John Pazmino 
 NYSkies Astronomu Inc 
 1994 July 27 initial 
 2018 January 7 current

Recent Astronomy Seminar
    The Recent Astronomy Seminar was a twice-monthly discussion group 
of astronomers in the New York area. It was conducted by the Amateur 
Astronomers Association in Yorkville, Manhattan, thruout the year, 
rain or shine. 
    Topics were drawn from the current litterature and experiences of 
the members. Many sessions feature handouts, slides and videos, and 
computer demonstrations and simulations. 
    In January 2005 the Seminar was converted to a 'members-only' 
function. These meetings were no longer announced thru NYC Events, 
NYSkies yahooogroup or other public medium. 1By summer 2005 the 
seminar skipped posting sessions for the coming fall season. and was 
terminated as an Association function. 

NYSkies Astronomy Seminar 
    In March 2005 NYSkies began its own series of astronomy meetings 
for local astronomers. It is free and open to the public, the NYSkies 
Astronomy Seminar. The sessions convened in Chelsea, Manhattan, on the 
first and third Thursdays of each month. Topics are drawn from the 
current litterature and experiences of the members. Sessions may 
feature handouts, topical talks, slides and other visuals, and 
demonstrations and simulations. 
    Notices of the meetings are in NYC Events, the NYSkies monthly 
roster of astronomy and related activities in New York, This was at 
first issued in the NYSkies yahoogroup and several astronomy Internet 
    NYC Events, with the Seminar announcements, shifted to the NYSkies 
web on October 2007 but remained in the newsgroups until about 2010. 
With the global attraction of the web, the newsgroup posting of NYC 
Events was ended. The Seminar now meets, on first and third Fridays of 
every month, on 14th Street bordering Chelsea and Greenwich Village, 
    Details about the NYSkies Astronomy Seminar are at

In addition to NYC Events, meeting notices ar sent to astronomers thru 
a separate mailing list several days before each session. The notice 
describes the topics and sometimes offer late-breaking astronomy news. 

'Cosmological Models' Paper 
    This paper on cosmology is a living textbook based on the debates, 
comments, discussions, announcements at NYSkies Astronomy Seminar 
meetings, starting in March 2005. Prior to then, until the fall 2004 
edition, it was released at the Recent Astronomy Seminar of Amateur 
Astronomers Association.
    Discs with files for the paper were distributed to the members 
only at the Seminar. Any astronomer may stop in at the next Seminar 
meeting and get the latest edition during the distribution season. 
Issuance by Internet email was limited due to the slow speed 
connections still in wide use then. 
    Altho the paper is continuously revised, new discs were 
distributed only twice per year near the equinoctes. The first was 
handed out in September 1994 and continued until the treatise was 
uploaded into the new NYSkies yahoogroup in march 2001. 

'Cosmological Models' Disc 
    The computer disc for 'Cosmological Models' was a standard 90mm 
hi-density stiffy disc with 1.44 megabyte capacity for use in IBM 
operating systems. Some The fisc contents erre plain textfiles with no 
peculiar chars or sodes embedded in them. The files could be viewed 
and printed thru a word-processing software. 
    The disc contained the complete paper with each chapter held in a 
separate textfile. The filenames were shown in the table of contents 
in the file '00100.txt'. You replaced just the revised files, as 
indicated by the filedates in the directory listing. New files whose 
dates match or precede those on your old disc can be disregarded. 

' Cosmological Models' in NYSkies 
    The NYSkies yahoogroup opened in January 2001 for a rapid 
announcment service  and discussion forum among New York astronomers. 
One of the earlier features of the NYSkies uahoogroup was the 
uploading in March 2001 of the 'Cosmological Models' disc into its 
article section. Then after the disc itself was no longer handed out. 
    The yahoogroup collapsed in Septembr 2001, a follateeral vicitim 
of the World Trade Center attavcks. It was revived later in September 
2001 with most of its contents restored, including the 'Csomological 
Models' disc. A notice in the yahoogroup called attention to new or 
revised files. 
    Over the years the 'Cosmological Models' paper expanded to cover 
important, but poorly treated, subjects relating to cosmology. Along 
the way the files were increasingly disorganized and ell into severe 
need of massive reworking. In fall of 2017 this work bean by first 
combining associated short files into a single larger one and 
clarifying the notation in maths. The first new portions, now loaded 
into the NYSkies web, cover special relativity, general relativity, 
gravity, and blackholes. The progress is slow but steady. 
Announcements of new material are posted in the NYSkies yahoogroup. 
    The files were revised or added irregularly since 2001. The 
initial date, posted above, of 1994 July 27 is that of the earliest 
surviving set of textfiles. When any one of the newly revamped files 
is modified, its modification date becomes the current date, entered 
above, for the entire treatise. 
    The original collection of 'Cosmological Models' files is no 
longer updated. As they are gathered into the new chapters they are 
archived in their final state. 

