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-------------------------- 2436 - GALAXIES - what rotating galaxies tell us?
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- What rotating galaxies tell us about the Universe? The Whirlpool Galaxy, M51 or NGC5194, is a beautiful image available to you with binoculars, telescope, or googling. It is in the constellation Canes Venatici, The Hunting Dogs, just below the end of the handle of the Big Dipper.
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- It is spectacular because you see the galaxy head on, and it is entwined with another galaxy, NGC5195, causing intense spiral arms. It is 60,000,000 light years away, appears four times wider than Saturn in the night sky (499 arc seconds versus 126 arc seconds)
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- Making a spectrum of the light can tell us the chemical composition of the light source. It amounts to setting a prism in front of the telescope. Spectrum lines are the fingerprint for each chemical element. Each element’s atom has a unique quantum ladder structure for the electrons orbiting its nucleus.
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- When an electron drops to a lower energy level in this ladder it emits a unique frequency of light that is equal to the difference in the two energy levels divided by Planck’s Constant.
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- For example: A hydrogen atom has four energy levels for the single electron that orbits its nucleus. Beyond the forth level the electron escapes the Electromagnetic Force holding it to the nucleus and becomes a free electron.
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- Less the one electron the nucleus becomes a positive ion. If the electron drops in energy from the 4th level to the 1st level ( ground level), the difference in energy is 13.6 electron volts.
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- The frequency of the photon emitted by the electron is equal to the difference in energy level / Planck’s Constant.
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------------------ f = E / h
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------------------ h = 4.136 * 10^-15 electron volts * seconds
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------------------ f = 13.6 eV / 4.136 * 10^-15 eV * seconds
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------------------ f = 3.29 * 10^15 cycles/second
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------------------ Wavelength = c / f
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------------------ Wavelength = 3*10^8 m/sec / 3.29 * 10^15 cycles/second = 91.4 nanometers / cycle.
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- c = the speed of light. I use 3*10^8 meters per second. The more accurate number is 299,792,458 meters per second.
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- 91.4 nanometers is the spectral line you would see on a spectrograph that is far into the Ultraviolet.( 400 nanometers is visible violet light).
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- In 1924 Harvard College Observatory had already archived 250,000 of star spectrographs. From these astronomers learned that not all stars contained the same elements. And, that the color (peak frequency) of the spectrum could be used to tell the temperature of each star.
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- Annie Jump Cannon was collecting these spectrograph in 1895. In 1924 Cecilia Payne started classifying the elements that she saw in Annie’s spectrums. Cecilia was the first to recognize that the lines in the spectrograph represented the quantum energy leaps of electrons jumping between energy shells of each atom.
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- Cecilia noted that in the coolest stars the calcium spectral line was strong. In the hottest stars the calcium line was weak. If a star is cool most of the calcium atoms will be at their lowest quantum energy state. If the star is hot then many quantum energy levels are activated and many electrons are moved to higher energy levels.
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- Cecilia made mathematical calculations based on the strength / weakness of spectral lines to determine the temperature of the star. Her analysis agreed closely with the color estimate of a star’s temperature done previously.
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- The more modern analysis of the spectrographs of galaxies have given us even more spectacular discoveries. The Whirlpool Galaxy is facing us head on so we can not easily measure its rotational velocity. We know that our Milky Way galaxy rotates at 250,000 meters / second (559,000 miles per hour) and completes one orbit in 225,000,000 years.
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- Many other galaxies, over 100, have been studied that have their disks near orthogonal to the axis of rotation. When we study these galaxies we can detect the Doppler effect of one side of the disk moving toward us (blue shift) and the other side moving away from us (redshift).
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- For example: the galaxy NGC7541 spectrograph was taken. It was enlarged to 5.5 feet in length and atomic hydrogen spectrum line looked like a “z” on the graph only 1/10 of an inch high.
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- The light from the side of the galaxy moving toward us was blue shifted to 253.5 nanometers wavelength from center. The light form the side of the galaxy moving away from us was redshifted to 284 nanometers wavelength from center . The center of the galaxy was redshifted to 270 nanometers. The width of the galaxy is 160 arc seconds, or 130,000 lightyears. Our Milky Way is 100,000 lightyears across.
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- Looking at the center of the little “z” we can see that the center of the galaxy is redshifted to 270 nanometers. The velocity of the galaxy moving away from us can be calculated as:
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------------------ delta wavelength/original wavelength = velocity / speed of light
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------------------ dw / Wo = v / c
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------------------ 386.3*10^-9m / 656.3*10^-9 * 3*10^5 km/sec = v
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------------------ v = 59% the speed of light
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------------------ v = 177,000 km/sec. (396,000,000 mph)
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- Looking backwards in time we see the galaxy at 63% the age of the Universe, 8.6 billion years old, or 5.1 billion years ago (1/1+dw/Wo). It is traveling away from us at 396 million miles per hour due to the expansion of the Universe.
