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- The age of the Universe is 13,700,000,000 years.
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- The oldest galaxy we can see formed 13,000,000,000 years ago.
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- The Universe was only 5% of its current age when this galaxy formed. If a human was 80 years old it would be analogous to her viewing a picture of herself when she was only 4 years old.
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-------------- 4 / 80 = 0.05 -------------- .7 / 13.7 = 0.051
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- The time that light has been traveling towards is 13 billion years. Space has been expanding during that time. Expanding space stretches out the wavelength of the light. Longer wavelength are towards the red end of the light spectrum, thus the “ redshift” of light. Light could leave the galaxy in the ultraviolet wavelengths and arrive at our telescopes in the far infrared. The time that has elapsed is a function of the amount of redshift.
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- Here is a formula that is given for calculating the elapsed time given the redshift. It is polynomial of the 5th order where “z” is the redshift.
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- time ( z ) = 0.0002 z^5 - 0.0072 z^4 + 0.1301 z^3 - 1.143z^2 + 5.014 z + 3.7677
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- The graph is constructed with billions of years on the y-axis and redshift on the x-axis. The graph becomes a linear function at higher redshifts. The graph is from 1 to 15 redshift. The astronomers are working between 9 and 12 redshift. They would like to be using a simpler equation for their calculations.
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------------------- Time (z = 9 ) = 13.11 billion years.
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------------------- Time ( z = 12 ) = 13.29 billion years.
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- Construct a straight line between these 2 points and construct a linear equation for that line that will give time as a function of redshift.
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--------------------------- y = mx + b, is the general equation for all straight lines.
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--------------------------- Time (z) = mz + b
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---------------------------- Where “ m” is the slope of the line and “b” is where the line crosses the y-axis, where x = 0. First let’s calculate the slope of the line connecting the 2 points:
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---------------------- slope = m = 13.29 - 13.11 / 12 - 9 = 0.18 / 3 = 0.06
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- Next we find the intersection of the line with the y-axis:
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----------------------- 13.29 - b / 12 = m = 0.06
----------------------- 13.29 - b = .72
----------------------- b = 12.57
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------------------ Time (z) = 0.06(z) + 12.57
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------------------ Time (8.6) = 0.516 + 12.57 = 13.086 billion lightyears
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------------------ Time (9) = 0.54 + 12.57 = 13.11 billion lightyears
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------------------ Time (11.9) = 0.714 + 12.57 = 13.1284 billion lightyears
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------------------ Time ( 12 ) = 0.72 + 12.77 = 13.29 billion lightyears
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- Note in the picture of deep field galaxies and the redshifts are shown ranging from 8.6 to 11.9. Their distances in billions of lightyears can be easily calculated with this equation.
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- I am puzzled by the 5th order polynomial when I us it to calculate the time.
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------------------- Time ( 9 ) = 15.7 billion years
------------------- Time ( 12 ) = 24.7 billion years
------------------- Time ( 15 ) = 48.3 billion years.
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- Apparently many more terms are needed in this equation to get better answers. Over the range of 9 to 12 our linear redshift equation works very well. An announcement will be made shortly, stay tuned, until I find the answer.
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- Redshifts less that 1.4 can use a much more intuitive formula that calculates the receding velocity of the galaxy. The further away a galaxy is the faster its receding velocity because there is more space between us that is expanding. The ratio of receding velocity, “ v” to the speed of light , “c” is:
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------------------ v / c = z^2 +2z // z^2 + 2z + 2
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- where z = 1.4 ------ v / c = 1.4^2 +21.4 // 1.4^2 + 21.4 + 2 = 4.76 / 6.76 = 70%
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- The ratio of the expanding velocity to the speed of light = 70%
- The galaxy is receding at a velocity of 70% *c = 210,000 meters per second.
- The lookback time = 9,000,000,000 years
- The co-moving distance = 13,000,000,000 lightyears
- The Universe’s age = 42% of its current age
- The Universe age when the light left the galaxy = 5,750,000,000 years.
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- The Cosmic Microwave Background light has a redshift of 1,100. It has a lookback time of 13,700,000,000 years. A co-moving distance of 46,000,000,000 lightyears
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(1) Other reviews on redshifts : #1501 Redshifting Back in Time
(2) The Redshift explained.
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RSVP, please reply with a number to rate this review: #1- learned something new. #2 - Didn’t read it. #3- very interesting. #4- Send another review #___ from the index. #5- Keep em coming. #6- I forwarded copies to some friends. #7- Don‘t send me these anymore! #8- I am forwarding you some questions? Index is available with email upon request. Some reviews are at http://jdetrick.blogspot.com Please send feedback, corrections, or recommended improvements to: jamesdetrick@comcast.net. ---- “Jim Detrick” -- www.facebook.com, -- www.twitter.com, -- 707-536-3272 Monday, January 14, 2013
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