which he correctly theorized to be caused by attraction to the Moon and notes that the height of the tides depends on the Moon's position relative to the Sun.[2] Alternatively, he may have determined the constants of a geometric model for the heliocentric theory and developed methods to compute planetary positions using this model, possibly using early trigonometric methods that were available in his time, much like Copernicus.[3] Some have also interpreted the planetary models developed by Aryabhata (476-550), an Indian astronomer,[4][5][6] and Albumasar (787-886), a Persian astronomer, to be heliocentric models.[7]

In the 9th century AD, the Persian physicist and astronomer, Ja'far Muhammad ibn Mūsā ibn Shākir, hypothesized that the heavenly bodies and celestial spheres are subject to the same laws of physics as Earth, unlike the ancients who believed that the celestial spheres followed their own set of physical laws different from that of Earth.[8] He also proposed that there is a force of attraction between "heavenly bodies",[9] vaguely foreshadowing the law of gravity.[10]

In the early 11th century, Ibn al-Haytham (Alhazen) wrote the Maqala fi daw al-qamar (On the Light of the Moon) some time before 1021. This was the first successful attempt at combining mathematical astronomy with physics, and the earliest attempt at applying the experimental method to astronomy and astrophysics. He disproved the universally held opinion that the moon reflects sunlight like a mirror and correctly concluded that it "emits light from those portions of its surface which the sun's light strikes." In order to prove that "light is emitted from every point of the moon's illuminated surface," he built an "ingenious experimental device." Ibn al-Haytham had "formulated a clear conception of the relationship between an ideal mathematical model and the complex of observable phenomena; in particular, he was the first to make a systematic use of the method of varying the experimental conditions in a constant and uniform manner, in an experiment showing that the intensity of the light-spot formed by the projection of the moonlight through two small apertures onto a screen diminishes constantly as one of the apertures is gradually blocked up."[11]

In the 14th century, Ibn al-Shatir produced the first model of lunar motion which matched physical observations, and which was later used by Copernicus.[12] In the 13th to 15th centuries, Tusi and Ali Kuşçu provided the earliest empirical evidence for the Earth's rotation, using the phenomena of comets to refute Ptolemy's claim that a stationery Earth can be determined through observation. Kuşçu further rejected Aristotelian physics and natural philosophy, allowing astronomy and physics to become empirical and mathematical instead of philosophical. In the early 16th century, the debate on the Earth's motion was continued by Al-Birjandi (d. 1528), who in his analysis of what might occur if the Earth were rotating, develops a hypothesis similar to Galileo Galilei's notion of "circular inertia", which he described in the following observational test:[13][14]

"The small or large rock will fall to the Earth along the path of a line that is perpendicular to the plane (sath) of the horizon; this is witnessed by experience (tajriba). And this perpendicular is away from the tangent point of the Earth’s sphere and the plane of the perceived (hissi) horizon. This point moves with the motion of the Earth and thus there will be no difference in place of fall of the two rocks."

After heliocentrism was revived by Nicolaus Copernicus in the 16th century, Galileo Galilei discovered the four brightest moons of Jupiter in 1609, and documented their orbits about that planet, which contradicted the geocentric dogma of the Catholic Church of his time, and escaped serious punishment only by maintaining that his astronomy was a work of mathematics, not of natural philosophy (physics), and therefore purely abstract.

The availability of accurate observational data (mainly from the observatory of Tycho Brahe) led to research into theoretical explanations for the observed behavior. At first, only empirical rules were discovered, such as Kepler's laws of planetary motion, discovered at the start of the 17th century. Later that century, Isaac Newton bridged the gap between Kepler's laws and Galileo's dynamics, discovering that the same laws that rule the dynamics of objects on Earth rule the motion of planets and the moon. Celestial mechanics, the application of Newtonian gravity and Newton's laws to explain Kepler's laws of planetary motion, was the first unification of astronomy and physics.

