Saturday, April 27, 2019

- Exploding Stars Create Life - Destroy Life

-  2345   -  Scientists estimate it takes 100,000,000 to 200,000,000 years for intelligent life to emerge and colonize a planet.  65,000,000 years ago, at the end of the Cretaceous-Tertiary (K-T) period, 50% of life on Earth was extinguished.  The dinosaurs did not survive.  But, some half of marine invertebrates, plankton, marine reptiles did survive.  65,000,000 years later here we are and you are reading about it.
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---------------------- 2345  -  Exploding Stars Create Life - Destroy Life
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-  The iridium layer found at the K-T boundary around the globe is evidence of an asteroid impact on Earth that so changed the environment half of all life was extinguished.
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-  Further back in our history is evidence of other mass extinctions.
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-  210,000,000 years ago, the end of the Triassic period, 48% of marine invertebrates, mammal-like reptiles, and amphibians were killed.
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-  250,000,000 years ago, at the end of the Permian period, 83% of all marine invertebrates and mammal-like reptiles were killed.
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-  365,000,000 years ago, at the end of the Devonian period, 50% of marine invertebrates, plankton (trilobites) and primitive fish were killed.
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-  440,000,000 years ago, at the end of the Ordovician period, 57% of all marine invertebrates were killed.
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-  What were these weapons of mass destruction that caused these extinctions?
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-  Archeologists learn of the extinctions by studying the bones and fossils in descending layers of the Earth’s crust.  Distinct lines in the ages show extinctions where certain fossils no longer exist beyond that point.  But, so far, archeologists have not found convincing evidence for these other mass extinctions.
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-  On December 27, 2004 the brightest flash of light ever seen in our Solar  System occurred.  This flash of electromagnetic energy, called a Gamma Ray Burst, occurred in 0.2 seconds and contained the amount of energy the Sun emits in 250,000 years.
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-   Earth was hit with the blast, but fortunately it came from 50,000 lightyears away.  If it had been 10 lightyears away we would have had another mass extinction here on Earth.
-
-  The damage of these bursts of radiation only lasts a short time, about 15 years.  The primary effect is on the Earth’s atmosphere.  The Earth is surrounded by a blanket of oxygen (O2) and nitrogen (N2).  In the middle of this blanket, in the stratosphere, is a layer of ozone (O3).  The ozone layer blocks the penetration of ultraviolet light from the Sun.
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-  During a 10 second Gamma Ray Burst the radiation would break up the O2 and N2 molecules.  The chemical reactions in the atmosphere would create nitric oxide (NO) and nitrogen dioxide (NO2).  The nitric oxide would destroy the ozone (O3) layer and the NO2 would become a toxic brown gas in the atmosphere.
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-   As the ozone (O3) layer is destroyed ultraviolet radiation penetrates the atmosphere and reaches the surface of the Earth.  This UV radiation would damage DNA in all living creatures.  After a few months the toxic brown gas (NO2) will cover the entire planet. 
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-  Over time, say 10 years later, the NO and NO2 falls onto the Earth’s surface and reacts with water to form nitric acid.  Acid rain and acid snow falls out of the sky.
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-  After 15 years the atmosphere is pretty much back to normal.  But, on Earth much of the land life is extinguished, much of the near-surface marine life is killed, and the climate is tipped toward global cooling possibly causing another ice age.
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-  From geological evidence this 15 year event is too small to be noticeable.  The ice age may leave some evidence but it is unlikely that scientists will be able to tie mass extinctions to supernova explosions or gamma ray bursts.
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-  The other difficulty is that the Earth is rotating around the Milky Way every 250,000,000 years.  The Milky Way is not a solid disk.  The stars in the Milky Way are rotating at different radii and different speeds.  After a few rotations the stars are hopelessly scrambled making it impossible to identify a supernova that could be the smoking gun for mass extinctions.
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-  At the same time exploding supernova may be extinguishing life they are creating life.  To begin with the exploding supernova create all the higher level elements in the periodic table above hydrogen, helium, lithium, and beryllium.  Oxygen, carbon, iron, magnesium and 90 other elements are all created in the explosion of stars.
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-  Also, the radiation from the explosion that destroys life’s DNA, killing 50% of life, mutates life’s DNA that remains causing the diversity of life and the foundation for evolution to create higher life forms, us.
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-  Our galaxy is big and mostly empty space, but it harbors millions of black holes that are remnants of supernovas and collapsing stars.  When a giant star burns all it’s fuel, no heat remains to create the pressure withstanding the compression of gravity. 
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-  The force of gravity collapses the stars mass into a singularity at the center of a black hole.  These creators of life are every where.  Our galaxy and other galaxies could be teeming with life and we would not know about it.
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-  We are still learning.  To learn more here are other book reviews on the topic:
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-  476 - Gamma Rays and Cosmic Rays 9-10-03
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-  508 - You Are Made of Star Dust  10-17-04
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-  504  -  Accelerating Universe from Unknown Force.
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-  510 - Supernova You Can See
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-  455 - Supernovae - A Cosmos, Everything but Quiet.  It is violent out there.
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-  541 - Cosmic Rays
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-  542 - Neutron Star Flare - Magnetar
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-  613  -  From supernova to our Sun.
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-  831  -  Supernova 1987A
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-  929  -  The youngest supernova. 
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-  984  -  The art of astronomy.
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- 1308  -  Picture a star exploding
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-  1881  -  Supernovae are like snowflakes.  Also lists 9 more reviews abut supernovae. 
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-  2149  -  Supernovae from blue super giant stars.  Summarizes 15 more reviews about supernovae.
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-  2173  -   How supernovae explode.
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-  2299  -  You are made of stardust.  Also lists 6 more reviews about supernovae. 
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- 2300  -  Supernovae you can see.
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-  April 27, 2019                                                                                    579                         
----------------------------------------------------------------------------------------
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--  email feedback, corrections, request for copies or Index of all reviews
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 --------------------------   Saturday, April 27, 2019  --------------------------
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Friday, April 26, 2019

Rockets - how do they work?

