3028 - INTEREST - The Growth and Decay of Money?

 -  3028 -  INTEREST  -  The Growth and Decay of Money?  Learn the math for the growth and decay of money.   Let’s study the growth of money.  The math is very interesting and it applies to many situations in nature that experience growth or decay.  It involves compound interest in the case of money.  In nature it is any continuous rate of change, usually with time.

---------------  3028  -  INTEREST  -  The Growth and Decay of Money?

-  Interest is really the price of money.  The higher the interest rate the more valuable the money is.  The interest rate is the rate of growth with time.  In stable economics the interest rate is normally a point or two above the inflation rate.

-

-    The inflation rate is how fast prices are rising.  Under ideal conditions the inflation rate is tied to the productivity which defines how efficiently the economy is growing.  

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-  Productivity is the ratio of the  value of the output to the cost of the inputs.  It all fits together as a natural process, ideally.

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-  Let’s start with money and cover other natural processes later:

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-  Starting with $100 and letting it grow at a 4% annual interest rate at the end of the first year you would have $104.   -  $100 is called the Principle and $4 is called the interest on that Principle.  For our purposes we will call the $104 the “Future Value of money“.

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----------------------  Future  Value  =  Present Value * ( 1 + interest rate) ^n

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-------------------  where: “n” is the number of years at 4% per year.

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--------------------------- FV  =  PV ( 1+i)^n

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-  If we let the money ride for another year,   n = 2

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----------------------  FV  =  100 ( 1.04)^2  =  100 ( 1.08)

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----------------------  FV  =  $108

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-  If we let it ride for 10 years:

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--------------------   FV  =  100 ( 1.04)^10  =  100 ( 1.48)

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--------------------- FV  =  $148

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-  After 10 years the $100 has grown to $148.  You have made $48 in interest on your money.  If that principle were $100,000 you would have made $48,024.

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-  When interest grows on top of interest we call that “compound interest”.  Getting interest on your interest.  The growth of compound interest is an exponential growth rate.  It is the natural growth rate found in nature with most types of growth and decay.

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-  In the money example we compounded yearly and got $148 after 10 years.  What would you get if you compounded interest hourly instead of yearly?  There are 8,760 hours in a year.

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-------------------  FV  =   PV ( 1 + i /n)^n

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-------------------FV  =  100 ( 1+ 0.04/8760)^ 87,600

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------------------  FV  =  $149.18

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-  Compounding hourly only gained another $1.16.  So, what would happen if you compounded continuously as normally happens in nature?  

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-  We introduce the natural constant “e” which is the base of natural logarithms.  A logarithms is another name for “exponent“, and, we are working with “exponential growth” .  e^x is the only function that has a rate of change that is the same e^x.

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--------------------  FV  =  PV * e^n*I

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--------------------  FV  =  100 * 3^10*(0.04)  =  100 * ( 1.4918)

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---------------------  FV  =  $149.18

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-  Compounding interest continuously did not get us any more growth in interest over 10 years of compounding hourly.  But, note that the exponential curve gave us the same answer, $149.18.

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-  Imagine a x-y plot and y = e^x as the exponential curve, y is a function of 2.7 raised to the power of “x”.  What is unique about the base “e”,  which is a constant that has a value of 2.718, the value of the function is the same as the slope of the curve.  The slope is rise over run, which is (delta y) / (delta x).

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-----------------------------  y = e^x

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-----------------------------  dy / dx  =  e^x

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- For an exponential curve the value of the function is the same as the change in y to a change in x as you travel up the curve.  dy / dx is the tangential slope of the curve.  e^x has some other unique properties.  It can be expanded into an infinite series.

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----------------  y  =  e^x  =  1  +  x / 1 + x^2 / 2!  +  x^3 / 3!  +  x^4 / 4!  +  x^5 / 5!  +  x^6 / 6!  +  x^7 / 7!  +  ………

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-  3! is 3 factorial which is shorthand for 3 * 2 * 1,   just as 5! is 5 * 4* 3 * 2 * 1

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-  When x + 1 the function y = e which =  1  +  1 / 1 + 1^2 / 2  +  1^3 / 6  +  1^4 / 24  +  1^5 / 120  +  1^6 / 720  +  1^7 / 5040 +  ………

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-  y = e  =  2  +  0.5  +  0.167  +  0.0417  +  0.008  +  0.001389  +  0.0001984 + ………

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----------------  e  =  2.718254

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-  Note that the series for compound interest is the same type of exponential function:

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--------------  FV  =  PV ( 1+i)  +  PV ( 1+i)^2  +  PV ( 1+i)^3  +  PV ( 1+i)^4  +  PV ( 1+i)^5  + ……… PV ( 1+i)^ n

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---------------  FV  =  PV e ^ n*i

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-  This is the equation for all exponential functions.  The equation appears everywhere in nature, not just in banking and mortgages.  Any situation where the amount (A)  of something  varies with the time , such that the time rate of change of (A)  is proportional to (A) itself.