After Isaac Newton published his book, Philosophiae Naturalis Principia Mathematica, maritime navigation was transformed. Starting around 1670, the entire world was measured using essentially modern latitude instruments and the best available clocks. The needs of navigation provided a drive for progressively more accurate astronomical observations and instruments, providing a background for ever more available data for scientists.

At the end of the 19th century, it was discovered that, when decomposing the light from the Sun, a multitude of spectral lines were observed (regions where there was less or no light). Experiments with hot gases showed that the same lines could be observed in the spectra of gases, specific lines corresponding to unique chemical elements. In this way it was proved that the chemical elements found in the Sun (chiefly hydrogen) were also found on Earth. Indeed, the element helium was first discovered in the spectrum of the Sun and only later on Earth, hence its name. During the 20th century, spectroscopy (the study of these spectral lines) advanced, particularly as a result of the advent of quantum physics that was necessary to understand the astronomical and experimental observations.[15]

See also:

Observational astrophysics

The Pleiades, an open cluster of stars observed in the constellation of Taurus. NASA photo

The majority of astrophysical observations are made using the electromagnetic spectrum.

Other than electromagnetic radiation, few things may be observed from the Earth that originate from great distances. A few gravitational wave observatories have been constructed, but gravitational waves are extremely difficult to detect. Neutrino observatories have also been built, primarily to study our Sun. Cosmic rays consisting of very high energy particles can be observed hitting the Earth's atmosphere.

Observations can also vary in their time scale. Most optical observations take minutes to hours, so phenomena that change faster than this cannot readily be observed. However, historical data on some objects is available spanning centuries or millennia. On the other hand, radio observations may look at events on a millisecond timescale (millisecond pulsars) or combine years of data (pulsar deceleration studies). The information obtained from these different timescales is very different.

The study of our own Sun has a special place in observational astrophysics. Due to the tremendous distance of all other stars, the Sun can be observed in a kind of detail unparalleled by any other star. Our understanding of our own sun serves as a guide to our understanding of other stars.

The topic of how stars change, or stellar evolution, is often modeled by placing the varieties of star types in their respective positions on the Hertzsprung-Russell diagram, which can be viewed as representing the state of a stellar object, from birth to destruction. The material composition of the astronomical objects can often be examined using:

Theoretical astrophysics

Theoretical astrophysicists use a wide variety of tools which include analytical models (for example, polytropes to approximate the behaviors of a star) and computational number figure outingness. Each has some advantages. Analytical models of a process are generally better for giving insight into the heart of what is going on. Numerical models can reveal the existence of phenomena and effects that would otherwise not be seen.[16][17]

Theorists in astrophysics endeavor to create theoretical models and figure out the observational consequences of those models. This helps allow observers to look for data that can refute a model or help in choosing between several alternate or conflicting models.

Theorists also try to generate or modify models to take into account new data. In the case of an inconsistency, the general tendency is to try to make minimal modifications to the model to fit the data. In some cases, a large amount of inconsistent data over time may lead to total abandonment of a model.

Topics studied by theoretical astrophysicists include: stellar dynamics and evolution; galaxy formation; large-scale structure of matter in the Universe; origin of cosmic rays; general relativity and physical cosmology, including string cosmology and astroparticle physics. Astrophysical relativity serves as a tool to gauge the properties of large scale structures for which gravitation plays a significant role in physical phenomena investigated and as the basis for black hole (astro)physics and the study of gravitational waves.

Some widely accepted and studied theories and models in astrophysics, now included in the Lambda-CDM model are the Big Bang, Cosmic inflation, dark matter, dark energy and fundamental theories of physics.