-  2344   -  -   Rockets are very interesting if you want to learn physics.  Rocket designs get right down to the fundamentals.  It all starts with the law of motion that says :
“Action = Reaction”.  Action in physics means the product of energy and time. (A=E*dt) 
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---------------------- 2344  -  Rockets  -  how do they work?
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-   Calculus is the math of change.  It there is change in the product of two quantities that is area ( length times width).  The summation of areas is Integration.  Example: 
Action = Energy * dt, kilogram*m^2/sec.)   If there is a ratio of two quantities, this is a slope or rate of change, and that is differentiation.  Example:  Velocity = ds / dt, meters per second.
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-  To learn more let’s put a rocket in outer space with no other forces acting on it.  And we can see how this math works.  We will burn the fuel and determine the velocity of the rocket.  The rocket fuel burns at a constant rate.  It exit’s the exhaust at a certain rate that is constant in kilograms per second. 
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-  How can the rocket go faster that the speed of the exiting gas?  Can we use a heavier gas and get more thrust from the rocket?  Can we use ion propulsion to generate higher velocity from the exiting gas and get a faster rocket?  Can we use photons exiting the rocket traveling at the speed of light and get light speed from our rocket?  Let’s do the math and see.
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-  Because Kinetic Energy is ½ m*v^2, which is ½ m*v*v, which is momentum times velocity, like action = reaction, the Conservation of Momentum is basically , again, the Conservation of Energy.
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-   The Conservation of Momentum means that mass of the rocket * the velocity of the rocket in one direction = mass of the gas * the velocity of the gas in the opposite direction. 
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-   Initially the rocket has an original mass, “Mr“, and we light the fuel and the gas exits out the back at a velocity, “Vg“, at a rate of so much mass per second, “dm/dt“, the amount of mass of gas per unit time.  Over the next instant of time, “dt“, the rocket increases its velocity, “dv” by ejecting the mass of gas, “dm“, which is equal to “dm/dt * dt“.
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---------  Rocket momentum  =  Exhaust gas momentum
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----------  Mr * dVr  =  Vg * dm/dt * dt
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-----------  dVr  =  Vg * dm/Mr
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----------  The differential of the velocity of the rocket =  the ratio of the velocity of the gas * the constant rate mass of gas exiting per second to the mass of the rocket.
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-    The Integral of dm/m can be looked at two ways, as a ratio or as a product of (1/m) dm.  The Intergral of dm/m is the natural log of “m”/  The natural log is the exponent to the base “e”, whare “e” = 2.71828.…..  The Intergral of e^x*dx is e^x.  The differential of e^x is e^x*dx.  e^x is the only function that has this property.
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-  Another way to say this is the rate of change of the velocity of the rocket = the ratio of the velocity of the gas * the constant rate mass of gas exiting per second to the mass of the rocket.
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--------  We have to use calculus to solve this problem because over every instant of time the rocket is loosing mass and getting lighter.  If we integrate the differential of the velocity of the rocket we can get the velocity of the rocket at each instant.
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-   To get the final velocity we have to integrate, or sum up, the rate of changes in velocity over the entire range from the initial mass of the rocket to the final mass of the rocket, which is much less after the fuel is all burned up.
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--------------------- Integrate:  dVr  =  Vg *  Integrate: dm/Mr
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---------------------   Vr  =  Vg *  Integrate: (1/Mr)  *dm
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---------- We can put “Vg” outside the integral because the velocity of the exiting gas is a constant.
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-  Now we have to go to the Calculus books to learn the Integral of the function (1/m) dm:  Calculus is the math you use for something that is continuously changing.
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---------  The Integral of 1/x dx  =  natural log of x (2)
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----------  Therefore:  Vr  =  Vg * natural log of m
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----------  If we have a rocket mass of 1000 than the natural log of 1000 = 6.9 so the final velocity of the rocket will be 6.9 times the velocity of the gas exiting the rocket.  If the mass of the rocket was 10 then the velocity of the rocket would reach the natural log of
 10 = 2.3 times the velocity of gas exiting the rocket. 
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-  The more rocket fuel you have the faster the rocket will go.  But, there is a trade-off here.  It takes more energy to lift a heavier rocket.  It takes more thrust from the rocket to accelerate it if the rocket is more massive.  And, the more energy you use the faster your fuel is used up.
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-  The velocity of the rocket is directly proportional to the velocity of the gas, or mass per second, exiting the rocket.  Why not make the exiting mass go faster out the tail of the rocket to make the rocket go faster?
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-   Let’s design an ion rocket.  Chemical reactions are limited to a few electron-volts of energy.  We can set up a negative electric charge at the rear of the rocket to 200,000 volts and have positive cesium ions at the front of the rocket.  The cesium beam of ions would accelerate out the back of the rocket with an enormous velocity.  Let’s recalculate the velocity of the rocket with this design.
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----------------  The formula for the Conservation of Momentum is the same:
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----------------  Momentum of the rocket  =  Momentum of the ion exhaust.
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------------------  Mr * dVr  =  Vg * dm/dt * dt  =  Vg * dm
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------------------  The thrust is the force that moves the rocket and force is the rate of change of momentum with respect to time.  Thrust is momentum / second.  Or, in Calculus language, it is the first derivative of momentum with time. ( F=dm*v/dt)
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-----------------  Trust  =  Vg * dm/dt
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-----------------  Thrust  =  the velocity of the ions * the rate of mass exhaust / second
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-  To find the velocity of the cesium ions we need to use the Conservation of Energy, again.  The Kinetic  Energy of the fast moving ions must equal the Potential Energy caused by the high electrical voltage, 200,000 volts.
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-   Kinetic Energy is ½ m*v^2.  Potential Energy is the one electron charge of the cesium ion * the 200,000 volts.  A volt is the energy per unit charge, “q”.   Therefore,  Potential Energy = q* Volts. 
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------------------  Kinetic Energy  =  Potential Energy
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-----------------   ½ m * v^2  =  q * Volts
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----------------------   v^2  =  2 * Volts * q / m
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A mole is a unit of measure of the quantity of atoms.  In this case cesium atoms.  One mole = 6.02*10^23 atoms.  There are 96,500 coulombs of charge per mole.  And, cesium’s atomic weight, which is mass per mole is 0.133 kilograms per mole. 
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-  What we need is the ratio so we will soon get rid of those pesky moles.  96,500 coulombs / mole  /  0.133 kilograms / mole  =  725,564 coulombs / kilogram  =  q / m.
 A volt is a joule of energy / coulomb.  So,
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------------------  v^2  =  2*200,000  joules / coulomb * 725,564 coulombs / kilogram
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-------------------  v^2  =  29 * 10^10 joules / kilogram  =  29*10^10 kg * m^2/(sec^2 * kg) 
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------------------  v  =  5.4 * 10^5 m / sec.
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-  The velocity of the ions is 540,000 meters per second, or, 1,200,000 miles per hour.  That is 200,000 times faster the then the gas exhaust from the chemical rocket.  So, with that extreme velocity this ought to be a great rocket.
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-   But, before we jump to that conclusion let’s calculate how much energy it takes to get that much thrust from ion propulsion.  The ions are a positive charge and, in effect, an electric current exiting the rocket.  If the current was one ampere, which is one coulomb of charge per second, that would be the reciprocal of the 96,500 coulombs per mole, which is 1.036*10^-5 moles / second.
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-    And, the atomic weight of cesium is 0.133 kilograms per mole.  Multiplying these together gives us 1.378*10^-6 kilograms / second / ampere.  Multiply this times the velocity, 5.4*10^5 m/sec and we get 0.74 kilogram* m/sec^2 / ampere.
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-   In other words we only get ¾ of a newton of force / ampere from these cesium ions.  That is not very much thrust per ampere.  Electric Current * Voltage = power.  Amperes are coulombs per second * volts are joules per coulomb =  joules per seconds which is watts of power.
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-   One ampere * 200,000 volts  =  200,000 watts.  In other words, the ion propulsion rocket is giving us ¾ of newton of thrust per 200,000 watts of power.  That is 3.7 *10^-6 newtons per watt.  This is not a very good rocket because it takes so much energy to get the thrust we need.
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-  What if we used photons instead of cesium ions.  Photons have the fastest velocities of anything in the Universe.  The velocity out the back of the photon rocket would be the speed of light. 
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-  We know that E = mc^2  =  m*c*c  =  momentum * c.  The momentum / energy = 1/c would be the thrust to power ratio for our photon rocket.  That is 3.3*10^-9  newtons / watt.  That is even worse than our ion rocket.  It is 1000 times worse than our ion rocket and 1,000,000 times worse that our chemical rocket.
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-   You probably knew that because you do not feel much of a thrust backwards when you turn on a flashlight.   It looks like the chemical rocket is our best rocket design after all.
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-  If the same energy per atom is released, since kinetic energy = ½ mv^2, then, the lighter the atom we use in our chemical fuel the faster the velocity, and energy is velocity squared.
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-   Therefore, for the chemical fuels, we should use the lightest atoms possible.  That would be hydrogen and helium.  Unfortunately helium won’t burn very easily so we are stuck with hydrogen and oxygen as the best choices available.  Or, hydrogen peroxide and oxygen. 
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-   Next you design the rocket nozzle to get the highest percentage of chemical energy transferred into outgoing velocity.   There you have it the best rocket design in thrust / energy and the physics behind why that is so.
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-  Reactions?  What is your reaction?  Could you follow the physics?  Could you follow the math?  My experience is that you have to have a pencil and paper and do it yourself before it starts to make sense.  That is the primary reason I write these reviews.  I learn better through my fingers than I do through my eyes, or my ears.
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-  April 26, 2019                                                                                   887                       
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--  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, April 26, 2019  --------------------------
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Thursday, April 25, 2019