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----------------------dA / dt  = k* A

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-  Solving this differential equation gets us to the same formula with different symbols:

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---------------   A  =  Ao * e^k*t

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-  This equation could be the growth of money, the decay of a voltage across a capacitor, the cooling of a voltage regulator in your car.  The voltage  across a capacitor decays at a rate proportional to the voltage.  It the voltage is 20 volts and 2 seconds later is 10 volts it has a decay rate of - 10 volts / second.  When will the voltage across the capacitor be 2 volts?   ANSWER:  6.64 seconds:

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----------------  A  =  FV  =  10 volts

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----------------  Ao =  PV  =   20  volts, the initial voltage at time equal zero.

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---------------  k  =  i  =  the rate of decay.  If it were linear it would be - 10 volts per second. But, it is exponential and we have to solve for it.

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---------------  t  =  time  =  2 seconds

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---------------  FV  =  PV * e^i*t

----------------  10  =  20  * e^ 2 i

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-  The unknown “i” is in the exponent so we need to take the natural logarithm.

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-----------------  10 / 20  =   e^2i

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-----------------   e^ 2i =  0.5

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-  The natural logarithm to the base “e” of 0.5  =  the exponent 2i

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--------------------  log e (0.5)  =  2*I

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-------------------   -0.693    =  2 * I

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--------------------  - 0.3465  =  i

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- In the next interval of time the capacitor discharges from 10 volts to 2 volts at this constant decay rate of - 0.3465 volts per second

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--------------------   2  =  10 * e^-0.3465 * t

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-------------------  log e 0.2  =  -0.3465* t

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-------------------   - 1.605  =  -0.3465 * t

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--------------------  t  =  4.64 seconds

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-  The voltage across the capacitor decays at an exponential rate.  It will decay from 20 volts to 10 volts in only 2 seconds , and, an additional 4.64 seconds for the capacitor to decay down to 2 volts. A total time of 6.64 seconds.

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-  How long does it take an amount of money to double if the investment is growing at 10% compounding interest?

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-------------------  FV  =  2

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-------------------  PV  =  1

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---------------------  n  =  ?

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--------------------  i  =  10%

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---------------  FV  =  PV  * e^n*I

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---------------  2  =  e ^ n*(0.1)

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---------------  log 2  =  0.1 * n

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--------------  0.693  = 0.1*n

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---------------  n  =  6.93 years

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-  It takes 7 years for money to double growing at 10% per year.  You will learn i * n  =  70 later on:

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---------------  FV  =  PV  * e^n*I

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----------------  FV  =  $100  *  e ^0.7  =  100 * ( 201)

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---------------  FV  =  $201

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-  Objects cool at an exponential rate, temperature decreases at a rate proportional to the difference of the units temperature (u) and the temperature of the surrounding environment (T).

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-------------------  du / dT  =  k (u-T)

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-  Integrating to solve the differential equation:

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----------------  (u - T)  =  (uo - T) * e^ k*t

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----------------  (u - T)  =  FV  =   the future temperature difference, then:

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-----------------  FV  =  PV * e^n*i

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-  The car’s regulator is at 90 decrees C and the garage is at 20C.  Turn off the ignition and 10 minutes later the regulator cools to 60 C.  At what temperature will it be after 20 minutes?

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-----------  PV  =   90 - 20  =  70

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----------  FV  =  60 - 20  =  40

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-----------  i  =  rate of decay in degrees per minute. ( - 3 degrees / minute if the decay was linear.)

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------------  n  =  is in 10 minute intervals and that doubles in time  n  = 1 for each interval.

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------------   40 =  70 * e^1* I

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-----------   0.5714  =  e^I

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-----------  log e (0.5714)  =  I

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------------  ( - 0.56)  =  i

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-  The next interval drops the temperature from 60 degrees , which is a difference of 40 degrees above ambient to some temperature u = ?.

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---------------  FV  =  u - T  =  40 * e^-.56

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---------------  u - T  =  40  / 1.75  =  23

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-------------  u  =  20 + 23  =  55 C

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-  After 20 minutes the regulator cooled 90 - 55 =  35 degrees to get to 55C.

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-  “e” has many unique properties:  “e” is a “transcendental” number, like pi, it is a series of decimals that goes to infinity and never repeats itself.  It is an “irrational” number that can not be written as a ratio of two integers.

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---------------  e^ square root of -1  .  pi  + 1  =  0   ( think about it )

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-----------------  e ^ix  =  cos x + i sin x

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------------------  i * t  = 70

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-  By dividing the interest rate into 70 you get how many years it will take for the investment to double.  This simple equation has a multitude of every day uses:

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-  If we double our national debt in 10 years what is the rate of growth of spending?

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------------------------  70 /  10 years  =  7% per year.

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-  If the population is growing at 2% per year when will it double?

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----------------------  70 / 2%  =  35 years

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-  If you got a 5% mortgage for 30 years, when will you double the amount of your loan with interest?

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-------------  70 / 5%  =  14 years.

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-  Put one penny in a kitchen jar on December 1st and double it every day.  How much will you have in time for Christmas?

------------------------   $117,772

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-  Google’s official revenue target was $2,718,281,828.     ( get it? )

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-----------------------------  Other reviews on math: 

-   1329 - The most important math you will ever learn.  

-

-   1281  -  Math was invented to solve problems.

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February 6, 2021       INTEREST  -  Growth  of Money?     1467     3028                                                                                                                                                          

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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”  -----------

--------------------- ---  Saturday, February 6, 2021  ---------------------------

3022 - COSMOLOGICAL CONSTANT - Einstein’s blunder?