    This treatise on cosmological models does contain dense 
letterpress and maths. The paper aims to give the home astronomer a 
sound and proper tuition in cosmology, beyond the mish-mash of facts 
and stories so commonly offered to them. Cosmology, while attractive 
to home astronomers, is not a simple or easy subject to understand. 
The text and equations are an integral feature of learning cosmology. 
They do call for close attention. 
    Conversance in first-year college maths and astronomy is presumed 
in order to follow this treatise of the cosmological models. The maths 
freely use algebra and some simple calculus, but very little 
    Due to typographic constraints, all maths are written in a BASIC 
or FORTRAN style without the fancy symbols of typeset works. .Formulae 
and equations are written as one line, sometimes with wrap to a second 
line, like extra-long web addresses. You may have to knit the lines 
    Certain operations are treated like functions. For example 
'1der(x,y)' means 'first derivative of x relative to y'. Symbols are 
written out. 'SIGMA' means 'large-sigma' and 'sigma' means 'small-
sigma'. When a derivation or conversion is discussed, each step is set 
out, not just the end result. 

Table of Contents
    This treatise consists of separate chapters, each a separate file. 
Because chapters may avail of mateial in previous chapters, the files 
should be studied in sequence within each series, between the '- - - ' 
    In the entries here only those with proper names, like 
'Newotn's universe', are linked to actual files in the NYSkies web.  
Those with a numbered name, like '004000', are old files not in this 
    Over time tte old filesy will be gathered into new files under 
proper names, updated, and cleaned. Eventually all files, minus those 
no longer useful, will be collected into the "Cosmological Models' 
book here. 
    Please check back here from time to time for the new files. 
 - - - - - - - - - -

NEWTON'S UNIVERSE -- Newton's Universe - Early Problems - Impossible 
World -  Gravitation under Newton - Definition of Force - Two 
 Interpretations of Field Strength

EINSTEIN'S UNIVERSE -- Cosmological Principle - Newton versus Einstein 
 Physics - The Lambda Force - The Acceleration of the Universe - 
Energy of the Universe - Friedmann Model - The Standard or Classical 
Model - Hubble  Parameter - Hubble Time - The Redshift in Galactic 
Spectra - Expansion or Hubble Redshift - Time Dilation - Hubble 
Expansion vs Recession Velocity - What's Going On Here? - Milne & 
McCrea's Trick - 17th Century Cosmology? - Misinterpretations 

COSMOLOGY APPLICATIONS -- Scalefactor Function of Time - True Age of 
the Universe - Deceleration Parameter - Density Parameter - 
 Radius of the Universe - Mass of the Universe - Is the Universe a 
 Blackhole? - Proper or Einstein Distance - Hubble Horizon -- Enclosed  
Volume -  Light Travel or Lookback Time -Inverse-Square Law - 
Spectroillumination - Hubble Expansion of lambda - Magnitude-Distance 
Relation - Angular Diameter - Angular Spectroillumination 

 - - - - - - - - - -

THE EARLY UNIVERSE - - The Early Universe - The Singularity of the 
Bigbang - Geometrical and Physical Cosmology - No Antimatter? - Matter 
-Antimatter Ratio - Abundance of the Elements - Helium in the Universe 
- Origin of the Helium - Nucleogenesis - Table of Particles -Table of 
Interactions - Initial Conditions - Conservation Rules - Interaction 
Flowchart - Other Reaction Chains - WWhy Stop at Helium? - The Neutron 
Decay - The Relics of the Bigbang 

 Electromagnetic Radiation -- Frequency versus Wavelength --
 Haphazard Nomenclature -- Disparate Units of Measure --
 Detection of EMR -- Miracle of Electromagnetic Radiation

 Ampere's Law -- Faraday's Law -- Lenz's Law -- Orthogonal Fields --
 Lines of Force -- Potential Surface -- Inverse Square Law