The Story of a Moon Rock

-  2343   -  About 30 Earth rocks have been found and identified as originating on the Moon.  This is the story of two of these rocks.  The first rock was found in Oman. a country southeast of Saudi, Arabia on the Arabian Peninsula.           
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---------------------- 2343  -  The Story of a Moon Rock
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-  A meteorite rock was found in Oman, Africa in September, 2002.  The rock tells us that it came from the Moon and it even tells us which crater on the Moon it was ejected from.
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-  By carefully analyzing the rock we learn that it came from the Imbrium Mare Basin, the crater Lalande on the Moon’s near side.  With a small telescope you can pick out that very crater about a day after the First Quarter Moon.
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-  The Oman rock was fist size and weighed 1.4 pounds.  It is called impact breccia which means it is rock composed of angular fragments of older rock melded together.  There are three types of rocks : igneous, sedimentary, and metamorphic.
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-  Igneous rock originates as a molten mass and forms by cooling.  The larger the crystals in the rock the slower the cooling process that made it.  This particular rock experienced three lunar impacts while on the Moon before a forth meteor impact ejected it and sent it towards Earth.
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-  The rocks composition was found to be richer in the radioactive element thorium than any other lunar rock known.  The decay time of radioactive thorium isotopes provides a reliable elapsed-time clock. 
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-  Thorium is a common rock that contributes to heating the Earth with its radioactive decay.  This decaying leads to the formation of the radon gas that may dangerously accumulate in building basements. 
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-  Thorium can be transmuted to Uranium 233, it melts at 3,182 degrees Fahrenheit.  The date for the rocks first gigantic impact was 3,909,000,000 years ago.  The impact crater is what formed the Imbruim Mare Basin on the Moon.
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-  The second impact occurred 2,800,000,000 years ago and this is what created the Lalande Crater.
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-  The third impact was 200,000,000 years ago creating another crater close to Lalande.  The 200,000,000 date did not come from radioactive dating, it was determined by the amount of cosmic ray absorption occurring in the regolith.  Regolith is the loose, disintegrated rock particles and mineral grains formed from the weathering of bedrock. 
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-  The forth impact came less than 340,000 years ago.  It ejected the rock off the Moon’s surface and into outer space.  This big of impact had to create a crater a few kilometers in diameter and in the neighborhood of Lalande.  The rock drifted through the solar system until it was captured by Earth’s gravity and smashed into the ground in Sayh al Uhaymir region of Oman, Africa 9,700 years ago.
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-  The 340,000 year age for the last impact was determined by dating the rock’s time on the ground plus the travel time from the Moon to Earth.
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-  The location on the Moon comes from the fact that there exists distinct chemical differentiation of the Moon’s surface as it formed its core, mantle , and crust.  The last stage of crustal formation left a chemically unique region rich in incompatible elements at the place the crust was struck by the Imbrium meteor.
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-  Around the Mare Imbrium Basin on the northwest side of the Moon lies an unusual region of rocks containing highly enriched potassium, rare-earth elements, and phosphorous along with thorium and uranium.  The crater Lalande is 25 kilometers (15 miles) across and lies right in the middle of this region.
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-  A more recent find was a rock in Dchira, Western Sahara that is 2,865,000,000 years old.  It was also an impact breccia rock made  up of fragments of the lunar surface welded together by the shock and heat of a meteorite impact.  -
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-  It had a large piece of olivine gabbro rock inside it that was dated at 2,865,000,000 years old making it the youngest lunar rock ever found.  Gabbro is a rock similar to basalt lava rock except it is cooled within the interior instead of on the surface.  It is rather low in silica for igneous rock, about 50% is silica.
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-  This Sahara rock probably came form the same region on the Moon as the Oman rock but their histories appear to be unrelated.  When the Moon’s magma ocean cooled various minerals began crystallizing in sequence.  Olivine was first to crystallize. 
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-  It is a magnesium iron silicate, (MgFe)2SiO4, that is olive green in color.  Pyroxene was next to crystallize out of the molten lava.  It belongs to another group of silicates that are unique with a characteristic cleavage angled at 90 degrees.
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- Next to crystallize was plagioclase feldspar.  Feldspar is a common mineral that is a combination of aluminum, silicon, and oxygen together with a metal of sodium or calcium, Na(AlS3O8).
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-   Plagioclase is the type of feldspar with a triclinic crystal shape.  Triclinic means the crystal has a unique three axes of unequal length all inclined at some angle.  When feldspar weathers into small particles it turns into clay.  Feldspar is lighter than the other rock so it floated on top of the magma to form the crust.
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-  These particular rocks contain high concentrations of radioactive elements, thorium and uranium.  The radioactive elements produce the heat which is the energy source to create the relatively young magna.  And therefore, this relative young rock, only 2,865,000,000 years old.
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It is so amazing to me that science can tell so much just carefully looking at a rock and knowing what they are seeing. 
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-  The rock has quite a story to tell if you can only read the writing.  I hope mine is easier.
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-  April 25, 2019                                                                                    74                         
----------------------------------------------------------------------------------------
---   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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 --------------------------   Thursday, April 25, 2019  --------------------------
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The Waves of Matter