 -  3022 - COSMOLOGICAL  CONSTANT  -  Einstein’s blunder?  Without the cosmological constant in the equation there is no term to counteract gravity and the Universe would collapse on itself.  With the term small enough the Universe would expand but gravity simply continuously slows the expansion into infinity.

---------------  3022  -  COSMOLOGICAL  CONSTANT  -  Einstein’s blunder?

-  How is Einstein’s Fudge Factor expanding the Universe?

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-   In 1917 Albert Einstein completed his equations for General Relativity and a new theory for gravity.  He recognized that a problem with his equations required the contraction or the expansion of the Universe but not the static condition that everyone thought existed at the time.

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-    So, Albert added a “cosmological constant”, a factor in the equations that allowed the Universe to exactly balance and remain static.

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-  In 1929 Edwin Hubble proved to Albert that the remote galaxies were accelerating away from us.  The further away the faster galaxies receded.  The Universe was expanding, it was not static.  Albert said the cosmological constant was “the greatest blunder of his life“.

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-  Today, we are not so sure it was a blunder.  We know the Universe is not only expanding its expansion is accelerating at an ever faster rate.  Now, science is resurrecting the cosmological constant in order to use Einstein’s equations to explain an accelerating expansion that began 5 billion years ago. 

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-   Dark Energy, a form of anti-gravity, a repulsive force,  started becoming more dominate than Dark Matter, and all matter/energy that creates gravity, an attractive force, 5 billion years ago.  Gravity decreases with distance.  Dark Energy and anti-gravity are constant in all space. 

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-   Therefore, Dark Energy becomes more and more dominate as the Universe continues to expand.  Its rate of expansion gets faster and faster.  Science can rearrange Einstein’s equation and insert the cosmological constant back in and get this observed affect in the Cosmos.

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-  Einstein’s original idea in creating his equations was to define gravity so gravity and accelerated motion were equivalent.  Without an outside reference you can not tell the difference between acceleration and gravity.

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-    Einstein’s equation had the Universe as static with no boundaries but curved back on itself like the surface of a balloon.  The cosmological constant term in the equation produced a cosmic repulsion on large scales enough that would just counteract gravitational attraction on large scales.  

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-  Without the cosmological constant in the equation there is no term to counteract gravity and the Universe would collapse on itself.  With the term small enough the Universe would expand but gravity simply continuously slows the expansion into infinity.

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-  Einstein’s original equation related the curvature of space to the distribution of matter and energy.  When he added the Constant he put it on the left side of the equation suggesting it was a property of space itself.  Today science wants to put the Constant on the right side of the equation and suggest that it represents a new form of energy density. 

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-   The Constant remains constant as space expands and eventually dominates gravity’s attraction that decreases with distance.

-  Since 1998 evidence  from supernovae explosions have convinced astronomers that over the past 5,000,000,000 years the expansion of the Universe has been speeding up.  Supernovae explosion were dimmer than expected which meant they were further away than expected because the Universe was expanding faster than expected.

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-  The measurement of the angular size of the small variations in the “Cosmic Microwave Background” radiation have convinced astronomers that the geometry of the Universe is flat.  It is not a positive curvature like the balloon shape as Einstein thought.  For the Universe to be geometrically flat the average matter/energy density must be equal to the “Critical Density“. 

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- The Critical Density is where the balance occurs between expansion and contraction.  When astronomers measure all forms of matter/energy in the Universe they come up with only 5% of the amount needed.   We were missing 95% with what we could see. 

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-   When they add Dark Matter they can get up to 27% of what is needed.  For the Universe to be flat and accelerating as it is there must be 73% Dark Energy, vacuum energy that is repelling gravity.  It is in the vacuum of space.

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-    The problem now is how do we measure the weight of “nothing” when it makes up 73% of everything?

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-  What we are left with to date is a flat Universe dominated by positive vacuum energy that will expand the Universe forever at an ever increasing rate.  How do you explain this?

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-  Our knowledge usually develops in an atmosphere of creative confusion.  I, at least, have the confusion part right!

-

February 4, 2021         COSMOLOGICAL  CONSTANT      1126      3021                                                                                                                                                           

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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”  -----------

--------------------- ---  Friday, February 5, 2021  ---------------------------

3021 - MATH - a learned discipline?

 -  3021 -  MATH  -  a learned discipline?  -  Mathematics is so amazing because it recreates and communicates so much of nature in its language and logic.  A simple “pi” can represent all the perfect circles in the Universe.  Their circumference is always 3.14 times larger than their diameter. 

--------------  3021  -  MATH  -  a learned discipline?

-   It is one of the laws of mathematics that “pi” is an irrational number that can not be formed as a fraction and as a decimal the numbers continue to infinity, never repeating,  pi  =  3.14176254254.…… etc

Yes, this is very irrational.

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-  Pythagoras (572-497 B.C.) introduced the term “ mathematics”.  He called it a learned discipline.  From that moment it has been controversial as to whether the discipline invents  or discovers the laws of mathematics, the laws of Nature.

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-  Here are some discoveries.  Take 365 days in a year.  You can get the number 365 by taking the sum of the  squares of 10, 11, and 12. 