Nucleosynthesis

Physical process Experimental tool Theoretical model Explains/predicts
Gravitation Radio telescopes Self-gravitating system Emergence of a star system
Nuclear fusion Spectroscopy Stellar evolution How the stars shine and how metals formed
The Big Bang Hubble Space Telescope Expanding universe Age of the Universe
Quantum fluctuations COBE Cosmic inflation Flatness problem
Gravitational collapse X-ray astronomy General relativity Black holes at the center of Andromeda galaxy
CNO cycle in stars


See also

References

  1. ^ Lucio Russo, Flussi e riflussi, Feltrinelli, Milano, 2003, ISBN 88-07-10349-4.
  2. ^ Bartel Leendert van der Waerden (1987). "The Heliocentric System in Greek, Persian and Hindu Astronomy", Annals of the New York Academy of Sciences 500 (1), 525–545 [527].
  3. ^ Bartel Leendert van der Waerden (1987). "The Heliocentric System in Greek, Persian and Hindu Astronomy", Annals of the New York Academy of Sciences 500 (1), 525–545 [527-529].
  4. ^ B. L. van der Waerden (1970), Das heliozentrische System in der griechischen,persischen und indischen Astronomie, Naturforschenden Gesellschaft in Zürich, Zürich: Kommissionsverlag Leeman AG. (cf. Noel Swerdlow (June 1973), "Review: A Lost Monument of Indian Astronomy", Isis 64 (2), p. 239-243.)
    B. L. van der Waerden (1987), "The heliocentric system in Greek, Persian, and Indian astronomy", in "From deferent to equant: a volume of studies in the history of science in the ancient and medieval near east in honor of E. S. Kennedy", New York Academy of Sciences 500, p. 525-546. (cf. Dennis Duke (2005), "The Equant in India: The Mathematical Basis of Ancient Indian Planetary Models", Archive for History of Exact Sciences 59, p. 563–576.).
  5. ^ Thurston, Hugh (1994), Early Astronomy, Springer-Verlag, New York. ISBN 0-387-94107-X, p. 188:

    "Not only did Aryabhata believe that the earth rotates, but there are glimmerings in his system (and other similar systems) of a possible underlying theory in which the earth (and the planets) orbits the sun, rather than the sun orbiting the earth. The evidence is that the basic planetary periods are relative to the sun."

  6. ^ Lucio Russo (2004), The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had To Be Reborn, Springer, Berlin, ISBN 978-3-540-20396-4. (cf. Dennis Duke (2005), "The Equant in India: The Mathematical Basis of Ancient Indian Planetary Models", Archive for History of Exact Sciences 59, p. 563–576.)
  7. ^ Bartel Leendert van der Waerden (1987). "The Heliocentric System in Greek, Persian and Hindu Astronomy", Annals of the New York Academy of Sciences 500 (1), 525–545 [534-537].
  8. ^ Saliba, George (1994a), "Early Arabic Critique of Ptolemaic Cosmology: A Ninth-Century Text on the Motion of the Celestial Spheres", Journal for the History of Astronomy 25: 115-141 [116]
  9. ^ Waheed, K. A. (1978), Islam and The Origins of Modern Science, Islamic Publication Ltd., Lahore, p. 27
  10. ^ Briffault, Robert (1938), The Making of Humanity, 191
  11. ^ Toomer, G. J. (December 1964), "Review: Ibn al-Haythams Weg zur Physik by Matthias Schramm", Isis 55 (4): 463–465 [463–4], doi:10.1086/349914
  12. ^ George Saliba (2007), Lecture at SOAS, London - Part 4/7 and Lecture at SOAS, London - Part 5/7
  13. ^ Ragep, F. Jamil (2001a), "Tusi and Copernicus: The Earth's Motion in Context", Science in Context (Cambridge University Press) 14 (1-2): 145–163
  14. ^ Ragep, F. Jamil (2001b), "Freeing Astronomy from Philosophy: An Aspect of Islamic Influence on Science", Osiris, 2nd Series 16 (Science in Theistic Contexts: Cognitive Dimensions): 49-64 & 66-71
  15. ^ Frontiers of Astrophysics: Workshop Summary, H. Falcke, P. L. Biermann
  16. ^ H. Roth, A Slowly Contracting or Expanding Fluid Sphere and its Stability, Phys. Rev. (39, p;525–529, 1932)
  17. ^ A.S. Eddington, Internal Constitution of the Stars

External links