-  2342  -  If all matter is waves then this could explain how matter interacts with all other matter in the Universe.  Maybe some day we will understand how gravity is produced by matter.  If all matter in the Universe is interconnected how big should the Universe be? 
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---------------------------- -  2342  -  The Waves of Matter
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-  In the early 1900 there were four experiments that failed.  Physicists were trying to explain the Universe and were not getting the answers they expected.
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-  The first experiment was Ernst Rutherford’s model for the atom.  The massive nucleus surrounding by orbiting electrons.  The nucleus and the electrons being held together by their opposite electric charges.   Nucleus having positive protons and the electrons having a negative charge.  Opposite charges attract, so what keeps them apart?  This is probably the atomic model you have in your mind.
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-   However, when you apply Maxwell’s equations to this model the atom would always collapse.  The orbiting electron is a moving electric charge.  It is accelerating because it is moving in a circle.  A moving charge emits electromagnetic energy.  If it is loosing energy it should soon spiral down into the nucleus.  Obviously, this is not happening.  So, what is keeping the atoms from collapsing?
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-  The next experiment had to do with measuring the light spectrum of all the elements in the periodic table.  Each element emits spectral lines at discrete wavelengths, or frequencies.  Each element atom has a distinct set of color lines in its spectra.  What causes these unique wavelengths to be generated?  (See review #38 Rainbows)
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-  The third experiment involved heating up objects.  If you heat an iron poker its atoms vibrate more and more vigorously and it turns red hot , yellow , then white hot.  Hot objects, since they are vibrating electric charges should give off electromagnetic waves. 
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-  However, using Maxwell’s equations again they should be giving off an infinite amount of electromagnetic radiation, concentrated at even  higher energies and shorter wavelengths, ultraviolet and X-rays.  Obviously this does not happen either.
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-  The forth experiment fails the photoelectric effect.  This happens in a cathode ray tube, a vacuum tube.  Where you shine light on a particular  metal surface and electrons are emitted from the surface.  This is the same effect that is used in the electric eye that controls your automatic garage door closure.  Except modern electronics uses semiconductor instead of vacuum tubes. 
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-  Physicists experimenting with the original photocells would get more electrons if the light was made brighter.  Theoretically, the color of the light should not matter, just its amplitude or brightness.  However, that is not what happened.  If the color of the light was red fewer electrons were ejected.  As the color was made bluer, the energy of the electrons increased.  Why?
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-  These four experiments were not getting the results expected.  The math was not working. Something is missing.  That something was the “quantum”.  All of these effects can be explained once we realize that matter and energy is not continuously subdivided.  It comes in discrete chunks.  Each chuck is a quantum.
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-  The quantum concept was first proposed in 1900 by Max Planck ( See review #8 Time Comes to Us in Particles).  Planck came up with this as a fudge factor, a constant, that he picked for each color of light to explain the amount of energy in the vibrating atom. 
-
-  Planck said:
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-------------------------------  Energy  =  Planck’s constant * frequency
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-------------------------------           E  = h * f
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-  In 1905 Albert Einstein used this explanation of for vibrating atoms to explain the photoelectric effect.  He declared that energy in a light wave is not spread uniformly over the wave but it is concentrated in particle-like bundles, called photons.
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------------------------------  Energy of a photon  =  h * f
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-  Red light is lower frequency and when it is lower than required energy to eject electrons, none will be ejected.  Bluer light is higher frequency, therefore blue photons impart more energy to the surface and more electrons are ejected.
-
-  The structure of the atom and the orbiting electrons can now be explained because only certain discrete orbits are allowed.  Each orbit corresponds to a discrete value of the electron’s energy.  Instead of energy Niels Bohr in 1913 used angular momentum in his equation to explain quantized orbits.
-
--------  Orbiting Angular Momentum  =  Planck’s constant / 2 * electron’s momentum
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-------------------------  Angular momentum  =  h / 2*m*v
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------------------------   Where m*v is mass * velocity  =  the momentum of the electron
-
-  Atom’s radiate electromagnetic waves only when electrons move between orbits.  This explains the spectra of atoms since each element has a unique atomic structure of electron orbits, each atom emit’s a unique color spectra.
-
-  So quantum‘s explain the results we are seeing.  But, quantum’s, Planck’s constant is a very small number.
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-------------------------   “h”  = 6.625 * 10^-34 kilogram * meters^2 / second
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-  Round this up and put in fraction from then Planck’s constant is:
-
-----------  “h”  =  0.66 / 1,000,000,000,000,000,000,000,000,000,000,000    kg*m^2/sec
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-  It is a very small number.  That is the reason quantization effects are not noticeable in everyday events.  The effects of quantum are only noticeable at the atomic scale or smaller.
-
-  The amount of energy in a light beam can not be less than that of a single photon.  For a given color light there is a minimum amount of energy we can use to observe the world
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--------------------------------------------  Energy  =  h * f
-
- This minimum energy is what causes the Heisenberg Uncertainty principle to exist.  (See review #40 Life is Uncertain).  This principle states that you can not measure the velocity and position of an atomic particle at the same time.  The measurement is always indeterminant, a probability.
-
-  If you try to measure velocity when the photon of minimum energy hit’s the particle the particle’s velocity changes.  If you try to measure its position the same thing happens.  When the photon hit’s the particle the position changes.
-
-  Heisenberg’s formal statement is one of tradeoffs.  He says that the product of the particles mass, the uncertainty of its velocity, the uncertainty of its position can not be less than Planck’s constant.
-
-----------------------------------  Mass * delta v * delta x  >  h
-
-  Again, because Planck’s constant is so small the principle has negligible effect in everyday life.  However, at the atomic scale it has enormous effect.
-
-  In order to make Maxwell’s equations work at the atomic scale the solutions must be given in the probabilities of detecting a photon.  The link between the wave equation and the particle becomes one of statistics and probabilities.
-
-  Small atomic structures like photons and electrons will behave like waves as well as like particles depending on the concentration of energies the size of the probabilities.  In 1923 Louis De Borglie proposed that matter has waves, that a particles associated wave depends on the particles mass and velocity.  This is the same as the particle’s momentum, mass * velocity.
-
--------------------------  Wavelength  =  Planck’s constant /  mass * velocity
-
-  Again, because Planck’s constant is so small the wave-particle duality is not noticeable in everyday life.  At the atomic scale it explains a lot.
-
------------------------------  Wavelength of an electron  =  h / m*v
-
------------------------------  “h”  =  Planck’s constant  =  6.625*10^-34 kg*m^2/sec
-
------------------------------  “m”  =  mass of electron  =  10^-30 kilograms
-
------------------------------  “v”  =  velocity of electron  =  10^6 meters / second
-
------------------------------   v  =   2,236,936 miles/hour
-
-------------------  Wavelength  6.625 * 10^-34 / 1^-30 * 10^6  =  6.625 * 10^-10 meters
-
-  This is about the same as the diameter of the atom, 10^-10 meters.
-
-  The diameter of an electron is 5.6 * 10^-15 meters.
-
-  The wavelength of the electron is in the same ballpark as the atomic structure.  In fact the allowed orbits of electrons within the atom can be explained as the “ standing wave” that can just fit in a specific orbit.  Just as a standing wave of a particular note played on a violin string are those that can just fit on the string at each specific length.
-
-  All matter has waves.  My brother is 180 pounds of matter and he has waves.  A baseball has waves.  Let’s see what happens when we calculate the wavelength of a baseball:
-
---------------------------------- Wavelength of a baseball  =  h / m*v
-
----------------------------------  “h”  = Planck’s constant
-
----------------------------------  “m”  =  mass of baseball = 0.1 kilograms
-
--------------------  “v”  =  velocity of baseball  =  10 meters / second (22 miles per hour)
-
---------------  Wavelength of baseball  =  6.625*10^-34 kg*m^2/sec  /  0.1kg * 10 m/sec
-
--------------------------------   Wavelength of baseball  =  6.625 * 10-34 meters
-
-  Granted it was a slow pitch but the wavelength of the baseball is so minuscule that it could never be used to explain the number of strike outs in the major leagues.
-
-  What we have shown is that at the quantum level matter is both waves and particles.  In fact, we could consider the particle to be the concentration of energy in the wave.
-
-  If you do your own experiment, take a glass slide, paint it black, hold two razor blades together tightly, and make two small scratches on the glass slide.  Now, shine a light through the glass slide and project the image on the wall.  The light emitting from the slots will project a circular interference pattern on the wall.
-
-   The wave characteristic of the photons will pass through both slots and begin emanating from the slide as two waves adding and subtracting as their peaks and troughs interfere with each other.  This will happen even if you shine one photon at a time on the slide.  The buildup of interference will eventually plot the same interference pattern.
-
-  Amazingly, the same experiment can be conducted using electrons instead of light photons.  These are thought of as particles with known mass.  We need to use the closely spread atoms of a crystal instead of slits on a glass slide, but the exact same interference pattern will be generated.  The electrons will behave as waves.
-
If all matter is waves then this could explain how matter interacts with all other matter in the Universe.  Maybe some day we will understand how gravity is produced by matter.  If all matter in the Universe is interconnected how big should the Universe be? 
-
-  The minimum size of a wave-particle is 10^-14 meter radius.  The number of particles in the Universe is 10^80.  If all these particles were connected in a sphere the surface area of the sphere would be:
-
------------------------  Area of one wave-particle  =  pi* radius^2  =  3.14 * (10^-14)^2
-
------------------------  All interconnected the total area  =  10^80 * 3.14 * (10^-14)^2
-
------------------------  The surface area of any sphere is   =  4 * pi * radius^2
-
-  If we set these two surface areas equal to each other we can calculate the radius of the Universe:
-
------------------------  4 * pi * radius^2  =  10^80 * 3.14 * (10^-14)^2
-
------------------------    Radius  =  0.5 * 10^26 meters.
-
-  The Coma-Virgo Cluster of galaxies is measured at 1.2 * 10^23 meters in radius.  It is just one of many galaxy clusters the trace the structure of the Universe.  This radius we calculated is about 1000 times bigger.  So it is in the ballpark for the observable universe, if not on the low side.
-
-   The wave characteristics of matter and make up of the Universe is still leaving a lot for us to learn.  The matter that we are made of and that we can see makes up only 5% of the observable universe.  There is still 95% we call dark matter and dark energy because we don’t know what they are.
-
-    It is so interesting that we are using the smallest things we know, the quantum, to help us explain the largest thing we know the Universe. 
-
-  April 25, 2019.                                                                                   51
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---   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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 ---------------------   Thursday, April 25, 2019  -------------------------
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Magnetism – from Atoms to Stars