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---------------   10^2 +  11^2  + 12^2  =  100 + 121 + 144  =  365

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-  Or, you can get the number 365 by taking the sum of the squares of 13 and 14.

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---------------  13^2  +  14^2  =  169  +  196  =  365

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-  How about the number 100.  You can get that number by summing the cubes of the first four numbers, 1 ,2, 3, and 4.

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---------------   1^3 + 2^3  +  3^3  +  4^3  =  1 + 8 + 27 + 64  =  100

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-  Then someone discovered that the sum of odd consecutive numbers always equals a number squared:

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---------------  1  =  1^2

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--------------- 1 + 3  =  2^2

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---------------  1+3+5  =  3^2

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---------------  1 + 3 + 5 + 7  =  4^2

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---------------  1 + 3 + 5 + 7 + 9  =  5^2

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-----------------  etc. …………….

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-----------------  Why is that? 

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-  Of course Pythagoras discovered that the square of the hypotenuse is always and everywhere equal to the sum of the squares of the other two sides.

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----------------  c^2  =  a^2  +  b^2

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-  But, also the discover was made that for any triangle, not just a right triangle, with the angles A, B, C and sides opposite a, b, c respectively.  

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--------------  a^2  =   b^2  +  c^2  - 2bc cosA

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-  The square of the side opposite the cosine angle is equal to the sum of the squares of the other two sides minus 2 times the product of these two sides and the cosine of the angle between them.  Another law of mathematics.

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-  The area of a triangle is ½ the base times the height.   A  =  ½ b*h

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-  But, the area of any triangle is    A  =  ½ a*b sinC

-  This ideas of areas bets even stranger for polygons.  The area of a polygon is equal to the number of points (vertices) plus ½ the number of boundary edges minus 1

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-------------  A  =  i  +  b/2 - 1

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-  “Epistemology” is the investigation into the limits of human knowledge.  How far can mathematics take us into our understanding of the Universe?

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-  Every even integer greater than 2 is the sum of 2 prime numbers:

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--------------  4  =  2 + 2

---------------  6  =  3 + 3

---------------- 8  =  3 + 5

---------------  10  =  3 + 7

---------------- 12  =  5 + 7

---------------  14  =  3 + 11

---------------- 16  =  5 + 11

---------------  etc.  ………………..

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----------------  Why is that ?

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-  Books have been written on each of these numbers, pi,  “e” the natural logarithm ,  the golden ratio 1.618  See the footnote for some of the book reviews.

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--------------  the Golden Ratio  =  (1 + 5^12) / 2  =  1.618 …….

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-  The Golden Ratio is the sum of 2 n umbers divided by the larger number:

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 ---------------  (a + b) / b  = 1.618

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----------------  (21  +  34  )  /  34  =    55 / 34  =  1.617

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----------------  10,946  +  6,675 ) / 10,946  =  17,711 / 10,946  =  1.618 

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-  “e”  the natural logarithm is in the most famous mathematical equation:

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----------------  e ^i*pi + 1 = 0

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-  The natural logarithm raised to the imaginary “pi” is equal to -1.  You can explore the limits of mathematical knowledge, it goes on forever:

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-----------------------------  Other reviews available:

-

(1)  #1086  “  Formulas for space, time and velocity “

(2)  #1087  “  Formulas for space, time and velocity “

(3)  #1088  “  Formulas for space, time and velocity “

(4)  #1089  “  Formulas for space, time and velocity “

(5)  #1090  “  Formulas for space, time and velocity “

(6)  #1042  “  Calculating areas by counting dots“

(7)  #1041  “  The star with the golden ratio “

(8)  #745  “  The calculus of a circle “

(9)  #853  “  Math, the golden ratio “

(10)  #803  “  Transcendental numbers “e” and “pi” “

(11)  #649  “  The Greeks invented numbers “

(12)  #805 “  Gambling “

(13)  #796  “  Science and math “

(14)  #798  “  Science and math, Part II  “

(15)  #799  “  Science and math , Part III“

-  

February 4, 2021      MATH  -  a learned discipline?               1095      3021                                                                                                                                                           

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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”  -----------

--------------------- ---  Friday, February 5, 2021  ---------------------------

MARS - returning rock samples to Earth?

 -  3023 - MARS  - returning rock samples to Earth?  - Fundamental questions about Mars  remain related to its potential for life; the geological history of the planet; the history of its climate and the driving forces behind these changes; the evolution of geologic processes and the interior composition and structure; and more recent atmospheric, polar, surface, and interior processes. 

---------------  3023  -  MARS  - returning rock samples to Earth? 

-  Returning some samples of Mars oil and rocks to Earth for detailed analysis is a dream for scientists.   NASA and its European counterpart, ESA, want to make the dream a reality.

-  It's worthwhile, but it isn't going to be easy. 

-

-   Scientists believe that the Mars sample-return program should proceed because its scientific value will be extraordinarily high, with the potential for world-changing discoveries about Earth's nearest planetary neighbor, and possibly about an independent origin of life on another world.

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-  The next launch window is in 2028.  The budget needed is between $3.8 billion and $4.4 billion.

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-  As envisioned, the Mars sample-return program is a vast endeavor shared by two large space agencies that will require several separate spacecraft operating over more than a decade, not to mention the first rocket launch from the Red Planet's surface and a host of measures to prevent sample contamination.

