JimsAstronomy

Friday, March 6, 2020

NATURAL CONSTANTS - are they changing?

- 2651 - NATURAL CONSTANTS - are they changing? The constants in Nature are very interesting. We depend on them being constant in all our mathematical calculations and scientific understandings of how nature works. But, we do not know where the constants came from, how they are what they are, they just are. Now, questions are being asked, have they always been constant and are they changing?
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--------------------- 2651 - NATURAL CONSTANTS - are they changing?
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- The fundamental constants in nature include the speed of light, the gravitational constant, Avogadro’s number, the gas constant, Boltzmann’s constant, the charge on an electron, the mass of electrons, protons, neutrons, the permittivity and permeability of free space, Planck’s constant and several more.
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- Science keeps trying to measure these constants to higher and higher accuracies. But, they have no theory the will derive any one number. It is what it is.
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---------------------The speed of light in a vacuum = 299,792,458 meters / second
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--- The constant of gravity = 6.673 * 10^-11 meters cubed / kilogram * seconds squared.
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--------------------- The mass of the electron = 9.10938188 * 10^-31 kilograms.
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- It is difficult to remember these numbers because there is no pattern and, of course, they all change if you use different units of measurement. For example:
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--------------------- The speed of light in a vacuum = 186,282 miles / second
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- Scientists have tried to simplify things by expressing constants in terms of ratios that have no units. For example:
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--------------------------- The constant mass of a proton is 1.67*10^-27 kilograms.
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------------------------- The constant mass of an electron is 9.11* 10^-31 kilograms.
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-------------------------- The ratio of proton / electron mass = 1840
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- This ratio is unitless, it is a pure number, and easier to remember, the mass of a proton is 1,840 times the mass of an electron. And, it is constant.
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- In 1916, Arnold Sommerfeld introduced a constant applying the theory of relativity and quantum mechanics to the electromagnetic interactions of charged particles in empty space, and, inside the atom between the positive nucleus and the orbiting electrons. It is called the Fine Structure Constant.
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--------------------------- Fine Structure Constant = e^2 / 2*Eo*h*c
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- Fine Structure Constant = electron charge squared / 2 * permittivity of free space * Planck’s constant * the velocity of light.
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------------------------ It is a constant measured to be = 1 / 137.03599976
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--------------------------- Or, what most people remember as 1 / 137
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- See footnote (1) for the calculation and how the units all cancel out.
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- Astronomers have a way of measuring the Fine Structure Constant. When the light from a distant star passes through some interstellar gas the light radiation excites some of the gas atoms moving their electrons into a higher energy state. When this happens the atoms absorb a discrete amount of energy.
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- When astronomers look at a spectrum of this light they see dark absorption lines in the frequency spectrum where discrete energy bands are missing. Each element in the gas has its own unique spectrum of absorption lines because each element has its own atomic structure.
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- The elements iron, zinc, chromium, and nickel are especially affected by any changes in the Fine Structure Constant. The energy levels of electrons within the atom describe the light energy absorption process.
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- The energy of a photon is transferred to an electron, which jumps up the ladder of allowable energy levels. Each possible jump corresponds to a unique wavelength. The spacing of levels depends on how strongly the electron is attracted to the atomic nucleus. This electromagnetic force is a function of the Fine Structure Constant.
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- If we compare the light spectrum from the distant interstellar gas with the same gas elements in the laboratory we can detect any change in the Fine Structure Constant. Astronomers are looking at a distant gas that is backlit by a quasar.
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- A quasar is a quasi-stellar object that releases far more energy than ordinary stars and can be seen at great distances. It is believed that quasars are central black holes in distant galaxies. When their light reaches Earth it is redshifted due to the expansion of the Universe.
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- For example: the gas element absorption line in the laboratory is 543 nanometers wavelength. While the same gas element absorption line from the interstellar cloud is 544.5 nanometers. From this amount of frequency shift to longer wavelength (redshift) astronomers can calculate the interstellar cloud to be 7,500,000,000 lightyears away, also that far back in time.
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- In effect, astronomers are then able to compare the orbital structure of electrons 7,500,000,000 years ago to today. In 1999, their calculation showed a small, but statistically significant difference in the Fine Structure Constant. After measuring 128 quasar absorption lines they calculated an average increase in the Fine Structure Constant of 6 parts in 1,000,000 over the past 6 to 12 billion years.
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- Their measurement had to be very precise in order to distinguish this small difference. There was detailed uncertainty analysis needed of random and systematic errors that could creep into the measurements. By 2003, many astronomers have tried to duplicate these measurements. So far, they can not detect a change in the Constant in 1 part in 1,000,000.
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- The Fine Structure Constant in the electromagnetic force calculations is essentially the balance between the electric field energy and the magnetic field energy. During our Cosmic history we started with a radiation dominated era, to a matter dominated era, and now to a Dark Matter dominated era.
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- Possibly, these changes in our Universe caused the Fine Structure Constant to change, to increase very slowly over time. However, 2003 studies of the Cosmic Microwave Background Radiation has determined that the Constant did not vary more than 1 part I 100,000,000 (1 in 10^8).
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- So, results are still inclusive. Are our natural constants truly constant over time? Will some scientists ever figure out where these constants come from? What theory can be used to derive them? So much to learn, so little time.
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- (1) ------------------------ Fine Structure Constant = e^2/2*Eo*h*c
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------------------------------- The charge on an electron = 1.6 * 10^-19 coulombs
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------------------------------- Squared = 2.56 * 10^-38 coulombs^2
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----------- Permittivity of free space = 8.85 * 10^-12 coulombs^2 / Newton * meter^2
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------------------------------- Planck’s constant = 6.63 * 10^-34 Joules * seconds
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------------------------- Velocity of light = 2.99 * 10^8 meters / second.