-  2341  -  Magnetism is one manifestation of the electromagnetic force, which is one of the four forces known in the universe.  All material that we know of is magnetic at some level. The electrons spin about the atom and the electrons themselves spin so that each atom becomes a tiny atomic magnet.  To go from the smallest to the very largest magnetic fields we need to go from atoms to stars.
-
-
-
-----------------------------  2341  -  Magnetism – from Atoms to Stars
-
-  Magnetism is one manifestation of the electromagnetic force, which is one of the four forces known in the universe.  Light is another manifestation of electromagnetic energy that propagates through space with electric waves and magnetic waves switching back and forth at right angles to each other, traveling through space at a constant speed of 670,633,500 miles per hour.
-
-   The speed at which the electromagnetic waves switch back and forth determines how we observe the energy.  If this speed, or frequency, is faster than light wave frequencies than we observe ultraviolet, x-ray, then gamma ray energy.
-
-   If the switching speed is slower than we observe microwaves, and radio waves. The frequency is how fast the energy is switching through time.  The electromagnetic wave’s speed through Space is constant, 300,000,000 meters / second.
-
-  The frequency of yellow light is 500,000,000,000 switches / second.  The frequency of radio is 300,000,000 switches / second.
-
-  In 1831 Michael Faraday first showed the relationship between magnetic and electric energy.  Faraday demonstrated that a bar magnetic passed through a coil of wire generated an electric current in the wire.  Motion through space, with the magnetic lines of force cutting across the wire set up the electric current.
-
-  The motionless magnet has no electric affect.  In reverse, the coil of wire around an iron core can create a magnetic field, as long as the electrons are in motion as current through the wire.
-
-  But, what about a stationary permanent magnetic that has a magnetic field without any electric current or motion involved?  There are still electrons in motion. Magnetism is a property of the atom itself.
-
-  In that sense all material that we know of is magnetic at some level. The electrons spin about the atom and the electrons themselves spin so that each atom becomes a tiny atomic magnet.
-
-  In most materials these atomic magnets are oriented in random directions and there is no net magnetic affect that we can easily detect.  However, some materials such as iron and nickel have the capacity to orient their atomic structure in such a way that the poles of the tiny magnets are lined up in the same direction.
-
-  Permeability is the measure of magnetic strength of material.  A vacuum is given a permeability of 1.00.  Ordinary material with weak magnetic properties may have a permeability of 1.01.
-
------------------------------------------  Permeability:
-
---------------------------------------      Iron        =  1000
-
---------------------------------------      Nickel =  40
-
---------------------------------------      Cobalt  =  55
-
-  In these stronger magnetic substances there are magnetic domains 0.001 to 0.1 centimeters in diameter where the tiny atomic magnets are oriented in the same direction reinforcing each other and creating an overall strong magnetic field.
-
-  Because the Earth has an iron core it was once thought that the Earth was a giant permanent magnetic because of the magnetic field that completely surrounds the Earth.
-
-  The Earth has an iron core but it cannot be a permanent magnetic because it is molten and iron loses its strong magnetic properties at 1033 degrees Kelvin. The higher temperatures and vibrating atoms destroys the magnetic domains.   The Earth’s core is 6500 degrees Kelvin  ( For example, the Sun’s surface is 5,800 degrees Kelvin ).
-
-  However, the Earth’s core is in two parts, an inner solid core and an outer molten core.  The inner core is iron and nickel, while the outer core is molten iron, nickel and sulfur.  These two cores do not rotate at the same speed.  The inner core rotates faster while the outer molten core is slowed down by friction of the mass and weight above it.
-
-   It is this rotating metallic core that creates the magnetic field around the Earth.  The strength of the field is currently weakening.  It will continue to weaken and eventually it will reverse North-South polarity, then strengthen again.
-
-   By studying the crystal alignment in rocks we can see that older rocks were magnetized in the direction opposite to Earth’s present magnetic field.  In fact, the Global Rift on the ocean floor shows magnetic reversals occurring every 50,000 to 20,000,000 years with the pattern on one side of the rift mirror-imaged on the other side.
-
- The Earth has switched its polarity nine times over the past 4 million years. The last polarity switch occurred 780,000 years ago.  Since then the magnetic strength has weakened and strengthened several gauss fourteen times without a polarity reversal.  If we drill core samples out of the ocean sediment we can identify 171 polarity reversals during the last 78 million years.
-
-  The smallest magnets are used in computer memory disks.  These disks have a metallic surface film that stores digital information in small magnetic domains.  These tiny regions of magnetic material can span only tens of atoms on an edge.
-
-  In the magnetic storage material, each atom acts as a minuscule bar magnetic due to the property of spin.  In the storage media of each magnetic domain, almost all of the atoms have the same one of two possible spin orientations.  These two possibilities serve as the ones and zeros of digital information.  The most advanced magnetic disks use magnetic domains comparable in size to a large virus, 200 nanometers by 10 nanometers in area (nanometer = 10^-9 meters).
-
-  Theory is that magnetic domains smaller than 10 nanometers on a side will be unable to maintain their spin orientation to store these ones and zeros unless the media is chilled well below room temperature.
-
-   Scientists have used Scanning Tunneling Microscopes to detect atomic spins in less than 10 nanometer wide domains.  These tiny domains were in ultrathin films of iron deposited on a tungsten backing cooled to 16 degrees Kelvin.  Scanning Tunneling Microscopes may someday serve as the reading head of future disk drives.
-
-  To go from the smallest magnets to the largest we need to compare the relative strengths of magnetic fields using the unit of measurement for magnetic flux density, the gauss:
-
-    Despite the fact that magnetic lines of force have no material existence, it is often convenient to picture them in a literal fashion in order to describe a magnetic field.  The strength of a magnetic field is described as the number of lines of force passing through an area of unit size.
-
-  This is called the magnetic flux density.  The flux density measures how closely the lines of force are crowded together.  The more closely they crowd, the higher the flux density and the stronger the magnetic field at that point.  We define one line of force as one Maxwell. And, the unit of flux density as one Maxwell per square centimeter as one gauss.
-
---------------------------------------------------------------  Gauss
-
-----------  Weakest sustainable in the lab             0.00000000008
-----------  The brain’s magnetic field                  0.00000002
-----------  Interstellar galactic space                   0.000001
-----------  Produced by the human body              0.000003
-----------  Refrigerator                                     0.001
-----------  Electric lamp                                    0.01
-----------  Household wiring                             0.1
-----------  The Milky Way                                0.2
-----------  Earth’s field at the poles                    0.6
-----------  Sun’s magnetic field                         2.0
-----------  Jupiter’s magnetic field                    4.3
-----------  TV set                                               5
-----------  Electric shaver                                  10
-----------  Hairdryer                                           25
-----------  Typical refrigerator magnet                 100
-----------  Sunspots                                          3000
-----------  Largest man-made permanent magnet 50,000
-----------  Strongest sustainable in the lab           387,000
-----------  Strongest found in normal stars         1,000,000
-----------  Strongest for < second in lab           10,000,000
-----------  Magnetic white dwarf star            200,000,000
-----------  Surface of atomic nucleus 10,000,000,000
-----------  Normal neutron star            5,000,000,000,000
-----------  Magnetar neutron star 1,000,000,000,000,000              10^15 gauss
-----------  Strongest field possible in theory                                  10^53 gauss
-
-  To go from the smallest to the very largest magnetic fields we need to go from atoms to stars.  The Magnetar produces the strongest magnetic fields known in the Universe.  It is a star that is 30 to 100 times the mass of our Sun.
-
-  These massive stars do not live very long, 1 to 10 million years, before they burn all their hydrogen, then helium, then carbon, then oxygen, then silicon fuel.  The next fusion is iron and it cannot generate energy with further fusion. So, the outward pressure stops and the star collapses under the force of gravity.  The center of the star becomes so massive it collapses itself into a black hole.
-
-  The material feeding the black hole forms a disk of high speed particles spinning at light speeds.  In 10 seconds after the collapse begins the spinning disk generates magnetically confined jets that explode out the poles of the star in cone shaped shock waves.  These concentrated energies aim magnetic fields in the two directions, ex: north and south.  The jets are only 2 to 5 degrees wide.
-
-  As the shock waves blast through particles from the star gamma rays are produced.  As the jets slow down from plowing into interstellar material lower energy radiation is also produced in the form of x-ray, optical, and radio afterglow’s that last from minutes to months.
-
-  Astronomers observe one of these events each day on average, coming from all directions in the Universe.  Because the beams are only two to five degrees wide that means there are 1000 bursts invisible to us because they are pointing in another direction.  Statistically that means we average 1500 supernova bursts of this magnitude occurring every day.
-
-  The magnetic strength of a magnetar neutron star is powerful enough to rip at kitchen knife out of your hand from a distance that is half way to the moon.  Not only could it erase your credit cards, it could pull the iron out of your blood.
-
-  We know that an asteroid struck Mexico 65 million years ago annihilating the dinosaurs that ruled the Earth at that time.  There was another devastating mass extinction at the end of the Ordovician period 440 million years ago.  During the Ordovician period all life on Earth was aquatic, and fossil records show that species living in deeper water fared better than shallow-water dwellers.
-
-  One possible explanation is that a magnetar neutron star focused its radiation at Earth breaking apart the atmosphere molecules that protect us from the Sun’s ultraviolet radiation.  This would explain the death of creatures near the water’s surface.  The same phenomena could explain a similar mass extinction that occurred to start the Cambrian period 544 million years ago.
-
-  Most of these gamma ray jets pass by unseen, but occasionally one is pointed right at us, as if we were sitting at the end of a gun barrel.  Let’s hope the gun is not too close.
-
-  The metric unit of magnetism is named after Johann Karl Friedrich Gauss who was born in 1877 in Brunswick, Germany.  His father was a gardener and his mother a servant girl.  Johann was a genius in mathematics at a young age.  At three years old he could correct math mistakes and keep all sorts of numerical records in his head.
-
-   He became one of the world’s three greatest mathematicians, Archimedes and Isaac Newton being the other two.  At age 22 he received his Ph D from Gottingen University.  As a student he calculated the orbit of the asteroid, Ceres, to allow it to be located after it was lost.  Johann also worked out the location of the planet Neptune to allow it to be discovered in 1846.
-
-  In 1842 he devised the set of units of measuring magnetism and the unit for magnetic flux density was eventually named the gauss.  His work with terrestrial magnetism allowed him to calculate the location of the magnetic poles on Earth, which proved to be remarkable accurate.
-
-  Johann even constructed an electric telegraph in 1833, about the same time Joseph Henry invented the telegraph in the United States.
-
-  April 24, 2019.                                                                                32
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---   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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 ---------------------   Thursday, April 25, 2019  -------------------------
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Wednesday, April 24, 2019