-

-  The mission will also require a new “sample-curation facility“. Mars exploration is never easy. The Red Planet is notorious for its tricky launch calendar, with favorable opportunities spaced 26 months apart, slow communications, and perilous landing conditions. 

-

-  NASA and ESA also hope to launch the mission while the Mars 2020 rover Perseverance, currently on its way to the Red Planet, is still operational. The rover will land on Mars on February 18, 2021,  and work on the Red Planet's surface for at least one Martian year (687 Earth days).

-

-  NASA has its hands full with other ambitious projects like the James Webb and Roman space telescopes and the Europa Clipper mission. 

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- Mars exploration today is at a critical juncture. A series of successful orbital and landed spacecraft missions have revealed a planet with:

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• A variety of environments that could be or could have been habitable to microbes,

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• An early, more Earth-like climate that changed dramatically over time,

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• A geologically recent epoch of ice ages, 

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• A dynamic planet that still changes today.

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-  These missions have also provided a first look at the processes by which the planet has evolved, addressing fundamental questions of planetary evolution and providing a valuable end-member in the comparative study of terrestrial planets both inside our solar system and beyond.

-

-   The program of orbital reconnaissance and ever more capable landed missions has taken the program to the point that it can undertake the challenge of returning carefully chosen samples from the Martian surface for intensive study by the full capabilities of laboratories here on Earth.

-

-  The Perseverance rover will be landing in Jezero Crater, where it will explore an ancient deltaic environment and collect samples for possible future return. 

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-  As important as Mars Sample Return (MSR) is--and it will result in a major step forward for planetary science--examination of material from a single site will not tell us everything that we need to know about Mars.

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-   Mars, like Earth, has a rich, complex history, with different locations capturing snapshots of its path in space and time. The history of one site must be integrated with a global context provided by both global observations and detailed local measurements at representative sites across the planet.

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-  Fundamental questions about Mars will remain related to its potential for life; the geological history of the planet; the history of its climate and the driving forces behind these changes; the evolution of geologic processes and the interior composition and structure; and more recent atmospheric, polar, surface, and interior processes. 

-

-   Currently, all planned surface missions are designed to be solar-powered, but adding nuclear power may make the mission less vulnerable.

-

-  But despite all the complications, bringing Martian rocks to Earth is worth it. The science would be very exciting.

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-  We've done a lot of analyses with Mars rocks on the surface of Mars, and clearly those have been very valuable.  But what you can do with a rock bringing it back and working in a terrestrial lab will produce a timeline essentially of the history of what was going on in this crater.

- 

February 4, 2021       MARS  - returning rock samples to Earth?         3023                                                                                                                                                           

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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”  -----------

--------------------- ---  Friday, February 5, 2021  ---------------------------

3024 - UNIVERSE - a short story?

 -  3024 -  UNIVERSE  -  a short story?   About 200,000 years ago, along came upright creatures capable of marveling at our mysterious universe and discovering how the whole thing came to be.  Here is their story.

--------------------------  3024  -  UNIVERSE  -  a short story?

-  In the beginning, there was nothing. Then, around 13,700,000,000  years ago, the universe formed. We still don't know the exact conditions under which this happened, and whether there was a time before time.  We think this is when time was created.  Space was also created as it started expanding.

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-  Using telescope observations and models of particle physics, researchers have been able to piece together a rough timeline of major events in the life of the universe. From its infancy to its eventual death.   Here is the short story.

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-  It all starts at the Big Bang, which "is a moment in time, not a point in space. It is the moment when time itself began, the instant from which all subsequent instants have been counted.

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-   The Big Bang wasn't an explosion but rather a period when the universe was extremely hot and dense and space began to expand outward in all directions at once. Though the model of the Big Bang states that the universe was an infinitely small point of infinite density, that's just saying that we don't quite know what was going on then. 

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-  Mathematical infinities don't make sense in physics equations, so the Big Bang is really the point at which our current understanding of the universe breaks down.

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-  The universe's next trick was to grow really big really fast. Within the first 0.0000000000000000000000000000001 (that’s a decimal point with 30 zeros before the 1) seconds after the Big Bang, the cosmos could have expanded exponentially in size, driving apart areas of the universe that had previously been in close contact. 

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-  This era, known as inflation, remains hypothetical, but cosmologists like the idea because it explains why far-flung regions of space appear so similar to one another, despite being separated by vast distances.

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-   A few milliseconds after the beginning of time, the early universe was really hot between 7 trillion and 10 trillion degrees Fahrenheit (4 trillion and 6 trillion degrees Celsius) hot.

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-   At such temperatures, elementary particles called quarks, which are normally bound tightly inside of protons and neutrons, wandered around freely. Gluons, which carry a fundamental force known as the strong force, were mixed in with these quarks in a soupy primordial fluid that permeated the cosmos. 

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-  Researchers have managed to create similar conditions in particle accelerators on Earth. But the difficult-to-achieve state only ever lasted a few fractions of a second, in terrestrial atom smashers as well as in the early universe.

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-  There was a lot of action in the next stage of time, which began around a few thousandths of a second after the Big Bang. As the cosmos expanded, it cooled, and soon conditions were settled down enough for quarks to come together into protons and neutrons. 

