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In the world of Asiyah, science is the body of the world and math its soul. Beauty is the soul of math above. I view this world like a helix with one side being science and the other deist simple good religion. Science without religion has no value system and we need a value system to even pursue good science. To believe in God leads us to value the gift of this world. Moreover in Judaism we are taught to believe in resurrection as a final reward. The greatest gift that God can give us is a physical resurrection! This teaches us how beautiful this world really is.

Torah teaches us to view the Earth as the center of God’s plan and Israel as the center of the world. Israel connects three continents like the center point of Panasia—God’s creative energy spreading forth first from the Rock on top Mt. Moriah then to the rest of the world. Astronomy teaches us that the Big Bang took place simultaneously everywhere such that there is no center to the Universe or better yet; everything is together the center of the Universe.

We live each day appreciating the beauty of the world. Though our days are short with silly ways, still; how great it is to live even a single day—to express our gratitude for even a single breath.

Maxwell’s equations predicted that light and radio waves have a fixed speed. Albert Michelson and Edward Morley showed that this fixed speed is independent of the movement of objects.^[2129] For example, an object moving towards the sun and an object moving away from the Sun would witness passing light beams to have the same velocity, the speed of light that is denoted c.

Since the upper limit of velocity is limited to the speed of light a second object moving at v₂ in relation to a first object v₁ has the following true velocity:

So with v₁ = c/2 and v₂ = c/2, the actual velocity of the 2^nd object is (c/2+ c/2)/(1+(c²/4 * 1/c²)) = 4/5 c.

The basic principle of general relativity is that mass curves space and time. As one walks around the Earth in an apparent straight light and ends in the same place, so likewise an object orbiting another object takes the shortest path between two points in curved space. If several people begin traveling north from different places on the globe, they will all end at the North Pole. This is an example of positive space. On the other hand, if two people start next to each other walking in parallel, the curvature of the Earth will cause them to diverge. This is an example of negative space.

The curvature of space towards an object resembles a funnel. For example, objects close to a singularity in a black hole experience spaghettification. That is they will be stretched in length towards the hole due to the negative curvature of space, and squeezed in width due to the positive curvature of space, since space itself is stretched and squeezed by the black hole.

While mass determines the magnitude of the gravitational force, distance to an object determines its tidal force. For example, the gravity of the Sun keeps the Earth in its orbit, but has little effect on the levels of the oceans. On the other hand, the closeness of the Moon produces high tides as it passes over oceans. The Moon also produces high tides on the opposite side of the Earth as the it slightly pulls the earth towards it leaving the oceans on the far side of the Earth out further or higher.

General Relativity predicts Time dilation within a gravitational field. In other words, time passes faster in a region of stronger gravity than a region with lesser gravity. Time on a mountain top passes more slowly than time at its base. Time on a spaceship will pass more slowly than time on earth, unless the ship has an artificial gravity from a centrifugal force. The theoretical limits of a singularity show gravity and the passage of time going to infinity.

Objects emit lower frequencies of light at lower temperatures while they require a higher temperature to emit higher frequencies of light. The reason that there is a temperature threshold for emitting higher frequencies of light is because objects emit energy at discrete values and a higher frequency of light requires a greater amount of energy to discretely occur. Objects prefer to radiate energy at lower frequencies if the rate of emission is sufficient as in the common case of infrared heat. Nevertheless, objects at very higher temperatures need to radiate larger quantities of energy more quickly which is done with higher frequencies of light. The minimum amount of energy at a particular frequency, the quanta, is found from this formula:

e = hν

Here ‘e’ is energy, ‘h’ is Planck’s constant 6.6256 × 10^-27 and ‘ν’ is the frequency of the emitted radiation. Higher frequencies of light have a higher level of energy for the same amplitude. Also from this formula we see that objects can radiate energy only as a multiple of their quanta of energy. Each quanta of energy is a photon emission at the wavelength of the object.^[2130] The total energy in ‘n’ photons is dependent on frequency and the constant ‘h’.

ne = nhν

As the temperature of objects go up they radiate energy up to a maximum frequency. This is expressed in Wien’s law as:

ν_max = kT

Here ‘k’ is a proportional constant and ‘T’ is temperature. From here we see that the color of star light indicates the temperature of the star. The hotter the temperature, the shorter the life left in the star.^[2131]

Reddish stars are comparatively cool, with surface temperatures of 2000-3000K. Orange stars have surface temperatures of 3000-5000K. There are also white stars with surface temperatures of 8000-12000K and bluish stars that are hotter still.