- How to Weigh a Galaxy

-  2340   -  About half the mass of the Milky is inside the Sun's orbit and half is outside.  This fact has proven to be a real problem for astronomers.  The inside orbit is much, much denser with visible light than the outside orbits.  The mass of the outside orbits is larger than we can visible see.  This fact has caused astronomers to invent another object in the Universe, Dark Matter
-
-
-
------------------------------------ 2340  -  How to Weigh a Galaxy
-
-  Weight is how much force gravity pulls on a given mass.  When we say weigh a galaxy we mean we want to determine how much mass is their creating how much gravity.  Let’s measure the mass of the Milky Way Galaxy.  We can not measure its mass directly.  We can measure its size directly:
-
-  The Milky Way Galaxy is 2,000 parsecs thick and 40,000 parsecs across.  From Earth the galaxy center is 8,500 parsecs away.  Parsecs is a distance measurement used by astronomers.  A parsec is a very long distance, it is longer than a lightyear.  A lightyear is the distance a beam of light will travel in one year traveling at 670,000,000 miles per hour. 
-
-  That distance is 5,880,000 million miles and the parsec equates to a distance of 3.26 lightyears.  A parsec is the distance one astronomical unit looks like when it is so far away it subtends an angle of one arcsecond.
-
-  An arcsecond is a very small angle.  A full circle has 360 degrees.  Each degree is divided into 60 arcminutes.  There are 21,600 arcminutes in a circle.  Each arcminute is divided into 60 arcseconds.  There are 1,296,000 arcseconds in a circle.
-
-    An astronomical unit is the distance between the Earth and the Sun.  The parsec is defined as the distance one astronomical unit would appear if it were the base of a triangle and the vertex was an angle of one arcsecond.
-
--------------  A parsec  =  3.1  *  10^16 meters   =  3.26 lightyears
-
---------------  A lightyear  =  .95 * 10^16 meters  =  1 lightyear
-
--------------  An AU  =  1.5 * 10^11 meters.  There are 633,757 AU’s in a lightyear.
-
Therefore, the Milky Way Galaxy is 6,400 light years thick and 128,000 light years in diameter, with the center 27,200 light years from Earth.  It takes 128,000 years for light to travel across our galaxy.
-
- That is how big the Milky Way Galaxy is.   We need to us Kepler’s laws of orbiting bodies to calculate the mass of the Milky Way:
-
-  The Sun is traveling 220,000 meters / second (492,130 miles / hour) in a near circular orbit around the center of the Milky Way with a radius of 8,500 parsecs.  It takes 230 million years for the Sun to complete one orbit, that is,  the last time we were at this point in our orbit  96% all species on Earth died out and the Dinosaurs began their rule of Pangaea.    Pangaea was the super-continent in the Jurassic period 230 million years ago.
-
-  Johan Kepler in 1619 discovered the laws that will allow us to calculate the mass from the data we can measure.  He determined  that the square of the period of revolution of a planet is proportional to the cube of its distance from the Sun.  He was working with planets but the same laws apply stars, and orbiting mass in general.
-
--------------  Period ^2 in  years =  distance of semi-major axis in astronomical units ^3
-
- Period is the time it takes for one full orbit.  Kepler's Third Law was originally applied to an ellipse, thus a semi-major axis rather than a radius was used.  It turns out the Sun’s orbit is a very flattened ellipse but it definitely was not a perfect circle. 
-
-  Using Newton's laws, Kepler's Third Law can be converted to:
-
---------------------  Period^2  =  4 * pi^2 * axis^3   /   G ( m+M )
-
-  M + m are the masses of the two bodies.  The Milky Way mass is so much larger than the Sun’s mass we will assume (M+m)  =  Mass.  And,  we will assume that the orbit is a perfect circle of Radius.  We can calculate the rotational velocity of the orbiting body:
 -
--------------------  Since velocity   =   distance  /  time  =  circumference  /  period:
-
--------------------  distance^2   /  velocity^2    =      4 * pi^2 * Radius^3   /   G * Mass
-
-------------------  The distance is the circumference of the circle  =  2  *  pi  * radius
-
-------------- 4 * pi^2 * Radius^2  /  velocity^2    =      4 * pi^2 * Radius^3   /   G  * Mass
-
--------------    G is the gravitational constant  =  6.67  *  10^-11  m^3  /  ( kg/sec^2) 
-
-  “G”  is a natural constant for the force of gravity and its value depends on the units used in the measurement.
-
-----------------------   1  /  velocity^2    =       Radius  /   G * Mass
-
-  Solving for the mass:
-
---------------------  Mass  =  velocity^2 * Radius  /  G
-
-----  Mass  =    (220,000 m/s)^2   *     8,500parsecs  / 6.67  *  10^-11  m^3  /  ( kg/sec^2) 