 Gauss's Law for Charge -- Gauss's Law for Poles -- Gauss's Law for
 Mass -- Cosmic Implications -- Maxwell's Equations -- Waves --
 Maxwell's Waves

 mu0 and epsilon0 -- mu0 -- epsilon0 -- Magnetic Field Strength --
 Magnetic Pole Strength -- Refraction of Light -- Cherenkov Effect

 Interacting Fields -- Electromagnetic Wave -- Creation of EMW --
 Speed of EMW

 Energy of a Field -- Energy in EMW -- Root Mean Square -- Electric
 Field Overwhelms -- Irradiation -- Sun's Irradiation -- Sun's EMR
 Disturbance -- Electric Power Damage -- Radiation Pressure --
 Radiation Momentum

 Spectroirradiation -- Irradiation -- Inverse-Square Law --
 Arcspectroirradiation -- [Spectro]irradiosity -- Radiation-Area Law

 Light Is Nothing But EMR -- The Grand Delusion of Light --
 Spectrosensitivity -- Photometric Units -- Spectroillumination --
 Color Temperature -- Irradiation versus Illumination

 Mechanism of EMR -- Blackbody Spectroirradiosity -- Two Planck
 Constants -- Stefan-Boltzmann Law -- Wien Law -- Photon-Temperature
 Law -- Density-Temperature Law -- Blackbodies in Nature -- Lowest
 Temperature in Nature

 Mass/Energy Ratio -- The Bigbang Photosphere -- Cosmic
 Background Radiation -- Time and Place of the Photosphere -- The

 Behavior of Heat -- Second Law of Thermodynamics --  Limit on Energy
 Conversion -- No Work from Single Reservoir -- Potential Work

 Entropy -- Irreversibility of Heat Engines -- Sun as a Heat Engine --
 Waste Energy in the Universe -- Total Accumulated Entropy

 Randomness -- Boltzmann's Entropy -- Clausius's Method -- Boltzmann's
 Method -- Equivalence of Clausius and Boltzmann --
 Number Density as Entropy

 Bigbang versus Starlight Radiation -- Conservation of Mass --
 Entropy from Starlight -- Thermal History

 Nucleus -- Isotopes -- Internal Structure -- Units of Measure
 -- Symbols -- Pseudoelements -- Avogadro Number -- Mass
 Defect -- Nuclear Size -- Compared to Solar System

 Radiosiotopes -- Decay Rate -- Halflife -- Alpha Decay -- Beta
 Decay -- Gamma Decay -- Electron Capture -- Other Decays --
 Summary of Decays

 Ionizing Radiation -- Ionization Detectors -- Scintillation
 Detectors -- Track Detectors

 Radiodating -- Suitable Materials -- Suitable Decays -- Ratio of
 Isotopes -- Major Flaw

 The Melt -- The Stable isotope -- Formation of Minerals --
 Crystallization -- As the Rock Ages -- Calculation of the Age

 Observational Difficulties -- Distance versus Redshift -- Hubble
 Parameter -- Deceleration Parameter

 Difficulties with the Standard Model --  Age Problem -- History of

 Flatness Problem -- delOMEGA vs Time

 Smoothness or Horizon Problem -- Horizons

 Missing or Dark Matter Problem -- Dark Matter --
 Candidates for Dark Matter

 NonEuclid Geometries -- Geometric Curvature -- Angles of a Triangle
 -- Curvature of the Universe -- Nonzero k

 Gravitational Curvature -- Bending of Starlight -- Visualizing 4-
 Dimensional Space -- Curvature in Strong Gravity Fields -- Inside the

 Preparing the Scenarios -- k = 0, q = 1/2, rho0 = rho@ -- k = -1, q <
    1/2, rho0 < rho@ -- k = +1, q > 1/2, rho0 > rho@ -- Recapitulation

 Neutrinos -- Neutrinos from the Bigbang -- Neutrinos as Dark Matter
 -- Neutrinos Not the Final Answer

 Orbits in 3D Space -- Other Dimensions -- Anthropical Cosmology --
 Life in the Universe

 Physical Constants -- Mass of the Electron -- Doubleheavy Electron --
 Halfheavy Electron -- Is All This an Accident? -- Maybe this is
 Uniquely Our Universe?