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- Let’s try handling the numbers, the magnitudes, and the units separately:
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------------------------- 2.56 /2 * 8.85 * 6.63 * 2.99 = .00729
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------------------------- 10^-38 / 10^-12 * 10^-34 * 10^8 = 1
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------------ Coulombs^2 * Newton * m^2 * sec / coulombs^2 * Joule * second * m
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-------------------------- This reduces to: Newton * m^2 / Joule * m
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--------------------- A Newton is a unit of force = mass * acceleration = kg * m / sec^2
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----------------------- A Joule is a unit of energy = force * distance = kg * m*2 / sec^2
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------------------------- Kg * m * m * sec^2 / kg * m^2 * sec^2
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----------------------- The units all cancel out and we are left with a pure number:
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----------------------------------- 0.00729 , or
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---------------------------- The Fine Structure Constant = 1 / 137
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- March 5, 2020 619 2651
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----- Comments appreciated and Pass it on to whomever is interested. ----
--- Some reviews are at: -------------- http://jdetrick.blogspot.com -----
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--------------------- Friday, March 6, 2020 --------------------
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SUPERNOVA - what is the youngest?

- 2648 - SUPERNOVA - what is the youngest? A supernova normally goes off in a galaxy every 50 to 100 years. However, we have not seen one in several hundred years. It could be that they are going off and they are out of sight. The last one astronomers had recorded for the Milky Way is Cassiopeia A. It went supernova 330 years ago, that would be in 1678.
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--------------------- 2648 - SUPERNOVA - what is the youngest?
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- Today the remnant of that 1678 explosion has an expanding shockwave that is 10 lightyears in diameter. The shockwave has an average velocity of 20,300,000 miles per hour.
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- The Tycho Brahe supernova was first seen in 1572 and Remember? That was 436 years ago.
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- Of course, there was the Supernova 1987A that exploded just 13 years ago. But, that was in another galaxy, the Large Megallenic Cloud, our neighboring galaxy. There are 24 of these neighbor galaxies.
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- The youngest supernova in our galaxy was just now spotted. It has been hidden from view by a thick cloud of interstellar dust. It’s radio waves first hit Earth 140 years ago, in 1860. It is called G1.9+0.3 Supernova.
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- It exploded towards the center of the Milky Way 26,000 lightyears away. It took that long for the radiation to reach us. The visible light portion of the radiation was blocked by the dust but astronomers were able to see it in radio waves and in X-rays that passed through the dust.
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- Supernova are the death of giant stars. It is the last instant when gravity wins over the thermonuclear pressure. Stars exist within a balancing act of these two forces. It starts with a large cloud of interstellar gas, mostly hydrogen gas. Gravity always tries to compress things, including gas, into a sphere.
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- A sphere is the most volume with the least surface area. It is the geometry of the lowest energy state. So, gravity is trying to pull everything in the cloud to a volume of 4/3*pi*r^3, the volume of a sphere.
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- The pressure of gravity increases density and increases temperature. The temperature continually rises until it reaches 18,000,000 F. At this temperature and pressure hydrogen begins a thermonuclear fusion that generates helium and converts a little bit of mass to a lot of radiation, E=mc^2.
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- The outward pressure of the radiation pushes against gravity until the two forces are in balance. Smaller stars will burn hydrogen for 10,000,000,000 years before they run out and die as White Dwarfs.
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- Larger stars, 10 solar masses, will live for only 10,000,000 years, burn all of their hydrogen, helium, neon, magnesium, silicon, sulfur right up to iron. At the iron core fusion stops the star collapses and the star explodes into a supernova.
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- The Milky Way contains about 250 supernovae. This latest discovery is the youngest on that list. The images of this young supernova going back to 1985 compared to today’s images have increased in size by 15%, in 23 years. This puts its age at 140 years old.
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- The supernova has continually increased in radio brightness over these 23 years. We can only view the star in radio and X-ray spectrums because the dust is blocking any visible light. Astronomers have just recently calculated that dust in the Universe is blocking half of all the visible light that is generated.
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- When a large star has fused all of its hydrogen into helium fusion stops momentarily. The star collapses further under the pressure of gravity. The temperature increase even higher until helium begins its thermonuclear fusion into carbon and oxygen. When helium runs dry the carbon fuses into neon, then magnesium, then silicon, then sulfur, then silicon into iron.
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- The star becomes layered like an onion with iron at its core surrounded by layers of burning silicon, magnesium, neon, oxygen, carbon, helium, and hydrogen at the surface. It took several million years to build up these layers but the iron core is built in one day.
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- The iron core will be 2/3 rds the size of Earth yet have the mass more than the Sun. Iron does not fuse into higher elements. Fusion stops. Thermonuclear pressure stops. In less than one second the entire star collapses from 5,000 miles wide to 12 miles wide.
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- This sudden crash releases a high amount of energy, 100 times more energy than our Sun will produce over its entire lifetime. This blast of energy is the supernova.
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- Neutrinos will carry most of the energy off into space with the explosion. The rest of the energy becomes a shockwave blasting radiation through the layers of the onion. The shells blast away at 10,000,000 miles per hour. The supernova burns brighter than a billion Suns for several weeks.
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- The iron core collapses into a Neutron Star, or a Black Hole. The shockwave continues to expand for millions of years plowing through the interstellar medium. All the elements in this explosion become the interstellar dust that has come from older stars and is blocking our view of this one. The shockwave hit us 140 years ago but we could not see it.
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- The thermonuclear pressure that was supporting the star before the explosion is proportional to the temperature, “T“, and the number density of the particles, “n”, particles/ cubic centimeter. Each particle has a mass, “m”. The entire interstellar cloud of particles has a mass, “M”. The number of particles is “M / m”. To get the density of particles we divide the number by the volume:
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------------------- number density = n = 3*M / 4*pi*m*r^3
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------------------ Thermonuclear pressure = n*k*T
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----------------- Force = pressure * area
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- The area can be assumed to be the two halves of the spherical cloud pressing on the center. Area = pi*r^2.