The proton-proton chain or cycle consists of a series of nuclear reactions for a fusion reaction. Byproducts include the beta particle, an electron or positron; an alpha particle, 2-proton, 2 neutron nucleus; Gamma ray, high frequency photon; and the neutrino, ultra-small mass with speed of light particle (3 types).

¹H + ¹H → ²H + e⁺ + ν = Deterium + Positron beta particle (positive charge electron) + Neutrino
²H + ¹H → ³H + γ = Helium-3 + Gamma Ray (high frequency-energy photon)
³H + ³H → ⁴H + ¹H + ¹H = Helium-4 alpha particle + proton + proton

The principle states simply that the uncertainty of the position of an object multiplied by the uncertainty of its momentum cannot be smaller than Planck’s constant.

ΔP*m*ΔV ≥ h

One measures the position of a particle with a laser.^[2132] The deflection of light between two wave ‘crests’ determines a particle’s position.^[2133] Hence, the higher the frequency and smaller the wavelength, the more precisely a laser will measure a particle’s position. The irony here is that the higher the frequency of the measuring laser, the larger the value of its energy from e = hν, and the larger the impact on the particle’s momentum. Thus, the more precisely we know the position of the object the more uncertain becomes its velocity.

All particles exhibit wave behavior. If we take the experiment of sending a single electron toward a partition with two slits at different distances from the electron, the electron will pass through both slits as waves that will interfere to form alternating light fringes on a screen behind the partition.^[2134] In essence the electron is a wave. When electrons travel around a nucleus, they have an orbit, which provides the proper distance so that they can form a standing wave. They accept or release energy if they can move to another orbit distance that is also a standing wave. This change of energy is a multiple of photons or quanta.^[2135] Quantum Mechanics explains Bohr’s theory on the limited number of orbits in an atom. Multiple atoms in molecules join up sharing electrons in forms that enable further extensions of the standing waves of electrons.

f = V/λ or ν = ς/λ in physics notation

Here frequency is equal to Velocity divided by wavelength by definition.

λ = h/(mV)

This equation is related to energy = hf or e = hν, where h is Planck’s constant. Since frequency includes the definition of wavelength, there is an aspect of Newtonian physics, energy = ½mV² included. Note the ½ factor is included in the e term.

Equation 28-9 shows that even heavy objects having a very small velocity would move as a wave given enough time. A heavy object with a visible velocity would have a wavelength too small for us to [2136]ure.²¹³⁶ For an electron with a constant mass, wavelength depends on velocity. High-speed electrons have a small wavelength and high frequency and thus high energy. Classical Physics deals with particle or object theory, while Quantum Physics deals with wave effects.

The Big Bang Theory stands opposed to the Static Universe Theory in suggesting that all matter existed in a singularity without space and time, i.e. with infinite density, and then exploded. Several recent observations support this theory.

Red shift is the spreading of the wavelength of light due to the Doppler effect of an object moving away from another object. Interestingly our observations show that the Red Shift increases with the distance an object is from Earth. This implies that the farther an object is away the faster it is moving away.

The Big Bang Theory is one simple explanation for the Red Shift. In the beginning of the Universe, all matter began its trajectory from the same point at the same time. Now objects that are further away from Earth in the expansion are also that way because they had a greater initial velocity from the center.

Penzias and Wilson discovered that there is microwave background radiation equal in all directions around the Earth. Microwave radiation having a wavelength with the order of magnitude of the hundred thousandth of a meter is the result of the Doppler effect on visible light whose wavelength has the order of magnitude of “four to seven ten-millionths of a meter.”^[2137] Gamov theorized that the initial Universe was “very hot and dense, glowing white hot.”^[2138] “Dicke and Peebles argued that we should still be able to see the glow of the early universe, because light from very distant parts of it would only just be reaching us now.” The Microwave radiation around us today is the initial ‘light’ of the Universe under the Doppler effect from those sources that are receding from the Earth at the greatest velocity, i.e. also furthest from the Earth. Hubble’s discovery of the Expanding Universe is based on measuring Red Shifts.