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-  One second after the Big Bang, the universe's density dropped enough that neutrinos, the lightest and least-interacting fundamental particle, could fly forward without hitting anything, creating what's known as the “cosmic neutrino background“.

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-  For the first 3 minutes of the universe's life, protons and neutrons fused together, forming an isotope of hydrogen called deuterium as well as helium and a tiny amount of the next-lightest element, lithium. 

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-  But once the temperature fell, this process stopped. 380,000 years after the Big Bang, things were cool enough so that hydrogen and helium could combine with free electrons, creating the first neutral atoms. 

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-  Photons, which had previously run into the electrons, could now move without interference, creating the “cosmic microwave background” (CMB), a relic from this era that was first detected in 1965.

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-  For a very long time, nothing in the universe gave off light. This period, which lasted around 100 million years, is known as the ‘Cosmic Dark Ages‘. This epoch remains extremely difficult to study because astronomers' knowledge of the universe comes almost entirely from starlight.

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-  By around 180 million years after the Big Bang, hydrogen and helium began to collapse into large spheres, generating infernal temperatures in their cores that lit up into the first stars. The universe entered a period known as “Cosmic Dawn“, or “deionization“, because the hot photons radiated by early stars and galaxies broke neutral hydrogen atoms in interstellar space into protons and electrons, a process known as ionization.

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-   How long reionization lasted is difficult to say. Because it occurred so early, its signals are obscured by later gas and dust.  It was over by around 500 million years after the Big Bang.

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-   Small early galaxies began to merge together into larger galaxies and, around 1 billion years after the Big Bang, supermassive black holes formed in their centers. Bright quasars, which produce intense beacons of light that can be seen from 12 billion light-years away, turned on.

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-  The universe continued to evolve over the next several billion years. Spots of higher density from the primordial universe gravitationally attracted matter to themselves. These slowly grew into galactic clusters and long strands of gas and dust, producing filamentary cosmic web that can be seen today.

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-  About 4.5 billion years ago, in one particular galaxy, a cloud of gas collapsed down into yellow star with a system of rings around it. These rings coalesced into eight planets, plus various comets, asteroids, dwarf planets, and moons, forming a familiar stellar system. 

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-  The planet third from the central star managed to either retain a lot of water after this process, or else comets later delivered a deluge of ice and water.

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-  On that third, watery world, between 3.8 and 3.5 billion years ago, tiny, simple microbes winked into existence. These life-forms emerged and evolved into wondrous sea monsters and gigantic, leaf-eating dinosaurs. 

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-  Then about 200,000 years ago, along came upright creatures capable of marveling at our mysterious universe and discovering how the whole thing came to be.

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-  The end (or not?)  Of course, that isn't the end of things. Physicists still don't quite know what's in store for the universe. That depends on the details of dark energy, a still-mysterious force driving apart the cosmos and whose properties have not been well measured.

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-   In one possible future, the universe will continue to expand forever, long enough that all the stars in all the galaxies will have run out of fuel, and even blackholes will evaporate into nothing, leaving behind a dead cosmos permeated by inert energy.

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-  Or, in another alternative gravity will eventually overcome dark energy's expansionary force, pulling all matter back together in a sort of reverse Big Bang known as the ‘Big Crunch“.

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-   Or, dark energy could accelerate everything apart farther and farther from everything else, creating what's known as the “Big Rip“, in which the universe literally tears itself apart.

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February 4, 2021         UNIVERSE  -  a short story?                          3024                                                                                                                                                           

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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”  -----------

--------------------- ---  Friday, February 5, 2021  ---------------------------

3019 - TELESCOPES - connect them all together

 -  3019 -   TELESCOPES  -  connect them all together?  There is no one single sensor that can collect data in all of those different wavelengths at the same time.  Therefore, scientists have developed a many different instruments that are extremely good at collecting data in one specific spectrum, such as radio (ALMA), or mid-range infrared (James Webb). 

---------------------  3019  -  TELESCOPES  -  connect them all together?

-  Anyone who has ever worked on a team knows that their strength lies in coordination and a shared vision.  Is it possible that earth and space based telescopes could work together to collect a single amazing image?

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-  Science is not immune to the difficulties of running effective teams.  There is plenty to be gained from more coordination between differing silos and physical locations.  Recently a meeting in Chile prompted a group of scientists to propose a plan to change that. 

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-   This suggests a different path forward where all of the space science community can benefit from the type of coordinated output that can only come from a cohesive team.

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-  The main reason why such coordination is important comes down to how imaging systems interact with different wavelengths of light.  The electromagnetic spectrum is extremely large.  It includes all types of light, such as radio, infrared, x-rays, ultraviolet and visible light. 

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-   There is no one single sensor that can collect data in all of those different wavelengths at the same time.  Therefore, scientists have developed a many different instruments that are extremely good at collecting data in one specific spectrum, such as radio (ALMA), or mid-range infrared (James Webb). 

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-  The down side of this specialization is that those instruments are blind in other spectral ranges.  If a scientific team is only observing in one type of light, there is a chance that they could miss important aspects of a phenomena they are studying that are only visible in a different spectral band.