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----------------- Force = n*k*T *pi*r^2
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----------------- Force = (3*M / 4*pi*m*r^3) * (k*T *pi*r^2)
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--------------- Outward Force = 3*M*k*T /4*m*r
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- To get the balancing inward force of gravity we make the same assumption the 2 halves of he spherical gas are attracting each other towards the center, “M/2” separated by the radius, “r”.
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--------------- Force = G* M/2 *M/2 / r^2
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--------------- Inward Force = G*M^2 / 4 r^2
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These equations are only approximations because these forces need to be integrated over the volume of the spherical gas cloud, which isn’t ever a perfect sphere. It requires Calculus. But, these equations are close enough to allow us to understand the balance in forces and pressures that create the star and eventually the supernova explosion.
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- An increase in temperature will increase the force of thermal pressure outward. An increase in mass raise total pressure and gravitational force. But its increase goes up as mass squared. An increase in density corresponds to a decrease in radius raising both pressure and gravitational force.
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- The gravity force depends on 1/r^2 while pressure depends on 1/r. All of these parameters change in unison until the sphere is in balance.
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- If we set these two force equations equal to each other we will define the precise balancing point for all of these parameters.
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---------------- Force of thermonuclear pressure = Force of Gravity
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------------- Outward Force = 3*M*k*T /4*m*r = Inward Force = G*M^2 / 4 r^2
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-------------- M^2 = 3*k*T*r / G
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- The math gets complex but if we ratio Mass to the mass of the Sun and we reduce the other factors this equation becomes:
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-------------- (M / Msun)^2 = 18 * T^3 / n
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- To illustrate this calculation a typical interstellar cloud has a temperature, T = 30 K, pretty cold. The particle density is 300 / cm^3, pretty sparse. The Mass at balance is 171 solar mass. When the cloud compresses to a number density of 300,000 particles / cm^3 a star is formed with 5.4 solar mass.
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- The cloud is not smooth in density, it is lumpy, so it can fragment into several 5.4 solar masses and form several stars. In fact, these typical numbers suggest that each cluster of stars found will have a minimum of 32 stars in them.
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- See Review 2636 for a list of more on supernova reviews. An interesting topic. Supernovae make star dust, we are made of star dust.
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- March 3, 2020 2648
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----- Comments appreciated and Pass it on to whomever is interested. ----
--- Some reviews are at: -------------- http://jdetrick.blogspot.com -----
-- email feedback, corrections, request for copies or Index of all reviews
--- to: ------ jamesdetrick@comcast.net ------ “Jim Detrick” -----------
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--------------------- Friday, March 6, 2020 --------------------
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SUPERNOVAE - how life is being created? -

- 2646 - SUPERNOVAE - how life is being created? Betelgeuse is still deep in the red supergiant phase of its life. Even though it has dimmed significantly of recent, it isn’t on the verge of exploding. The gradual dimming and brightening we see suggest that it won’t be exploding in our lifetimes. It suggests that the core of Betelgeuse is still chugging away at a steady pace.
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--------------------- 2646 - SUPERNOVAE - how life is being created?
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- See Review 2636 about the two supernovae explosions being studied. This review is about Betelgeuse that is a supernovae we can view with backyard binoculars.
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- Betelgeuse is a star that is now beginning to slowly brighten. This behavior is exactly what astronomers expected. Betelgeuse is a very different star from our Sun. While our Sun is a main-sequence star in its prime of life, Betelgeuse is a red giant star on the verge of death. But the death of a star is not a simple process.
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- Stars shine so brightly and for so long because of a delicate balance of gravity and nuclear fusion. Gravity would like to collapse a star under its weight. Without nuclear fusion, gravity would crush a star into a white dwarf, neutron star, or black hole.
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- But, the crushing pressure gravity creates allows hydrogen in the star’s core to fuse into helium. The process is known as the proton-proton chain and combines four hydrogen nuclei into one helium nucleus. About 3% of the original mass is converted to energy in the form of gamma rays. This energy heats the core even further, letting it push back against gravity.
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- For stars larger than the Sun, another fusion process known as the Carbon-Nitrogen-Oxygen because the process fuses helium into those three elements. This process is why those three elements are the next most abundant in the universe, except for hydrogen and helium.
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- Over time the CNO cycle increases as hydrogen become more scarce and helium more abundant. Since the CNO cycle releases more energy at a faster rate, this means a star’s temperature increases over time. We see this gradual heating in our own Sun. By the time the CNO cycle dominates in a star, it’s core is so hot that the outer layers of a star swell and expand.
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- This is the stage Betelgeuse is in now. For millions of years, it was a main-sequence star of about 20 solar masses. But it is now fusing helium so furiously that it has bloomed into a “red super giant“. Betelgeuse is running out of fuel, and in the end, gravity will win. It’s only a matter of time.
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- But that time isn’t necessarily soon. Betelgeuse has enough helium to stay in the red supergiant stage for about 100,000 years. Even after it runs out of helium, it will be able to fuse carbon into heavier elements for about a millennium.
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- After that things will change fairly quickly. When it runs out of carbon it will try fusing heavier and heavier elements for about a year. Then its core will collapse, Betelgeuse will become a supernova explosion.
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- Betelgeuse is still deep in the red supergiant phase of its life. Even though it has dimmed significantly of recent, it isn’t on the verge of exploding. The gradual dimming and brightening we see suggest that it won’t be exploding in our lifetimes. It suggests that the core of Betelgeuse is still chugging away at a steady pace.
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- The changing brightness of Betelgeuse is due to a process known as convection. The upper layers of the star are heated by the core, and this generates a flow of hotter and cooler regions. Material in the interior is heated and rises to the surface. It then cools and sinks into the star, and the cycle continues.
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- Convection happens in the outer regions of most stars, including our Sun. On the surface of the Sun, these convection regions are known as granules, and they are typically the size of Texas. That sounds large, but for the Sun that’s smaller than most sunspots. So even though the Sun has bright hot regions and dimmer cool regions, they are so small compared to the Sun’s surface there isn’t an overall change in solar luminosity.