----------------------  Mass  =  1.9 * 10^41 kg
-
-  The Mass of the Milky Way inside the Sun's orbit  =  1.9  *  10^41 kilograms
-
-  The mass of the Sun is 1.99 * 10^30 kilograms
-
-  So, the mass of the Milky Way inside the Sun's orbit is about 10 ^ 11 or 100 billion solar masses.
-
-  When Johan Kepler was doing this math in 1609, he was using data on the planets orbiting the Sun.  Kepler was a German astronomer, born in 1571, the son of a professional soldier.  He had smallpox as a child that crippled his hands and eyes so his parents put him into a religious school because they thought the work would be less strenuous for him as a minister.
-
-   He got his masters degree in 1591, abandoned ministry and taught mathematics in the University of Graz, Austria.  Because of the Thirty Years' War Graz was too dangerous and he moved to Prague were he worked with astronomer, Tycho Brahe.  Tycho died in 1601 and left Johan all his data on the orbiting planets.
-
-  With his religious background, and influence of Plato and the Greeks, Johan tried for years to fit the data on orbiting planets to circles and spheres.  The circle was recognized as the perfect geometry and ,of course, the heavens would not be ruled by anything less than perfect. 
-
-  Johan could not make the math work.  He nearly gave up before he tried making Mar's orbital data fit  an ellipse.  It matched up with a high degree of accuracy.  Valhalla !
-
-  Once Johan was working with ellipses he discovered these three laws:  Planets orbit in ellipses, with the Sun at one focus;  the line connecting the planet and the Sun will sweep over equal areas in equal times as the planet moves about its orbit ( also stated as the product of distance from the focus and transverse velocity is a constant); and, the square of the period of the revolution of a planet is proportional to the cube of its distance from the Sun.
-
-----------------------------  Radius  -------  Period^2  -------Radius^3  ----- Velocity
-----------------------------    AU     -------  years^2  -----------  AU^3  -----  Km/sec
-
-------  Mercury  --------  .39    -----------  .06  ---------------.06  ---------    47.9
-------  Venus   ----------  .72    -----------  .37  ---------------.37 ---------     35.0
-------  Earth  ------------  1.00    -----------1.00  -------------1.00  --------    29.8
-------  Mars    -----------  1.52    ----------- 3.53  ------------3.51  ---------   24.1
-------  Jupiter  -----------  5.20    --------  140.7  ----------140.6  -----------  13.1
-------  Saturn   ----------  9.54    ---------  867.9  ----------868.3  -----------   9.6
-------  Uranus  ---------  19.19    -------- 7,058  ----------7,067  ------------   6.8
-------  Neptune  --------  30.06    ------- 27,160  ----------27,160  ------------5.4
-------  Pluto  ------------  39.53    ------  61,770  ----------61,770 ------------- 4.7
-
-  Note in the above table that for each of the 9 planets (Pluto included) the square of the period of the orbit is equal to the cube of the radius from the Sun.  Also note that as you go further out from the Sun the rotational velocity of the planet decreases.  Let’s see what happens when we do similar calculations for the Milky Way?
-
-  If we go to the very edge of the Milky Way, at a distance of 16,000 parsecs , the orbiting speed of the stars is 230,000 meters / second.
-
-   Again substituting in to Kepler's formula:
-
---------------------  Mass  =  velocity^2 * Radius  /  G
-
--  Mass  =  *   (230,000 m/s)^2    *  16,000 parsecs  /  6.67  *  10^-11  m^3  /  (kg/sec^2) 
-
-  The mass of the entire Milky Way is  =  3.9 * 10 ^ 41 Kg.  Or,  2* 10^11 solar masses.
-
-  Conclusion, about half the mass of the Milky is inside the Sun's orbit and half is outside.  This fact has proven to be a real problem for astronomers.  The inside orbit is much, much denser with visible light than the outside orbits.  The mass of the outside orbits is larger than we can visible see.
-
-  This fact has caused astronomers to invent another object in the Universe, Dark Matter. This invention assumes that each galaxy is surrounded by a giant halo of invisible mass that accounts for the constant rotational velocity.  (See #718“ Dark Matter, What Could it Be“?)
-
-  Johan and Galileo were pen pals although they never met and Galileo sent Johan one of his first constructed telescopes.  Johan used it to study the moons of Jupiter.  Johan must have had some time away from the telescope because he had thirteen children in two marriages.  He died in 1631 due to a fever and an over enthusiastic doctor that was practicing medical bleeding as a remedy.
-
-  He taught us how to weigh a Galaxy.  His laws are used universally in Astronomy today.
-
-  (1)  See " Time Comes to Us in Particles"  to learn more about G
-
-  (2)  See Review  33 to learn more about Kepler’s laws of physics.
-
-  (3)  See Review  718 to learn more about Dark Matter
-
-  (4)  See Review 2283  “Galaxies that make up the Universe”  that also lists 14 more Reviews about galaxies.
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-  April 24, 2019                                                                                    13                         
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 --------------------------   Wednesday, April 24, 2019  --------------------------
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Tuesday, April 23, 2019

Brown Dwarfs - too small to be a star.