Planck’s radiation law shows the relationship of intensity with wavelength. In the early Universe the high energy would require smaller wavelengths of energy to radiate heat at sufficient rates. Today’s temperature of the Universe is now 5º Kelvin. “As the universe expanded, the temperature would have dropped, each photon being redshifted by the cosmological expansion to longer wavelength, as the American physicist Richard C. Tolman had already shown in 1934.”^[2139]

General relativity implies an Expanding Universe to counter the Newtonian effects of gravity that would have otherwise pulled all matter together. Alexander Friedmann made two assumptions to prove this:

The first item is validated by the discovery of the Microwave Background, which is the same in all directions. The second item is interesting and suggests that matter is on the perimeter of an expanding Universe like the surface of Earth or as Hawking symbolizes, a balloon that someone is blowing up.^[2140] While we are not in the position to prove the second item, Friedmann’s assumptions derive the theory that galaxies further away are moving faster away from each other.

Newtonian conservation of momentum with Einstein’s E=mc² suggests an initial explosion from a singularity would spew matter, which previously didn’t exist, equally in all directions. Hence, Friedmann’s assumptions are sufficient conditions to prove an expanding Universe. We could construct a scenario where one large lump of matter on one side of the Universe conserves momentum with numerous lumps of matter on the other side of the Universe and still have an expanding Universe. Hence Friedmann’s assumptions are not necessary conditions for an expanding Universe.

Hubbles law states that the velocity of an object in space away from another object is equal to its distance times a constant. In the scenario, the velocity is not limited to the speed of light, space itself is expanding as light propagates through. This suggests that there are some galaxies that are traveling away from us faster than the speed of light and are thus not visible.

Velocity = H * D
where H is about 65 km/sec/megaPc

Since 1998, astronomers have observed that the Universe is accelerating in expansion instead of slowing down like one would expect due to gravitational forces. The reason is uncertain. Some speculation includes the existence of an antigravity. Perhaps the “expanding of space” cancels out “gravitational slow down” and results in a net acceleration.

In the centers of galaxies, yes, but not in the center of the Universe which you are clearly aware of since there is no Center.  This is from the Cosmological Principle that implies the Universe has no center or edge (flat piece of paper of infinite width & height, i.e. the surface of a sphere, a balloon).  Simply the universe exploded and looks the same everywhere around.    There are two princples here:
1. Homogeneous - observed on a scale of 500,000,000 Light Years where galaxies are aligned on the edges of cosmic Bubbles pressed up against each other.
2. Isotropic - we can count the same # of galaxies in every direction.
 
This is also observed by the fact that there is the same background radiation everywhere.  Hence the Big Bang explosure occurred everywhere.  Of course everywhere was a lot smaller a long time ago.   At t=100,000 years, T=5000 K and background radiation was light at optical frequency.  At t=10,000,000 years T=500K and background radiation is Infrared light.  Now t=15x10^9 years and background radiation is T=3 Kelvin and back ground radiation is microwave.
 
Also the Cosmological Principle defines complete curvature of space and hence light, so we see the samething everwhere.  The blackhole also curves light back into itself because of the curvature of space.

Black holes in the center of galaxies, this seemingly obvious idea took a long time to be accepted.  Basically scientists detected in the constellation of Sagittarius X-Rays that could only be produced by a star 3 million times the size of the Sun (extend the Sun to the orbit of Mars).  Since we are clearly not seeing this bright star in the sky and a sun could not exist at this size, there must be a black hole there.  This is also close to the center of the galaxy and by definition the center of mass of the galaxy.
 
There are three scenarios for the Universe:
1. density > critical density  -- Finite Universe, big crunch, closed universe, positive curvity, looks like a sphere
2. density = critical density  -- Flat Universe, barely expands forever
3. density < critical density  -- Open Universe, Infinite, Hyperbolic, Negative Curvature, 
 
Here are the results:

1.  Normal Matter   Den/Crit = 0.02   2%     --- Negative curvature, Infinite, Hyperbolic Universe
2.  Dark Matter      Den/Crit = 0.30   30% --- supporting Negative curvature, Infinite Universe

----------------------------------------------------

Total Universe!                                 32%  Up until 1998 everyone thought we had an Open Universe

 
After 1998:  Scientists see that the Universe appears Flat because of Cosmic background radiation from Angular Scale correlations.

New Problems:  
1. Where is the rest of the ~70% of the matter in the Universe since Den/Crit != 1?
2. We know that the Universe was expanding slower in the past by observing super nova in the past.
 