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- The outer layer of Betelgeuse is much less dense than that of the Sun. It is even less dense than Earth’s atmosphere. It’s basically a thin soup of glowing gas. That means the convection regions on Betelgeuse can be huge. A single region can cover a large part of the star. When one of those regions rises to the top, Betelgeuse gets brighter, and when it cools the star dims. Betelgeuse is starting to brighten because hot material is convecting to its surface. This is normal for Betelguese and is likely the way things will be for millennia.
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- There other supernovae happening every day somewhere in our universe. The biggest explosion seen in our universe has recently been found. This record-breaking, gargantuan eruption came from a black hole in a distant galaxy cluster hundreds of millions of light years away.
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- You could fit fifteen Milky Way galaxies in a row into the crater this eruption punched into the cluster's hot gas. This unrivaled outburst was detected in the Ophiuchus galaxy cluster, which is about 390 million light years from Earth. Galaxy clusters are the largest structures in the Universe held together by gravity, containing thousands of individual galaxies, dark matter, and hot gas.
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- In the center of the Ophiuchus cluster, there is a large galaxy that contains a supermassive black hole. Although black holes are famous for pulling material toward them, they often expel prodigious amounts of material and energy. This happens when matter falling toward the black hole is redirected into jets, or beams, that blast outward into space and slam into any surrounding material.
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- Chandra observations reported in 2016 first revealed hints of the giant explosion in the Ophiuchus galaxy cluster. The wall of a cavity, because it borders a region filled with radio emission, is from electrons accelerated to nearly the speed of light. The acceleration likely originated from the supermassive black hole.
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- The amount of energy required to create the cavity in Ophiuchus is five times greater than the previous record holder, and hundreds and thousands of times greater than typical clusters.
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- The densest and coolest gas seen in X-rays is currently located at a different position from the central galaxy. If this gas shifted away from the galaxy it will have deprived the black hole of fuel for its growth, turning off the jets.
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- This gas displacement is likely caused by "sloshing" of the gas around the middle of the cluster. Usually the merger of two galaxy clusters triggers such sloshing, but here it could have been set off by the eruption.
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- One puzzle is that only one giant region of radio emission is seen, as these systems usually contain two on opposite sides of the black hole. It is possible that the gas on the other side of the cluster from the cavity is less dense so the radio emission there faded more quickly.
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- As is often the case in astrophysics we really need multiwavelength observations to truly understand the physical processes at work. Having the combined information from X-ray and radio telescopes has revealed this extraordinary source, but more data will be needed to answer the many remaining questions this object poses.
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----------------------- See Review 2636 about two supernovae explosions being studied. This review also has an index listing 20 more reviews available about supernovae. These explosions are how all the elements that make up your body and the essentials for life are created. Fortunately our Earth was formed after many such explosions preceded us.
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- March 2, 2020 2646
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----- Comments appreciated and Pass it on to whomever is interested. ----
--- Some reviews are at: -------------- http://jdetrick.blogspot.com -----
-- email feedback, corrections, request for copies or Index of all reviews
--- to: ------ jamesdetrick@comcast.net ------ “Jim Detrick” -----------
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--------------------- Friday, March 6, 2020 --------------------
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SUPERNOVA - the runaway universe?

- 2649 - SUPERNOVA - the runaway universe? Nuclear fusion will occur when a star’s central temperature reaches 10,000,000 degrees. The collisions of the atoms are so rapid at that temperature that all electrons are stripped away from their nucleus. And, nuclei collide to such an extent as to overcome the repulsive electric force of their mutual positive charges.
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--------------------- 2649 - SUPERNOVA - the runaway universe?
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- The Strong force acts over a distance of only .0000000000001 centimeters (10^-13), the width of an atom, but, it completely overpowers the electromagnetic force and the nuclei fuse together.
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- When two protons fuse they form the nucleus of deuterium, but the mass is about 1% less than the combined mass of the two protons. This amount of mass is converted into energy according to E = mc^2 and in the form of a positron (a positive or anti-electron) and an anti-neutrino.
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- Collisions and annihilations of these subatomic particles with other subatomic particles spreads this kinetic energy throughout the interior of the star. When the energy eventually reaches the surface of the star it has slowed down enough to become infrared, visible and ultraviolet light. ppp
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- When the star is in equilibrium it radiates as much electromagnetic energy at its surface as it produces in fusion energy at its interior core.
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- Nuclear fusion occurs at the center because gravitational pressure and the highest temperature occur at the core. Temperature is simply a measure of the average velocity of particles.
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- There hydrogen is fused into helium. When hydrogen is gone and the more massive stars continue their gravitational pressure helium fuses into carbon and oxygen. If the core continues to get hotter and denser these nuclei fuse into silicon, neon, magnesium and iron.
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- When the element iron is fused the nuclear fusion process stops because fusing iron into higher level elements requires that iron nuclei absorb energy rather than produce energy. When iron is at the core fusion stops and the star collapses.
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- The total collapse of the star happens in less than one second. A giant implosion produces a neutron star where all the protons and electrons are squeezed into neutrons at the center.
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- This sudden collapse cause a bounce to occur at the core creating a giant shockwave that shoots outward. The shockwave becomes an explosion, a supernovae, that blasts the stars outer layers into space at thousands of miles per second.
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- The supernova explosion crunches elements together even more that fusion at the core does. Elements heavier than iron are produced in these collisions that are spread throughout space in the form of interstellar gas.
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- Our Sun contains some of these elements which means that our Sun is a second or third generation star made from the interstellar gas created by previous sun supernovae.
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- The mass our Sun has only diminished 4% since the Solar System was first formed. So we still have more time. Enjoy the sunshine while we have it!