 Fastest Communication by Light -- Four Dimensional World -- What Can
 We See? -- Who Can See Us? -- The Observability Zones

 Recent Observations -- Texture and Clumpiness -- Primordial Galaxies
 -- Keck Deuterium -- Tidal Movements -- Nearby Supernovae

 Quasars -- Microwave Relic Radiation -- Tully-Fisher Distances -- M87
 Blackhole -- Cepheid Variables -- Dark Galaxies

 - - - - - - - - - -

STEADY STATE UNIVERSE -- Steady State Universe - Furtherance of the 
Bigbang Theory - Age Problem with the Bigbang - Singularity Problem 
with the Bigbang - Perfect Cosmological Principle - Hubble Parameter -
Redshift - Density of the Universe - Proper or Einstein Distance - 
Luminosity Distance - Angular Diameter - Curvature of Space - 
Deceleration  Parameter - Comparison with Acceleration/Energy -
Continuous Creation - Nature of New Matter - Formation of Galaxies -
Minibangs - Cosmic Microwave Radiation - Helium Abundance -- No 
Cosmology? - Closing Remarks 

HISTORICAL COSMOLOGIES -- Historical Models of the Universe -
Diversity of Cosmological Models - Einstein (Original) Universe -
deSitter Universe - Einstein-deSitter Universe - Eddington Universe -
leMaitre Universe - Tolman (Oscillating) Universe - leMaitre-Tolman 
Universe - Milne Universe - Dirac Universe - Alpher-Bethe-Gamow 
Universe - 'Bigbang' - Bondi-Gold (Steady State) Universe - Godel 
Universe - Alfven-Klein Universe - Arp Universe - Hoyle-Narlikar 
Universe - Brans-Dicke Universe - deWitt (Many-Worlds) Universe -
Guth (Inflationary) Universe 

 - - - - - - - - - -

SPECIAL RELATIVITY -- Einstein's Physics of Relativity - Time and 
Space-- Spacetime -Natural Gravity - Inertial Platform or Frame - 
Impossibilty of Absolute Rest - The Speed of Light - Maxwell's Laws-- 
Michelson-Morley Experiment - Laws of Physics - The Term 'Speed of 
Light' -Comparing Clocks-- The Scenario - Equation of Motion - Home 
and Target Frame - Spacetime Interval - Four Roads to Follow -The 
Newton Road - Einstein's Mistake? - Behavior of Time - Why Is this 
Case Wrong? -  Einstein's Solution - Time Dilation - The Barrier of c 
- The Fourth Case 

RELATIVITY APPLICATIONS -- Doppler's Debacle - Absurd Doppler Speeds - 
Fizeau's Fixup -Frequency and Wavelength - The Historical Blunder - 
Reality versus Perception -Observed Time  DIlation - Einstein and 
Doppler-Fizeau - The Low-Velocity Approximation - The Missing Step - 
Space Travel Near c - Twin Paradox - Simultaneous Events - Spacetime 
Interval for Simultaneous Events - Platforms Can Not Agree - 
Simultaneous in Space and Time - Lorentz Transformation - Addition of 
Velocities -Comparison  with Newton - Fizeau's Experiments --Shift of 

GENERAL RELATIVITY -- Energy and Mass - dePretto's Ideas - Rest Mass-- 
Conservation Law - Mass into Energy - Energy into Mass-- Electron-volt 
-Critiques - Atomic Bombs - Atomic Power - Recycling of Fuel - New 
York Els -Mass Increase - Early ideas - Relativistic Mass - Mass-
Energy Equation --- No Real Increase of Mass - Invariant Mass 

GRAVITY -- A Bit of Newton Physics - Ideal Spherical Body - Gravity 
Outside a Spherical Shell - Gravity Inside a Spherical Shell -Gravity 
Field within a Solid Globe - Range of Applicability - Nonspherical 
Bodies - No Defense Against Gravity -Gravity is Cumulative - Gravity 
Field Strength - A Useful Equivalence - Gravity Work and Energy - 
Gravitational Potential Energy - Gravity Well - Escape Velocity 
BLACKHOLES  -- Schwarzschild Blackhole  - Idealized Blackhole - Spacetime 
with Mass - Schwarzschild Surface or Radius - Schwarzschild 
Spacetime  Schwarzschild Blackhole - Idealized Blackhole - 
Space tEquation - The Safe Frame - No Change of Gravity Regime - 
Time Dilation versus Distance - Nonsymmetrical Nonreciprocal Relation 
- Tests of Schwarzschild  Spacetime - Redshift of Spectral Lines -
ercury's Orbit Precession - Bending of Starlight - Astronomers Neglect 
Relativity - Features of Schwarzschild Spacetime - Near the 
Schwarzschild Surface - Length and Mass near a Blackhole - Geometry 
near the Schwarzschild Surface -  Thermodynamics and Blackholes - The 
Singularity - Newton Escapes the Singularity - Einstein Mandates the 