Albert Einstein postulated antigravity, a balancing gravity to support the theory of a static universe.  While he regretted this theory, he was actually once again brilliant before his time.    Here is his theory:
 
    Curvature of the Universe SpaceTime = MatterEnergy + CosmologicalConstant
 
The Cosmological Constant is the force of anti-gravity.  Now scientists believe it exists but they don't know how.  But how do we get all that missing matter, Problem 1) above.  One explanation is that the Cosmological Constant makes it unnecessary.  The constant derives from a fundamental characteristic of space that provides an anti-gravity force.   The Anti-gravity force also gets bigger as the Universe expands.  The second explanation posits the existence of Dark Energy, which no one understands.  So Einstein's theory instead of explaining a static Universe explains a Flat Universe.
 
One question is why should the Universe be flat since that requires a precise equality of density and critical density, which seems unlikely by chance?
 
Now enters the Theory of Inflation or the Balloon Theory.  This Theory explains problem 2) above by stating that the Universe started with positive curvature and expanded like a balloon so that any 2 points on the surface will eventually appear to be connected by a straight line.  Hence the bigger the balloon gets the closer we approximate a Flat Universe.
 
What is very interesting is that at some time in the past, the Universe had sufficient density to be in a big crunch scenario but inflated beyond that due to the negative gravity of space.  Also we are certain of the occurrence of a Big Bang from Hubble’s Law, which is proved by observation, since if everything is moving away it must have all been very close at one time.
 
Hubble's law states that VelocityOfAGalaxy = Hconstant * Distance
 
A consequence of this law is that far enough away, there are galaxies receding from us at faster than the speed of light that we will never see.

The existence of anti-gravity due to spatial expansion may be similar to a rubber band snapping. As gravity has a pull on an object, there may be a distance from an object that results in a snap of gravity. The snap or escape point results in a counter-force or anti-gravity for a brief period. That small force would accumulate to push galaxies away at faster than the speed of light. The distance of the snap should be dependent on the mass of the object, but would only apply to an object moving away from the source. An object must be making an effort to leave another object before it will receive assistance to leave. An effort results in a supporting effort.

If we are in a Black Hole, then there is an event horizon.  Also from Hawkings on the 2nd law of thermodynamics, we know that the entropy must be increasing in our Black Hole Universe, so heat must be given off and yet the gravity is too strong for particles to escape the event horizon.  So our Black Hole Universe is creating particles and anti-particles on the event horizon to evaporate itself.   Black holes slowly evaporate away.   Theoretically, there can be a number of black hole universes out there in the "multi-Verse". 

Quarks are elements of protons and neutrons.^[2141] Two ‘up’ quarks and one ‘down’ quark make up a proton, while two ‘down’ quarks and one ‘up’ quark constitute a neutron.

According to Encyclopedia Britannica on the graviton:

Graviton: postulated quantum that is thought to be the carrier of the gravitational field. It is analogous to the well-established photon of the electromagnetic field. Gravitons, like photons, would be massless, electrically uncharged particles traveling at the speed of light and would be emitted only by highly accelerating, extremely massive objects such as stars. Since gravitons would apparently be identical to their antiparticles, the notion of antigravity is questionable.

When we look at the planets in the heavens what do we imagine? I see lonely matter pulling together with other matter so as not to be alone in the emptiness of space. What is the graviton for this pulling? Love is the graviton. Love creates fields around objects longing for others to come close and see. The gravitational field is an intrinsic property to matter in the same way that love is an intrinsic property to life. Perhaps they are the same. Loneliness and love are also the same. The planet takes the shape of a sphere; the smallest shape possible, so that all the constituent particles can be as close to each other as possible. When I look at a ball, a planet, I see love. There is no anti-graviton; there is no antiparticle for love J.

Non-rotating black holes are always perfectly spherical.^[2142] This results from the gravitational waves that the shifting core emits. The matter will finally come to rest in the lowest potential energy, which is a perfect sphere. On the other hand, rotating black holes are always oblong around the rotating direction, due to the centripetal force of the rotation. The shape of the space around a black hole reveals whether the black hole is rotating or not.

The Second Law of Thermodynamics states that entropy should always increase. Also an object that possesses entropy should also have a temperature. The law holds according to probability.^[2143] The question here is if a black hole cannot emit light, how can it possess a temperature. Simply put, a particle may not escape from a black hole carrying with it heat. The answer is that the black hole is creating particles and anti-particles instead at its event horizon.

The event horizon is not empty space but consists of fields and their rate of change. In quantum theory this is analogous to position and velocity. As for a particle, one cannot know the exact field value and its rate of change simultaneously. This uncertainty is the result of quantum fluctuation. The quantum fluctuation is represented by the creation of particle-antiparticle pairs at the event horizon.