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- See r\review 2636 that lists 24 more reviews all about supernovae
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- March 3, 2020 613 2649
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----- Comments appreciated and Pass it on to whomever is interested. ----
--- Some reviews are at: -------------- http://jdetrick.blogspot.com -----
-- email feedback, corrections, request for copies or Index of all reviews
--- to: ------ jamesdetrick@comcast.net ------ “Jim Detrick” -----------
- https://plus.google.com/u/0/ -- www.facebook.com -- www.twitter.com
--------------------- Friday, March 6, 2020 --------------------
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Monday, March 2, 2020

PLANET NINE - may be a blackhole?

- 2647 - PLANET NINE - may be a blackhole? One theory is that it is a “blackhole“. Maybe there is an ancient, grapefruit-size blackhole hiding out in our solar system. This tiny, heavy object might in fact take the place of a theoretical planet that might be tugging on other objects in our solar system. This so-called “Planet 9” could explain the math calculations and why we cannot find it.
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--------------------- 2647 - PLANET NINE - may be a blackhole?
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- All kids know there are nine planets in our Solar System. Well, older kids. The younger kids today know there are “eight” planets and several “Dwarf Planets”, Pluto being one of those. So, what is this talk about “Planet Nine“?
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- It all has to do with Kepler’s Laws , equations” for orbiting bodies. The eight planets orbit according to the math, except when you get to the outer planets where the math suggests there is another orbiting mass outside the orbit of Pluto. But, we can not find it.
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- Here is how the math argument goes: Far away in the outer reaches of the solar system, past where the planet Neptune orbits, there are a handful of small objects that behave strangely. These "trans-Neptunian objects" cluster together in unusual ways, and they tend to spin around axises that point toward one broad swath of the sky, away from the larger known planets.
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- Also the objects orbit in a different plane than the eight known planets. That suggests that something else is tugging on them with its gravity.
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- Astronomers have looked at that strange pattern, run some calculations, and concluded that there must be another planet out there, one that’s 10 to 20 times the mass of Earth and following an orbit that carries it many hundreds of times Earth's distance from the Sun.
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- This theory is called "Planet 9" . The hunt for Planet 9 has gone on for years, with astronomers using visual light and infrared telescopes to scan the outermost parts of the solar system.
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- Over the past few years, astronomers have uncovered about a dozen objects in the distant solar system that defy expectations. In addition to a few other odd attributes, this special subset of icy objects orbiting past Neptune, dubbed Trans-Neptunian Objects, or TNOs, all make their closest approaches to the Sun at about the same spot in space.
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- To account for these bizarre orbits of the outer planets astronomers recently invoked a wild yet increasingly convincing explanation for how they came to be. Namely, a goliath planet some five to 15 times the mass of the Earth is hiding far beyond Pluto, hundreds of times farther from the Sun than Earth. It's this giant world, Planet Nine proponents argue, that is shepherding the TNOs into their unusual orbits.
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- Astronomers have discovered a number of far-flung objects that all have very similar perihelia, meaning they make their closest approaches to the Sun at about the same location in space.
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- This could be a primordial black hole instead of a planet. Primordial black holes are predicted to have popped into existence within the first few fractions of a second after the Big Bang. However, their existence has never been confirmed.
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- If true, the proposed blackhole likewise would be located hundreds of times farther from the Sun than Earth. But because blackholes are incredibly adept at crushing down matter, a blackhole equivalent to roughly five Earth-masses would be only about the size of a baseball.
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- Astronomers are also monitoring the sky in search of gravitational microlensing events, which occur when a massive foreground object (such as a blackhole) passes directly in front of a background object (such as a star). If the alignment of the objects is perfect, the heavy foreground object acts as a sort of lens, distorting and amplifying the light from the object behind it.
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- Based on five years of observations, researchers uncovered six strange microlensing events that seem to have occurred when objects roughly 0.5 to 20 times the mass of Earth acted as gravitational lenses. These objects, located about 26,000 light-years away toward the Milky Way's galactic bulge, could just as easily correspond to an unexpected population of primordial blackholes rather than free-floating planets.
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- If such a blackhole, rather than a rogue planet, were captured by the Sun and is now roaming the outer solar system, then it would influence the orbits of TNOs in exactly the same way as Planet Nine.
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- Blackholes are usually thought to be enormous objects formed when giant stars collapse into themselves, trapping their masses in infinitely dense singularities, surrounded by giant "event horizons" from which no light can escape.
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- But, this theory also contends that in the first moments of the universe, when everything was hot and dense and rushing away from the Big Bang, and no stars had formed yet, blackholes were already emerging.
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- These primordial blackholes formed during the universe's creation would have formed when chunks of that early matter were crushed together so tightly that they condensed into singularities. Therefore these blackholes would be smaller than stellar blackholes that formed from collapsing massive stars.
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- A blackhole of that mass would be tiny , about the size of a grapefruit yet five times the mass of Earth, and the size of a bowling ball would be 10 times Earth's mass.
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- The blackhole would orbit the Sun like a planet would, and it would tug on dwarf planets and asteroids just like the theoretical Planet 9 would. There would not be any way to tell the effects of a planet's gravity from that of a primordial blackhole of the same mass.
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- Some astronomers still think there's a planet out there. We need more data!
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--------------------------------- Other Reviews available upon request:
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- 2448 - PLANET NINE - could it be a blackhole? Maybe there is an ancient, grapefruit-size blackhole hiding out in our solar system. This tiny, heavy object might in fact take the place of a theoretical planet that might be tugging on other objects in our solar system.
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- 965 - The chemistry of planet formation. . Astronomers are using 2 different methods to find these planets. The “Transit Method” and the “Radial Velocity Method”. With both of these methods we have to be lucky and happen to be viewing the planet orbits edge-on. If we are viewing the orbits face-on we can never discover planets with these methods.
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- 935 - Planet temperatures.
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- 928 - Planet formation. . Astronomers have found more than 4,000 planets in other solar systems. How they formed and how they contain such wide diversity is a new mystery. We thought we had a design for planet formation that matched our Solar System. In contrast, other solar systems are so diverse and supposedly formed out of chaos.