-  2339  -  Brown Dwarfs are not stars.  They are not quite big enough to start hydrogen burning, the thermonuclear reaction.  Brown Dwarfs are providing much more information about how stars were formed. 
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---------------------------- -  2328   -  Brown Dwarfs  -  too small to be a star.
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-  All stars are destined to evolve into one of these three:
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-------------------------------  (1)  White Dwarfs
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------------------------------   (2)  Neutron Stars
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------------------------------   (3)  Black Holes
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-  Review 625 explained how “ Neutron Stars” fit into this evolution of stars depending on their size.  Where do “Brown Dwarfs” fit into this star evolution?  Technically, Brown Dwarfs are not stars.  They are not quite big enough to start hydrogen burning, the thermonuclear reaction, that makes a star shine.
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-    Brown Dwarfs range in size from 12 times to 75 times the mass of Jupiter.  Jupiter would have to be 80 times larger to cause the nuclear fusion of hydrogen.  That is the tipping point for Brown Dwarfs as well as planets.  Our Sun is 1,000 times the mass of Jupiter.
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--------------------------  Mass of Sun  = 1,989 * 10^27 kilograms
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 -------------------------  Mass of Jupiter  =  1.899 * 10^27 kilograms
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--------------------------  Sun is 1,047 times more massive than Jupiter.
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-  Brown Dwarfs were only discovered 2 dozen years ago.   Some 24 years ago astronomers from Vanderbilt University at Kitt Observatory discovered a binary pair of Brown Dwarfs in mutual orbit.  This orbit is edge-on and allows the dwarfs to eclipse each other.  This in turn causes dimming and brightening when one dwarf eclipses the other.  Astronomers have made over 1,600 measurements of these occultation’s and their mutual orbit over 300 nights.
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-  The existence of Brown Dwarfs was first proposed in 1980, but, astronomers did not concede that Brown Dwarfs actually existed until 2000.  The reason is that these Brown Dwarfs are about the same size as big planets and it is difficult to tell the difference.  The difference is how they are formed.
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-   Planets are formed in the accretion disk of stars causing them to have a higher density than stars of the same size.  On the other hand, Brown Dwarfs are formed just like stars, through the concentration of interstellar gas through the constant compression of gravity.  In the star evolution process the Brown Dwarf would be mostly hydrogen gas throughout and would be far less dense than a planet the same size.
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-  Jupiter is a gaseous planet but it was formed in the accretion disk of our Sun, like the Earth, and Jupiter has an iron core.  We believe this because Jupiter has a magnetic field 19,000 greater than the magnetic field surrounding Earth.
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-  The Sun is a gaseous star, mostly hydrogen gas, but its mass is large enough, to have enough gravity, to create enough pressure at its center, to have a high enough temperature, to start a thermonuclear reaction fusing hydrogen into helium.
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-   Our Sun fuses 600,000,000 tons of hydrogen gas into helium gas every second.  When this fusion occurs a small amount of the mass of hydrogen is converted directly into energy, E=mc^2, radiating gamma rays out from the center.  It is these gamma rays that power the Sun.
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-   When gamma rays make their way to the surface they loose energy and escape from the Sun’s surface at the frequency of visible light.  We see the Sunlight.  Brown Dwarfs have the compressed hydrogen gas but never gather enough mass to have enough gravitational pressure to start thermonuclear fusion. 
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-   From the outside a failed star and a giant planet would look the same.  We really need to know the density of the object before we can decide which it is.  To know the density we need to know the mass and the volume so we can calculate density.
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-  This is where our breakthrough comes in.  Measurements of these binary Brown Dwarfs in the Orion Nebula some 1,500 lightyears away have yielded this data.  By timing the orbit and timing the eclipse as one dwarf moves in front of the other we have measured the diameter of one dwarf to be 70% the diameter of the Sun and the diameter of the other to be 30% the diameter of the Sun.
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-  The mass is calculated from the measurements of the mutual orbit.  Using Kepler’s formula that the square of the period is proportional to the cube of the radius.

Period^2  =  4*pi^2*(radius)^3 / G * (m+M)

This formula allows the calculation of the sum of the two masses.  But, using their relative sizes you can deduce the mass of each dwarf.

Their masses were found to be 55 times the mass of Jupiter and 35 times the mass of Jupiter, but, only 5.5% and 3.5% the mass of the Sun.  The density of the larger Brown Dwarf is only 16% the density of Jupiter so it definitely qualifies.
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-   But, my calculations show the density of the smaller object to be the same as Jupiter, so that qualifies as a planet.  There must be a mistake somewhere?
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------------------------  The diameter of Jupiter  =  1.42984 * 10^5 kilometers
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------------------------  The diameter of the Sun  =  13.92 * 10^5 kilometers
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------------------------  70% the diameter of the Sun  =  9.74 * 10^5 kilometers
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------------------------  30% the diameter of the Sun  =  4.14 * 10^5 kilometers
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-------------------------------------------  The volume of a sphere  =  4/3*pi* (radius)^3
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------------------------  Volume of 70% Dwarf  =  484.3 * 10^24 m^3
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------------------------  Volume of 30% Dwarf  =  38.13 * 10^24 m^3
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---------------------------------------  The mass of the Sun  =  1,989 * 10^27 kilograms
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------------------------  Larger Dwarf 5.5% the mass of the Sun  =  109 * 10^27 kilograms
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------------------------  Smaller Dwarf 3.5% the mass of the Sun  =  70 * 10^27 kilograms
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--------------------------------------  The mass of Jupiter  =  1.899 * 10^27 kilograms
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----------------------   55 times the mass of Jupiter = 104.4 * 10^27 kilograms
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----------------------   35 times the mass of Jupiter = 66.5 * 10^27 kilograms
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-------------------------------------------  Density  =  mass / volume
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---------------------  The density of the larger Brown Dwarf  =   216  kilograms / meter^3
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---------------------  The density of the smaller Brown Dwarf  =  1,744 kilograms / meter^3
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---------------------  The density of Jupiter  =  1,244 kilograms / meter^3
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-  Astronomers put the density of Jupiter at 1,330 kilograms / meter^3.  Our calculation is too low because we assume Jupiter to be a perfect sphere and actually it bulges at its equatorial diameter.
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----------------------  The density of water is 1,000 kilograms / meter^3
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----------------------  The density of the Sun is 1,410 kilograms / meter^3
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-   Brown Dwarfs are dim red in color.  They do have a temperature and do radiate infrared energy.  It was surprising to learn that in this case the smaller Brown Dwarf had a higher temperature than the larger Brown Dwarf, 2,790 Kelvin versus 2,650 Kelvin.  We would expect the more massive the star the hotter it gets ( See Review 167 ). 
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-  This discovery has lead astronomers to believe that the two Brown Dwarfs were not formed together out of the same gas and dust.  They are likely not the same age but formed at different times in different places and somehow later were captured and locked into their mutual orbits.
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-  Many astronomers believe the brown dwarf is the most common product of the star formation process.  In other words, there many more failed stars in the Universe than there are stars.  Today, astronomers have cataloged hundreds of small, faint objects that they think are Brown Dwarfs. 
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-  It is only in recent years that our telescopes have gotten powerful enough to find these small dim objects.  They are all about the same size as planets have a reddish cast and probably look like a big Jupiter with weather clouds, bands and spots.
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-  At the high end of their mass range, 60 to 80 Jupiter mass, the volume of Brown Dwarfs is governed primarily by electron degeneracy pressure. (See Review 625 ).
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-   At the low end of their mass range, 1 to 10 Jupiter mass, the volume is governed primarily by Coulomb pressure, the same as the volume of planets.  Throughout this wide range of masses the size, or radius, of Brown Dwarfs varies only by 10 to 15%.  They are about the same size as planets which makes them so hard to differentiate.
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-  Density is the clear giveaway.  At the low end of the mass range, under 13 Jupiter mass, they are never hot enough to undergo even deuterium fusion.  At the high end of the mass range deuterium fusion can occur but it can only last on the order of 10,000,000 years. 
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-  Some Brown Dwarfs emit X-rays and all Brown Dwarfs continue to glow in the red and infrared spectra until they cool to planet like temperatures under 1,000 Kelvin.  Brown Dwarfs range in temperature from 300 to 3,000 Kelvin.  The minimum temperature for stars is 4,000 Kelvin.  Stars warm continuously with steady internal fusion.  Brown Dwarfs cool quickly.
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-  One of the more recent tests is called the Lithium Test.  If a star starts to fuse hydrogen it rapidly depletes the Lithium that is present.  A collision of Lithium-7 and a hydrogen nucleus ( a proton ) fuse to produce Helium-4 nuclei.  This occurs just below the temperature at which Hydrogen will fuse into Helium.  Measurements of the presence of Lithium become a good indicator if the object is a Brown Dwarf or a light star.
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-  Brown Dwarfs are providing much more information about how stars were formed.  And, we have just begun to study them.  Each new instrument, new technology, new capability opens up a new window of knowledge and new discoveries.  We do live in interesting times.
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-  April 23, 2019.                                                                                626
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 ---------------------   Tuesday, April 23, 2019  -------------------------
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