Now when an antiparticle falls into the black hole and the positive particle escapes, the black hole will exhibit a temperature, and hence act according to the Second Law of Thermodynamics. The antiparticle will cancel out some of the mass in the black hole giving it a slow rate of evaporation. This dispersion of energy represents the increase in the entropy of the black hole.

Black holes are able to produce X ray and gamma ray radiation because objects emitting light falling into a black hole will have their wavelengths shortened as they approach the event horizon. On the other hand microwave radiation is indicative of the first light of the big bang due to the expansion of the universe.

Observing a great deal of X-ray radiation from an area of space without visible light suggests the presence of a black hole. The center of galaxies also produce a lot of X-ray radiation though one cannot see it because of the disc of superheated swirling matter falling into the black hole obscuring its view. X-ray and gamma radiation are also produced with a high amount of power, i.e. where a lot of energy must be released quickly.

The inert gases suggest that there are certain electron configurations that create a greater degree of stability in an atom. Researching this, Neil Bohr conceived of a set of orbits whose size he determined by the number of electrons in an inert gas filling up the next outer orbit. If we take a look at the elements in the periodic table, we can see the size of these orbits and when they become full for inert gases. Inert or noble gases are in bold Blue. Light metals are in Brown. Non-metals are in Teal.

Molecular stability occurs when the orbits fill up. Hence atoms draw together into molecular patterns to achieve this state. For example in the case of methane gas, CH₄, the Carbon shares its four electrons with each of the Hydrogen atoms and vice versa. The Carbon shares up its Second Orbit while each Hydrogen atom shares up its First Orbit. Similarly we can see the reason for the stability of salt, NaCl where the sharing fills the Third Orbit of each atom. We define an orbital to consist of two electrons. A complete orbital within an orbit has greater stability than an incomplete one. The electrons in an orbital must have opposite spin—they proceed around the central atom in opposite directions. The first orbital is called s. In the second electron shell (L-shell) there are 3 p orbits. In the third shell (M-shell), there are 5 d orbits. In the fourth shell (N-shell) there are 7 f orbits. It is possible for say the 5d orbital to have a wider orbit than say the 1f orbital. Hence the K-shell has 2 electrons, the M-shell 6, the N-shell 10, and the F-shell 14.

Carbon and Silicon only have 4 electrons in their outer shell which makes them very suitable for electron conduction. This is why most semiconductor materials make use of these atoms. Similarly, Germanium which also only has 4 electrons in its outmost shell is also suitable for electrical applications, but the material is more fragile and less common than silicon.

Stars have a life span like a human being and are remarkably similar and predictable in there makeup. This similarity suggests that solar systems would also develop similarly. The natural expansion of a star with age will cause planets within a solar system to under go multiple climactic changes, such that a very cool planet may at some point for say a billion years be suitable for life.

Star distance is determined by parallax for close stars. The parallax angle is the vertex formed by the Earth to a star for the Earth in two positions a half year apart. The farther the star is away the smaller the parallax angle. A parallax angle of 1 second corresponds to a parsec (parallax second) distance of the earth to the star.^[2144] The diameter of the major axis of the Earth’s orbit determines the value of the parsec constant.^[2145] The star distance has a linear relationship with the parallax angle. Stars that are farther than 30 parsecs are difficult to measure using the Earth. In this case, the spectrum of light of the star is analyzed to give its true brightness and then the parallax angle is computed from:

M = m + 5 + 5 log p where M is true brightness m is apparent brightness

Star speed has two components, the radial motion (to or away from the earth), and the transverse motion. We determine the star’s radial speed from the Doppler Shift, by comparing the light frequency when the earth is moving towards or away from the star with the frequency when the earth is stationary. Comparing the position of the star at half-year intervals reveals the transverse speed using the star’s position change and its distance.