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- 919 - Planet travel. . First, astronomers recorded the star’s light spectrum without the planet in front of it. Then, later, they obtained the light spectrum of the star with the planet and the planet’s atmosphere in front of it. Now, subtract the two spectrums. What you have left is the spectrum of light through the planet’s atmosphere. Analyzing that spectrum astronomers learned that the planet’s atmosphere was mostly sodium, that is salty air. The planet was too close to the star and too hot for life.
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- 840 - Planet Pegasi and Dopper astronomy. The planet 51 Pegasi b was discovered in 1995. It was the first planet discovered orbiting a normal star, like our Sun. When watching the star astronomers were able to detect a rhythmic wobble using the Doppler Shift Technique.
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- 839 - Our gaseous planets. Astronomers have discovered over 4,000 planets outside our Solar System. An the same time they reduced the number of planets in our Solar System from nine to eight. After 75 years the ninth “planet” got “plutoed” and kicked out of the planet category and in to the Kuiper Belt with the rest of the big icy comets.
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- 710 - Fourier discovers the terrestrial planets. Astronomers have been working hard adding the number of planets found to exist in other solar systems in our Milky Way Galaxy. Astronomers have discovered over 4,000 planets in 164 other solar systems The first planet outside our own solar system was found in 1995. We do not have sensitive enough instruments now to determine if there is life on any of these planets. And, we tend to find the giant gaseous planets like Jupiter because the smaller rocky planets like Earth are too small to detect.
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- 591 - Osiris , a planet around another star. This review is the start of a series entitled the 8 wonders of the Universe. 592 - Black Holes. 593 - Gamma Ray Bursts. 594 - Dark Galaxies. 595 - Galaxy Clusters. 596 - Quasars. 597 - Cosmic Background Radiation. 508 - The Milky Way Galaxy
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- March 1, 2020 2647
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----- Comments appreciated and Pass it on to whomever is interested. ----
--- Some reviews are at: -------------- http://jdetrick.blogspot.com -----
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--- to: ------ jamesdetrick@comcast.net ------ “Jim Detrick” -----------
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--------------------- Monday, March 2, 2020 --------------------
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Sunday, March 1, 2020

RANSCENDENTAL NUMBERS - numbers : “e” and “pi”

- 2645 - TRANSCENDENTAL NUMBERS - numbers : “e” and “pi”. Transcendental means “beyond human experience“; but, not beyond human knowledge. Supernatural, but still natural numbers. Numbers are just inventions man created for counting. 0, 1,2,3,4,5, ….. How could numbers be supernatural?
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-------------- 2645 - TRANSCENDENTAL NUMBERS - numbers : “e” and “pi”
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- Could numbers be supernatural? We started by simply counting our fingers. We started with positive numbers and it took a while for man to accept negative numbers. For several centuries man could not believe that there could be something less than nothing.
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- Finally, a number line was invented that extended positive numbers to the right all the way to infinity, and to the left all the way to negative infinity. Later, man ran into the problem of taking the square root of a negative number. The only way that was possible was to invent “i” the imaginary number that was the square root of negative one,
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----------------------------------- (i = -1^½), and i^2 = -1.
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- Now, we have real numbers and imaginary numbers together. We make the number line the real axis , or x axis, and the imaginary line the vertical, or y axis, and that plane can define all real and imaginary numbers that exist. 4 + 3i is an imaginary number, a point 4 counts to the right and 3 counts up on the imaginary axis is a unique point for this number on the plane.
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- If we plot all the points of radius one on the graph where x^2 + y^2 = 1 then we define the equation of a unit circle, of radius one. This is simply the Pythagorean Theorem where any right triangle inside the circle has three sides r^2 = x^2 + y^2.
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- But, in this case the hypotenuse is the radius, “r”. Remember, the sum of the squares of two sides of a right triangle are equal to the hypotenuse squared. All points on a unit circle can be defined by the equation:
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---------------------------------------- x^2 + y^2 = 1.
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- Now, put 2 radii at right angles and the hypotenuse is a cord across the circle. The cord according to the Pythagorean Theorem is equal to the square root of 2. If we do this 4 times around the unit circle we create a square. The area of the square is simply 2 square units. The sides are each the square root of 2 which is an irrational number. A decimal number 1.414.….. that goes to infinity never repeating itself.
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----- Two infinite series decimal numbers multiplied together equal the simple number 2.
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- Now, we can define the number “pi” which is the ratio of the perimeter, or circumference, of a circle divided by the diameter. “pi” = c / d. or, c = 2*pi*r. “pi” is one of those Transcendental numbers. It is supernatural. It appears to not be an invention of man but an invention of nature.
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- The area of the unit circle is “pi” = 3.14.….. to infinity. the circumference of the unit circle is 2*pi = 6.28.……. to infinity. A circle with a simple radius 1 has an area and a circumference that are irrational numbers whose decimal numbers go on to infinity.
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- “pi” in addition to being a Transcendental number is an Irrational number. Irrational numbers are real numbers that can not be written as a fraction of two integers. A Rational number can be written as a fraction, like 1/3 = 0.33333333 …….. Its decimal expansion goes on to infinity.
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- But, for Rational numbers the pattern always repeats itself. For Irrational numbers the pattern goes to infinity and never repeats itself. The square root of 2 is an Irrational number just like “pi”.
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------- 2^½ = 1.414213562 …….. goes to infinity but the pattern never repeats itself.
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------- “pi” = 3.141592654 …….. goes to infinity but the pattern never repeats itself, it is Irrational. Is it not amazing that “pi” is defined as a fraction of circumference/diameter of a circle but it can not be defined as a fraction of any two integer numbers?
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- Another way to say this is that Irrational numbers can not be written as a termination or a recurring decimal. But, “pi” is also a Transcendental number because it also can not be written as a polynomial equation with rational coefficients of which “pi” is a root.