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-  Much of the planetary science data collected is the result of spacecraft that are sent to a planetary system to perform in the observations.  However, due to the high cost of developing space-based systems and then launching them into orbit, mission planners for these missions must be very selective about what types of instruments they allow on board their spacecraft.  What this normally means is that they are not able to bring imagers that are capable of covering the entire electromagnetic spectrum.

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-  That is where coordination with ground and near-earth-orbit based telescopes comes in.  There are many telescopes in those locations, such as the Atacama desert or Hawaii’s Mauna Kea, that are extremely large, and can provide very high resolution images in specific spectral bands, such as radio, microwaves, or infrared. 

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-   Infrared is particularly useful as there is a lot of physical data points that can be obtained in a single measurement, such as pressure, temperature, and molecular abundances. If a mission planner of a planetary exploration spacecraft mission can coordinate observations with these much larger, specialized observatories, they will no longer need to include them on their own spacecraft.  

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-   Another advantage that earth-based observatories have over their counterparts is their ability to image a whole planet at once.  Many orbiter or fly by missions are only capable of measuring part of their subject at a single point in time.

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-  This results in a loss of contextual understanding, as dynamic phenomena that might be observed in a single place by the in situ spacecraft might not be present over the entire surface of the planet or moon.  Support from earth-based telescopes, whether on the ground or in space, could provide that larger context that the spacecraft itself lacks.

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-  This sort of coordination to cover all of the spectral bases has already been accomplished with one planetary mission, the ‘Juno spacecraft” currently in orbit around Jupiter.  The resulting coordination between the Juno spacecraft and a series of earth-based observatories resulted in over 40 papers that used data from more than one observational source of the Jupiter system during that time.

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-  Observing simultaneous parts of Jupiter in three different wavelengths,  proves that some features that particularly interesting are only visible on one wavelength.

Three separate images captured as part of the Juno multi-spectral survey shows the same segment of Jupiter simultaneously in three different wavelengths. 

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-  Mars is of particular interest, as it is the most studied planet outside of Earth, and the only one with active rovers physically on its surface.  Scientists interested in understanding where the methane from Mars’ atmosphere comes from would certainly benefit from a coordinated observational campaign between several of the orbiters around Mars (TGO and MAVEN), and earth-based telescopes such as NASA’s Infrared Telescope Facility in Hawaii. 

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-  The orbiters around Mars provide excellent two-dimensional slices of spectral data as they are passing over a specific strip of the planet.  However, observatories closer to Earth can provide data on the entire hemisphere of the planet that is facing them, and add a layer of depth that would allow scientists to piece together a three-dimensional picture that would be impossible using only data from the orbiters.

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- There are still some limitations to earth-based observations, such as the fact that methane is present in Earth’s atmosphere as well, which could skew the data when looking at Mars. 

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-  To get around this problem, scientists came up with an ingenious method of only observing Mars while it is moving away from (or toward) Earth at more than 13 kilometers a second.  This differential speed red- (or blue-) shifts the spectral signature of the Martian methane enough that it can be differentiated from that simply present in Earth’s atmosphere.

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-  Another particularly interesting target of joint observations is Titan, which has been the subject of intense scrutiny in recent years due to its hydrocarbon lakes, and its methane/ethane based hydrological cycle.

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-  The moon is so interesting it is about to receive it’s own visitor in the form of the “Dragonfly” mission.  When Dragonfly lands in 2034, the team hopes that many Earth-based telescopes will turn their eyes toward Titan, as the data collected from the surface can then be coordinated with more remote observations.

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-   Dragonfly will be equipped a mass spectrometer, which allows the detection of molecules which are impossible to see remotely, and reveals the full composition of the atmosphere.  Earth-based observation could in turn provide context for these measurements.

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-  Dragonfly's lander will be the first to reach Titan's surface, and can provide local data to any coordinated observation program.  The mission will prove an excellent opportunity for coordinated observations. It can provide on the ground data that can be contextualized with other, larger observatories.

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-  Those combined observations will focus on the organic chemistry that is taking place on the moon.  A particularly useful Earth-based tool is ALMA.  ALMA is a series of radio telescopes, which are particularly good at observing organic compounds and making detailed maps of its observational subjects.  Both capabilities would be particularly helpful in helping the Dragonfly mission, and ALMA’s operators are already very familiar with Titan. 

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-  The array actually used Titan as a calibration target for a number of years after it first launched, due to its brightness and seeming stability.  The wealth of observations allowed researchers to study Titan and the evolution of its atmosphere, revealing dynamic processes, and leading to improved understanding of the moon. Unfortunately, it also revealed Titan is actively changing, making it less suitable as a flux calibration target.  The ALMA team then switched to using a pulsar for future calibrations.

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-  All of the data the ALMA team has collected, as well as almost all astronomical data from all of the observatories that might be conscripted into the joint observational efforts is eventually made free to the public.  However, unless the data on a given object was collected simultaneously by more than one observatory, the benefits of coordination are lost as transient phenomena would not be present in both those sets of data. 

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-  There might be some simultaneous data of an object collected by more than one observational platform buried in their data archives.  However, coordinating future observational efforts is much more likely to result in new discoveries rather than trawling through old data. Concerted observations may reveal phenomena that wouldn’t be visible without combining the datasets, revealing new and exciting glimpses into foreign worlds.  

