- 1713 - Colors change for far away galaxies. We can calculate their radial velocity by the amount of shift that happens to colors of light as it travels through expanding space. Using Hubble’s constant rate of space expansion we can calculate the distance to the galaxy.
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----------------- - 1713 - Colors change for far away galaxies
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- The frequency of the electromagnetic spectrum covers a wide range , say from 3 cycles per second for electric power to 3,000,000,000,000,000,000,000,000 cycles per second for Gamma Rays.
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- The speed of light remains constant at 300,000,000 meters per second. ( 670,633,500 miles per hour).
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- And, the frequency * the wavelength = the constant speed of light.
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---------------------- f * w = c
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------------------- cycles per second * meters = meters per second
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- Since the product of (f * w) is s constant when one increase the other decreases.
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- Therefore the wavelength covers a long range as well in the opposite direction from electric power 100,000,000 meters to Gamma Rays 0.000,000,000,000,0001 meters.
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- Visible light is in the middle of the electromagnetic spectrum covering the range 400 to 700 nanometers ( 10^-9 meters). All the colors together are white light. The colors separately each have a different wavelength.
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---------------------- blue -------------- 450 nanometers
---------------------- green ------------ 550 nanometers
---------------------- yellow ----------- 600 nanometers
---------------------- orange ---------- 650 nanometers
---------------------- red -------------- 700 nanometers
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- The wavelengths are created by the different energy levels an electron jumps inside an atom. Every element atom has different energy levels, and a different number of electrons.
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- In the hydrogen atom, when the single electron jumps ( falls ) from level 5 at -3.4 electron volts to level -13.6 electron volts at the ground state it jumps 10.2 electron volts. Which means it emits 10.2 electron volts of energy.
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- The wavelength of energy for that change in energy level can be calculated by:
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------------------------------ E - Eo = h * c / w
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---------------- h = Planck’s constant
---------------- c = speed of light
---------------- w = wavelength
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----------------- 10.2 = ( 6.63*10^-34) * (3 * 10^8) / (1.6022*10^-19) * w
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------------------ w = 121.6 nanometers.
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- Different atoms all have different energy levels for the electrons and have different wavelengths of radiation emission or absorptions when their electrons change energy levels. Hydrogen is the most dominate representing 90% of all elements in the Universe.
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----------------- hydrogen ----------- 121.6 nm ( electron jumps from level 5 to level 1)
----------------- ethanol ------------ 290 nm and 186 nm
---------------- carbon monoxide ----2700 nm
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- If we know the atom that is emitting the particular radiation and say it is coming from the star Vega, and it was 656.285 nanometers when it left Vega, and it was 656.255 nanometers when we received it on Earth, we can calculate the radial velocity of the star Vega:
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----------------------- The change in wavelength measures the velocity of the source:
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---------------------- v / c = w - wo / wo
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---------------------wo = 656.285 nm
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-------------------- w = 656.255 nm
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------------------ v / c = - 4.5712*10^-5
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- “-” , negative means the star Vega is moving towards us
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--------------- v = 113.7 kilometers / second = -30,647 miles per hour.
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- Vega is in a galaxy group where gravity overpowers the expansion of space. More distant galaxies will have a recession radial velocity rather than a closing radial velocity.
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- If we know the recession speed of a star at a distant galaxy, we can calculate its distance using Hubble’s Constant expansion of space , “H”.
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---------------- Distance = rate * time
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---------------- H = 1 / time
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--------------- Distance = recession velocity / H
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------------------ H = constant 2.5 * 10^-18 / second
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------------------ H = constant 47,000 miles per hour / million lightyears.
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- We have to assume the expansion of the Universe is a constant rate, or, that this recession velocity is an accurate average. But, if we detect a hydrogen emission line at 358 nanometers in the Infrared and we know it left the Quasar’s hydrogen gas in the distant galaxy at 121.6 nanometers in the ultraviolet then the calculation for the distance comes from:
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------------- recession velocity / speed of light = (w/wo)^2 -1 / (w/wo)^2 +1
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---------------- “w” = wavelength measured
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-----------------”wo” = wavelength emitted by the source, hydrogen gas
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---------------- w/wo = 358 / 121.6 = 2.96
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-------------- recession velocity / c = (2.96)^2 -1 / (2.96)^2 +1
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-------------- recession velocity / c = 0.78
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--------------- recession velocity is 78% the speed of light
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-------------- recession velocity = 0.78 ( 3 *10^8) = 2.35 * 10^8 meters per second.
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- Using Hubble’s constant:
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---------------- Distance = velocity / H = 2.35*10^8 m/sec / 2.5*10^-18 /sec
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--------------- Distance = 9.45*10^26 meters
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- one lightyear = 9.4605 *10^15 meters
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-------------- Distance = 10^10 lightyears
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- Distance to the galaxy is 10 billion lightyears.
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------------------------------------------------------------------------------------------------
(1) Redshift formula : (w/wo)^2 = (1 + v/c) / (1 - v/c)
-----------------------------------------------------------------------------
(2) Measuring frequency instead of wavelength:
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-------------------- f = fo ( 1 + v/c)
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--------------------------------------------------------------------------------
- (3) 1 / H = age of the Universe
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-------------- 1/H = 1 / 2.5*10^-18 sec / 3.16*10^7 sec/year = 13 billion years.
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- (4) If he age of the Universe is 13.862 billion years. The Hubble constant is 1/ age.
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------------------------- 1 / (13.862*10^9 years) * (5.88 *10^18 miles / lightyear) * year / (8.76 * 10^3 hours) = 48,400 miles per hour / million lightyears for the average expansion velocity.
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--------------------- H = 48,400 mph / MLY
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---------------------- H = 74.2 kilometers / second / mega parsec
-
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- (5) Other reviews on the subject:
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- #1695 Measuring astronomical distances
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- #1603 Finding the farthest galaxy
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- # 1550 the redshift tells us how old it is?
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---------------- time = 12.65 + 0.6 z
---------------- “z” = redshift
---------------- v/c = (z^2 + 2z) / (z^2 + 2z + z)
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- #1501 Redshifting back in time. The most distant quasar galaxy had a redshift of 7. That means the signal left the galaxy 770,000,000 years after the Big Bang.
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- #835 The redshift explained.
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RSVP, with comments, suggestions, corrections. Index of reviews available ---
--- Some reviews are at: -------------------- http://jdetrick.blogspot.com -----
---- email request for copies to: ------- jamesdetrick@comcast.net ---------
---- https://plus.google.com/u/0/ , “Jim Detrick” ----- www.facebook.com ---
---- www.twitter.com , --- 707-536-3272 ---- Tuesday, December 30, 2014 ---
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