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- This statement is abstract and Transcendental in math takes a little getting used to. Both “pi” and “e” are Transcendental numbers that fit this definition. A little later we will create “e” using polynomials but never with the root “e”.
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- “pi” defines circles. “e” defines everything that grows. Let’s use $1,000 to illustrate. Suppose you put a thousand dollars in the bank and the bank gave you a 100% annual interest rate. At the end of a year you would have $2,000 with interest.
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------------- That is $1,000 *( 1+1.00) = $2,000 (If it were 6% interest it would be $1,000*1.06 = $1,060.)
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- If we kept our money in the bank for another year the total would be:
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---------- $1,000*2*2 = $4,000.
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- The third year we would have $1,000*2*2*2 = $8,000. The equation is $1,000 * (1+1.00)^n, where “n” is the number of years.
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- But, what if the bank compounded the interest monthly, instead of annually. Then the equation becomes $1,000 *(1 + 1.00/12)^12 = $1,000 *(1.0833)^12 = $2,613. You made $613 more by compounding interest monthly instead of yearly.
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- Compounding grows things faster.
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- How about if the bank compounded interest daily? $1,000 *(1+1.00/365)^365 = $1,000*(1.1.0027397)^365 = $2,715. You made $715 more by compounding daily. Not that much more.
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- What would happen if the bank simply compounded continuously? Notice we are doing two things at once. We are making the base in the equation a smaller and smaller number by compounding more often. And, at the same time, we are making the exponent larger and larger.
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- Whenever you grow anything like this in the limit you approach the magical, transcendental number “e” . The limit of (1+1/n)^n always equals 2.718281828459045 ……. We define this number as “e”.
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- Therefore , the maximum we can earn compounding 100% interest continuously for a year is $2,718.
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- We can generalize this equation mathematically to become:
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-------------------------------- e^x = (1+x/n)^n
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We can generalize the financial equation starting with a principle “p”, with an interest rate, “r” and “t” years with interest compounding continuously to:
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------------Principle with Interest = p*e^r * t = $1,000*e^1.00 * 1 = $1,000 * 2.1718 = $2,718 at the end of the first year. After 10 years you would have: $1,000*e^1.00*10 = $1,000 * 22,026 = $22,026,466.
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- You would be a millionaire 22 times over in just 10 years if you could get a 100% compounded interest rate.
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- Another way to create “e” is with polynomials. A polynomial is a math expression of 2 numbers added together and raised to some power. For example: ( x+2)^2 = (x+2)(x+2).
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- If we continuously make the base smaller and the exponent larger we eventually get to “e” using this polynomial series: (1+1/10)^10 = 2.59374246 ….. (1+1/100)^100 = 2.704813829 …… (1+1/1000)^1000 = 2.716923932 …. As the base gets closer to 1 and the exponent gets larger and larger we approach “e” = 2.718281828 ……..
“e” surfaces as a tug of war between 1 and infinity.
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- “e” and “pi” are Transcendental numbers that are found everywhere in nature. “e” is linked to calculus both integration and differentiation. Integration is the summation of tiny rectangles to calculate the area under a curve. If you have a curve where x*y = 1, or, y = 1/x then the area under that curve from 1 to “e” is 1.
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- In differentiation, calculus is the calculation of a rate of change of one variable versus another. Velocity is miles / hour, the rate of change of distance with time, or the differential of distance versus time. It is the slope of the curve.
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- A slope is a rate of change. Velocity is the slope of the curve of distance versus time. The slope of another curve y = e^x is e^x = dy/dx, at every point along the curve. e^x is its own differential, e^x. A curve y = e^x always has a slope of e^x.
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- “e” = an infinite series of factorials. A factorial is the multiplication of a series of numbers 1 less than the last number. 4 factorial = 4! = 4*3*2*1 = 24.
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-------------- “e” = 1 + 1/1! + 1/2! + 1/3! + 1/ 4! + 1/5! + ……
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-------------- “pi” is also related to an infinite series:
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-------------------------- “pi“^2/6” = 1/1^2 + 1/ 2^2 + 1/ 3^2 + 1/ 4^2 + …..
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----------------- “pi”/ 4, which is 45 degrees, = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 - 1/15 + ……
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- But, the most intriguing equation of all relates “e” and “pi” together:
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-------------------------------------- e^i * pi +1 = 0
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------------------------- “e” raised to an imaginary “pi” is equal to -1.
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--------------------------- “e” raised to (-1)½ * pi = -1.
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- This the most amazing equation in all mathematics, bar none. A transcendental number raised to the power of an imaginary number +1 becomes nothing.
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- It is easy to memorize “pi” out to 15 places:
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------------- “How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics.”
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------------ “How(3) I (1) want(4) a (1) drink(5) , alcoholic(9) of(2) course(6) , after(5) the(3) heavy(5) lectures(8) involving(9) quantum(7) mechanics(9) .”
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------------- 3.14159265358979.……. The sequence goes on forever and never repeats itself. Pi shows up in many equations in physics.
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- Heisenberg’s Uncertainty Principle in Quantum Mechanics states that you can not determine with certainty the position and the momentum ( mass*velocity) of an atomic particle. The better you know one the less you can know the other.
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- Mathematically, (delta x)(delta p) = h / 4*”pi”. Where, the delta is either a certainty of position ( x) or a certainty in momentum (p) equal or greater than Planck’s constant (h) / 4*”pi”. There is always a trade-off knowing one or the other, and “pi” is in there.
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--------------------- Einstein’s general Theory of General Relativity is:
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---------------------- R ik - ½ gik*R + lamda gik = 8*pi*G / c^4*Tik
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---------------- I will not try to explain this equation, but there is “pi” again.
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- Everybody that remembers school remembers the “Bell Curve”. This is the curve of a random distribution. And, it was used to grade the class for A’s, B’s, C’s, D’s, and F’s. The equation for the Bell Curve is f(x) = 1/pi^½* e^-x^2. A rather imposing equation that represents a Normal distribution, or a random distribution of unrelated events. Note that both “e” and “pi” are in the picture.