 - - - - - - - - - -

 Introduction to Quantum Physics -- The Hydrogen Atom --  Quantized
 Orbital Motion -- Energy Levels of Hydrogen -- Spectrum Lines

 Waves and Particles -- The Uncertainty Principle -- Role of Humans --
 Quantum Reality

 Angle Measure -- Degrees of Angle -- Radians of Angle --Triangles --
 Ratios of Sides -- Trigonometric Functions -- Special Angles --
 Alternate Functions

 Some Relations -- Sine/cosine -- sin^2 + cos^2 -- Law of Sines -- Law
 of Cosines -- Summary of Relations -- Trig Operations -- Small Angles
 -- Arclength -- How Small is Small?

 Angles in Other Quadrants -- The Quadrants -- Limits of Functions --
 Inverse Function -- Arcfunction

 Vectors -- Specifying Vectors -- Adding Vectors -- Subtracting
 Vectors -- Multiplying Vectors -- Dot Multiplication -- Angle between
 Vectors Cross Multiplication -- Special Cases

 Logarithms -- Logs as Powers -- Exponential Notation -- Symbolism --
 Finding a Logarithm -- Uses of Logarithms -- Inverse Logarithm --
 Changing Bases -- Logarithmic Progression -- Log of Trig Functions

 Units of Measure -- The Meter -- Meter as Derived Unit -- Meter,
 Metre  - The Stadion -- Columbus's Earth -- The Kilogram

 The Second -- Secular Acceleration -- Ephemeris Second --
 Atomic Second -- Leapsecond -- The Offset -- Coordinated
 Universal Time -- GPS Time

 Systems of Units -- Gauss Units --  Electrostatics -- CGS System --
 Heavyside-Lorentz System -- Special Names

 MKS System -- Systeme Internationale -- 4*pi -- Special names --
 Prefixes -- Binary Prefixes

 Europe Slowly Adapts -- America Stands Down -- Oldstyle Measures --
 Metrics Percolate In -- Home Astronomy Metrics -- Vernacular
 Metrics -- The New Millennium -- The Future

 Standard Time - US Standard Time -- Greenwich Mean Time --
 Universal Time -- Timezones -- Zulu -- Specifying Local
 Time -- International Dateline

 Daylight Savings -- US Daylight Savings -- Arizona
 and Hawaii

 Hours of the Day -- Minutes and Seconds -- 12x12 and 24 -- 12
 AM, 12 PM -- Planetarium Clocks -- 12-Hour Dial -- Time

 The Week -- Days of the Week -- Order of the Days -- Sequence
 of Weeks

 Year Numbering -- Julian Calendar --  Leapyear -- Proleptic
 Julian Calendar -- Gregorian Calendar -- Acceptance of
 Gregorian Calendar -- Date Notation -- Dates on Other Worlds
 -- Day Counts

 Olber's Paradox -- Mach's Principle -- Proton Decay

 Blackholes -- Density inside a Blackhole -- Destruction of Identity
 -- Four Kinds of Blackhole -- No Vacuum Cleaner or Drainhole -- No
 Funnel or Well -- No Tidal Shredding -- No Remote Relativity

 Tidal Forces -- Roche Limit -- Applicability of the Roche Limit --
 Roche and Schwarzschild Limits

 Cosmological Tables -- Table of beta = (1-(V/c)^2)^(1/2) --

 Table of Useful Values -- Older Metric Units

 References  -- 1920s -- 1930s -- 1940s -- 1950s -- 1960s -- 1970s

 References -- 1980s -- 1990s

 References -- 2000s

 Anceint elements -- Naming elements -- International names --
 Numerical names -- Loose latin

 Table of heavy elements -- Transuuranium -- Name confusion --
 Atomic address

 Chart of Nuclei

 Symbols Used in the Boxed Equations