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-  Coordinating as many of those future observational efforts as possible is the main intent. 

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February 4, 2021       TELESCOPES  -  connect them all together?     3018                                                                                                                                                           

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

-----  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”  -----------

--------------------- ---  Thursday, February 4, 2021  ---------------------------

3018 - GALAXIES - the most distant galaxies?

 -  3018 -  GALAXIES  -  the most distant galaxies?    Most of the galaxies in the Universe are “ over the horizon” and beyond what we can see.  Astronomers estimate that 98.4% of the galaxies in the Universe lie in the zone that we can never observe. (Unless we find something we can detect traveling faster that the speed of light.)

----------------------  3018  -  GALAXIES  -  the most distant galaxies?

-  The Hubble Space Telescope that takes an image of galaxies that are 13,000,000,000 years back in time.

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----------  What you see is that old, 13 billion years old.  The light is that old.  The image you see is that young.  It is what it looked like 13 billion years ago.

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----------  What you see is moving away from us and has been moving away for that whole duration of time it took for the light to get here.

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---------  The Universe is expanding.  The space between galaxies is increasing at an ever accelerating rate.  The Galaxy is far further away by now.

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----------  The image we see of the distant galaxies is not what exists today because it took the light 13,000,000,000 years to get here.  The photons that reach the Hubble camera are that old.  A lot can happen in the time it takes light to make the journey.

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-  The Hubble Space Telescope took its pictures using a very long time exposure lasting many days or more.  The Hubble camera used CCD’s, charge coupled devices, that can collect photons over that entire time of exposure. 

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-  Our eyes can not do this.  Photons fire nerve cells in the back of our eyes and send the image to the brain.  We do not have the ability to collect the photons until the image gets bright enough to see. 

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-   The Hubble camera has much greater sensitivity and can see very faint objects accumulating photons over a long period of time.  Faint objects are very far away and strange things happen while the light is traveling those distances.

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-  We do not notice this behavior with galaxies in our neighborhood.  If we point our backyard telescope at M87 Galaxy in the Virgo Constellation that light has been traveling 50,000,000 years to reach us.  We can say that M87 is 50 million lightyears away.  M87 Galaxy is 8 billion years old, so 50 million years is less than 1% of its current age (0.63%).  Therefore, the image we get is relatively current.  That is probably what the galaxy still looks like today.

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-  At that distance of 50 million lightyears M87 is moving away from us at 800 miles per second.  This recession velocity will red shift the light a very small amount making the galaxy appear slightly dimmer due to the Doppler Shift of the frequencies of the light. 

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-   However, this redshift is barely noticeable.  M87 is considered as what you see is what you get and that is true for astronomers viewing the 60,000,000 galaxies that are in our neighborhood within 1 billion lightyears away.  The galaxies probably are today what they appear to be today.  This is not true with the most distant galaxies.

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-  The Hubble Deep Field was of images that are the faintest and farthest galaxies 13,000,000,000 light years away ( Galaxy: A1689-zD1).  The image we see is really very ancient and not at all like it is today.  

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-  When the image left this distant galaxy we were much closer together.  We were only 3,350,000,000 lightyears apart.  The image appears bigger corresponding to a 3 billion lightyear distance rather than the 13 billion lightyear distance we have today.  Therefore, the galaxy appears to us to be much closer than it actually is.

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-  The galaxy size is bigger, but, it is dimmer than we would expect it to be at 13 billion lightyears distance.  Space has been expanding, stretching the lights wavelengths causing a loss of energy and a dramatic redshift and weakening of the light.  

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-  In fact, it appears dim enough that it should be 263 billion lightyears away at that brightness.  The Doppler effect of the expanding Universe causes this ultra-faintness.

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-  Over the entire time the light was trying to reach us the Galaxy was moving away from us.  Today it is 30 billion lightyears away.  

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-  If we  calculate the very edges of the Observable Universe what distances would we get?

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---------------  The first stars and galaxies were born about 100,000,000 years after the Big Bang.

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--------------  The size of the image we would see would make these galaxies appear as if they were 1,200,000,000 light years away.  1.2 billion lightyears, much bigger than we would expect.

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--------------  The dimness of these galaxies would indicate that they were 1.2 trillion lightyears away.  Way dimmer that we could ever detect.

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--------------  The actual distance that the galaxies would be today at the edges of the Universe would be 38 billion lightyears distant.

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-  38 billion lightyears is considered to be the distance to the edge of the Observable Universe.(3.6*10^26 meters) or (2.2*10^23 miles). 

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-   However, most of the galaxies in the Universe are “ over the horizon” and beyond what we can see.  Astronomers estimate that 98.4% of the galaxies in the Universe lie in the zone that we can never observe. (Unless we find something we can detect traveling faster that the speed of light.)

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-  Some say the Universe is infinite, but, what does infinite mean?  To us it must mean that it is so big we will never see it all. “Never” must mean longer than the life of the Universe, over 13.7 billion years.  

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-  There must be some things we will just will never know, but, don’t let that stop us from trying.  

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February 3, 2021      GALAXIES  -  the most distant galaxies?         3018                                                                                                                                                           

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

-----  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”  -----------

--------------------- ---  Thursday, February 4, 2021  ---------------------------