We can observe the apparent brightness of a star in the sky and computer the true brightness or luminosity of its source by recognizing these relationships:

Apparent Brightness ~ L / D²

The reason that brightness declines with the square of distance is due to the fact that starlight emits in an expanding sphere from its source. Analogously, the surface area of a cube expands as W². One can derive the surface area of a sphere from the surface of revolution.^{[2146],[2147]}

A = 2π ∫ y (x′ + y′)^½dt where x = r cosine t and y = r sin t and t is integrated from 0 to π
A = 4πR²
Apparent Brightness = L / 4πD²
True Brightness or Luminosity = Apparent Brightness * 4πD²

We know the distance to a star by parallax. Alternatively spectroscopic analysis, the spectrum of the star light, provides a good estimate of the luminosity. The spectrum suggests the surface temperature, hence energy, hence luminosity of the star. Henry Draper classified the temperatures of stars with their spectrums in his HD system with the decreasing temperature types O, B, A, F, G, K, and M. Now, taking a main-sequence star along the Hertzsprung-Russell diagram of luminosity vs. temperature^[2148] we find the bright hot blue giants at the top left and the cool, dense, dimmer red dwarfs to the lower right. The ten percent unstable stars are more difficult to categorize. The Red giants are in the upper right hand corner and the white dwarfs in the lower left of the H-R diagram.

A star’s magnitude specifies its apparent brightness. A magnitude 1 star is (2.5)⁵ ~ 100x brighter than a magnitude 5 star.

The core of a star must reach 10⁷K = 10,000,000K for nuclear fusion to begin. Spectral lines occur when atoms have electrons that block photons at a particular frequency. In very hot stars, the atoms are ionized so there are no spectral lines.

The Luminosity of a star is also proportional to projected area and temperature. Luminosity is how much energy a star gives off.

πR² where R is the radius of the star

One finds the size of a star by measuring its radius. The radius provides the area of an equatorial slice of the star, which is its visible projection throughout the Universe.

Astronomers determine the mass of stars by observing binary systems. Giants will have no more than 100x the mass of the Sun, with volumes a million times larger. The large volumes give a much larger size and thus, brightness.

The position of a star is determined by its declination and right ascension. The declination is measured in degrees north or south of the celestial equator, that is the projection of the equator. The Right Ascension has a value of zero in Pisces and advances two hours though every constellation.^[2149] One can compute the passage of time by the advancement of the constellations across the sky.

The constellations rise in the East and set in the West. Hence, Virgo would have a RA of 12. Pisces lies directly over the projection of the equator and has a declination of zero. Orion’s belt also lies directly over th equator with a declination of zero.

Stars in the Polar Circle of the sky are always visible.

Table 1: Relative Abundances of the Elements

Organic chemistry deals with the study of molecules consisting of covalent and polar covalent bonds. Such molecules can be very long in length and vary in constituency with the same atoms forming multiple isomers. Carbon which has 4 valence electrons in its outer shell is ideal for shared electron bonding. The degree of polarization of such bonds increases with electronegativity, which increases in the periodic table from left to right and bottom to top.

Ionic bonds are formed when an atom gives an electron to another atom and are very stable molecules requiring a lot of energy to ionize. Covalent bonds require much less energy to separate atoms. Polar covalent bonds lie between the two extremes and are between different atoms, which have different electronegativity. Applying an electric field to a polar covalent molecule will orient the molecule with the positive atom pulled towards the negative force and the more electrically negative atom toward the positive side of the force.

^[2129] A Brief History of Time, Stephen Hawking, 10^th edition, page 20.
^[2130] Later we will see that all objects, i.e. particles are waves.
^[2131] Understanding Physics, Isaac Asimov, Vol. 2, pp 127-128.
^[2132] Single frequency light source
^[2133] Stephen Hawking’s terminology
^[2134] A Brief History of Time, Tenth ed. Stephen Hawking, p. 60.
^[2135] Quanta is the plural of quantum, an indivisible unit of energy.
^[2136] Understanding Physics, Isaac Asimov, Vol. 3, p. 102.
^[2137] A Brief History of Time, Tenth Anniversary Ed., Stephen Hawking page 40.
^[2138] Ibid., p. 44
^[2139] Encyclopedia Britannica
^[2140] Ibid., p. 45
^[2141] The name is from a James Joyce novel where a character in a bar refers to ‘Three quarks’ instead of quarts.
^[2142] A Brief History of Time, Stephen Hawking, pp. 93-94.
^[2143] Ibid 107.
^[2144] Angle units here are 60 seconds equals a minute, 60 minutes equals a degree. 90 degrees equals a right angle.
^[2145] 3.26 Light Years
^[2146] Calculus and Analytic Geometry, Fisher and Ziebur, pp. 442-443.
^[2147] Archimedes discovered the surface area of a sphere.
^[2148] Temperature is from left-hot to right-cold on the x axis.
^[2149] Salt Lake City Community College lecture on astronomy, 9/07/2001.

^[2150] Encyclopaedia Britannica 1994-1998

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