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- The mean of the Bell Curve is “mu” and the variance is “sigma” , one standard deviation from the mean. If you calculate one sigma on either side of the mean you include 68% of the distribution. Those were the C students.
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- If you go 2 sigma you encompass 95% of the distribution. Those were the B or D students depending on which side of the “mu” you were on.
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- And, +or- 3 sigma includes 99 % of the Bell Curve distribution. Those were the A and F students. Under a normal distribution just as many students should flunk as get A’s. Many teachers did not like to grade on the curve. They prefer to give A’s.
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- “e” and “pi” are Transcendental numbers and they exist in their own right as part of the natural world. Other illustrations are in the math that describes population growth. Or, in the math for radioactive decay. These two numbers are even finding their way into Quantum Mechanics. The more we study “e” the more important it reveals itself to be.
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- Google in 2004 announced that its revenue target was $2,718,281,828. When Google went recruiting it used as its hiring scheme, the first 10-digit prime number found in the consecutive digits of e.com. Google wanted only math savvy applicants to apply for the jobs.
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- We have introduced only “e” and “pi” as two Transcendental numbers, but, would you believe there are actually infinitely more Transcendental numbers then there are integers and fractions.
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- That happens to be a conjecture that I take on faith and will not attempt to prove. Math is just too amazing for words, that is the reason we use numbers.
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- March 1, 2020 803 2645
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----- Comments appreciated and Pass it on to whomever is interested. ----
--- Some reviews are at: -------------- http://jdetrick.blogspot.com -----
-- email feedback, corrections, request for copies or Index of all reviews
--- to: ------ jamesdetrick@comcast.net ------ “Jim Detrick” -----------
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--------------------- Sunday, March 1, 2020 --------------------
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TOPOLOGY - dealing with too much information?

- 2644 - TOPOLOGY - dealing with too much information? Topology is the mathematical study of properties of geometric forms that do not change with transformations, bending or shaping. It is the mathematical study of shapes. How can information have shapes. Well, graphs, bar charts, power point presentations offer thousands of ways to shape information
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--------------------- 2644 - TOPOLOGY - dealing with too much information?
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- In this information age we are drowning in data yet thirsting for knowledge.
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- Combining math, information science, and software scientists are starting to study patterns and shapes on their vast collections of data. Math is great because it is not limited to three dimensions.
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- We have a problem visualizing it but math sees higher dimensions as business as usual. Visualize a cube connecting 8 corners. Ok, now visualize a tesseract, a four dimensional hypercube connecting 16 corners. Topology can mathematically describe these shapes in multiple dimensions without flinching.
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- To illustrate this concept a study was done on diabetes. Each patient with diabetes was measured with four metabolic and one weight related number. So in effect each patient was looked at in 5 dimensions. When the shape of the data was studied it became clear that there were two distinct clusters of data, two distinct types of this disease. They became known as Type 1 and Type 2 diabetes.
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- You can see how complexity quickly rises as we go from 5 dimensions to 100 dimensions. Yet, in the topology of the data we can still find distinct shapes. Learning how to do this analysis could bring new insights into our understanding of the data. This science is coming of age none too soon.
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- Think of the large Hadron Collider, the giant particle accelerator in Geneva, Switzerland. This device is measuring 40,000,000 particle collisions that are occurring every second. The detectors are expected to process only 25% of 1% of the collision data, but, even that will generate 2,000 petabytes of data per year.
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- How would you like to analyze that? The Library of Congress has 29,000,000 books that contain only 15,000 Gigabytes. So, the Hadron Collider detectors are processing over 130,000 Libraries of Congress every year.
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- To analyze this data scientists need high speed, massively parallel computers. They will be trying to discover new physics, or new particles. So, they need to subtract all known physics from the data and see what is left. Like trying to find a particular sequence of words in 130,000 Libraries of Congress’s books.
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- In 1995 the National Archives had 57 Gigabytes of data in electronic storage. In 2004 it was 1.9 Terabytes. This year it is 5.1 Terabytes by July. All these Bytes are making me dizzy.
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----------------------- A 3x5 photograph is 100,000 bytes, 100 Kilobytes.
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----------------------- A floppy disk is 1,400,000 bytes, 1.4 Megabytes.
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----------------------- A Gigabyte is 1,000,000,000 bytes, equivalent to a pickup truck filled with books.
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- A Terabyte is 1,000,000,000,000 bytes. The records gathered for 9/11 Commission Report contained 1.2 Terabytes of information. That is equivalent to 60,000 trees made into paper and printed. That is just for the first copy.
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- A Petabyte is 1,000,000,000,000,000 Bytes All the material ever printed in the world to this date is 200 Petabytes. The National Archives preserves all White House records and 2% of other federal records. By 2022 it will have 347 Petabytes of information.
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- A Exabyte is 1,000,000,000,000,000,000 Bytes. All the words every spoken by human beings is 5 Exabytes. (and that is just the women. The average woman says 7,000 words a day. The average man 2,000 words. By 5:00 o’clock I have used up all my words for the day)
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- Let there by no data without records. Let there be no records without analysis. Let there be no analysis without a decision. Let there be no decisions without action. Let there be no action without data measuring the results. Let there be no data without records…...
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- You get the idea. How do you decide what actions to take with all this data?
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- Topological analysis may be the only answer. A picture is worth a thousand words. We need one a few hundred pictures worth a Petabyte each to deal with this problem.
I have just read more bytes than I can swallow.
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- March 1, 2020 605 2644
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----- Comments appreciated and Pass it on to whomever is interested. ----
--- Some reviews are at: -------------- http://jdetrick.blogspot.com -----
-- email feedback, corrections, request for copies or Index of all reviews
--- to: ------ jamesdetrick@comcast.net ------ “Jim Detrick” -----------
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--------------------- Sunday, March 1, 2020 --------------------
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