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- That is the center of the NGC7541 galaxy that is moving away. At the same time the side of the galaxy moving toward us has blue shifted to 253.5 nanometers wavelength us is moving 184,123 km/sec. The side of the disk moving away from is redshifted to 284 nanometers moving 170,181 km/sec. So, the orbital velocity at a radius of 32,600 light years, which is 3.08*10^20 meters, is moving + or - 6,971 km/sec velocity
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- We measure the redshift of stars half way out from the center. The wavelength of hydrogen is 656.3 nanometers. It is redshifted to 253.5 nanometers, stretched 402.8 nanometers. The ratio delta wavelength over original wavelength, dw/Wo, is 61%. Which means it is traveling 61% the speed of light or .61*300,000 kilometers/second = 184,123 km/sec. The other side of the galaxy disk is redshifted to 284 nanometers. This ratio is 56.7% or 170,181 km/sec. The difference is 18,283 km/sec or + or- 6,971 km/sec. Therefore the rotational velocity of stars half way out from the center of the galaxy is 6,971 km/sec ( 15,600,000 mph)
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- This is half way out from the center of the galaxy where the circumference for one orbit is 1.938*10^21 meters. At this orbital velocity it will take 2.78*10^14 seconds or 8,800,000 years to complete one orbit. By comparison our Milky Way has a 225,000,000 year period.
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- The distance out from the center is 10,000 parsecs (32,600 lightyears). There are 3.1*10^16 meters in a kilo parsec. So the radius is 3.1*10^20 meters. The circumference is 2*pi*radius = 19.47*10^20 meters. Distance = rate * time. Time = 19.47*10^20 meters / 9,142 km/sec = 2.13 *10^14 seconds. There are 3.16*10^7 seconds in a year. The period of one rotation is 67,400,000 years.
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- Now that we know the period of one orbit we can calculate the mass of the galaxy. Using Kepler’s law that period squared = radius cubed:
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---------------- p^2 = 4*pi^2*radius^3 / G*(m+M)
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---------------- G = 6.67*10^-11 m^3/(kg*sec^2)
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---------------- Interior Mass = 2.237*10^44 kilograms
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---------------- Mass of the Sun = 1.9891*10^30 kilograms
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---------------- Mass at 32 LY from center of Galaxy = 1.12 * 10^14 solar masses.
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- We can repeat these same calculations at a distance of 20,000 parsecs from the center of the galaxy. That is 65,200 light years out from the center where the stars fade away. For comparison our Milky Way radius is 50,000 lightyears. The total interior mass of the galaxy inside this radius is:
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---------------- Mass at 65 LY from center of Galaxy = 4.83 * 10^14 solar masses.
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- Another approach to these calculations is to realize that the galaxy is not flying apart. Therefore, the centripetal force must equal the force of gravity.
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--------------- Centripetal force = m*v^2/R
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--------------- Centripetal force = mass*velocity^2/Radius
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--------------- Gravity force = G*M*m/R^2
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--------------- Gravity force = Gravitational Constant * product of masses/Radius^2
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--------------- Set these to forces equal to each other and solve for Mass:
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--------------- Mass = v^2*R/G
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- At 32,600 light years radius the velocity is:
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--------------- v = 6,971 km /sec
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--------------- R = 3.09*10^20 meters
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--------------- Mass = 1.13*10^14 solar mass
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- At 65,200 light years radius the velocity is:
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--------------- v = 10,188 km /sec
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--------------- R = 6.17*10^20 meters
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--------------- Mass = 4.83*10^14 solar mass
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- Either method of calculation tells us that the farther out from the center of the galaxy the rotational velocity remains essentially the same and the interior mass of the galaxy grows immensely, over 430%. The farther out from the center there is less starlight but there is more mass.
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- The conclusion is that most of what contributes to the galaxy’s weight does not shine. We call it “Dark Matter“. The weight of Dark Matter is 10 times greater than the weight of what we see. (Do not believe “truth” without evidence. Is 95% of the Universe really Dark Matter?)
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- Is there another explanation? What else could cause the flat rotation curves in galaxies? Over 100 galaxies have been studied and the results are consistent. Could it be that Kepler’s and Newton’s laws have to be modified for large masses or large accelerations?
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- Recall the Newton’s laws for gravity did not hold at high velocities approaching the speed of light. Einstein’s General Theory of Relativity modified these equations to make them more accurate at high velocities, which are changes of space versus time.
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- One proposal is the F=ma needs to be modified at high accelerations. Force = mass * acceleration needs to be changed to F=m*a^2/ao. Where “ao” is a constant that represents the acceleration needed to take us from rest at the Big Bang to the speed of light in the lifetime of the Universe ( 13.7 billion years). “F=ma” may work fine for the Solar System and not work well at all for galaxies that are 100,000 times bigger.
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- If Newton’s laws of physics need to be changed then we do not need Dark Matter. Mordehae Milgrom, an Israeli physicists, published this idea in 1981. Jacob Bekenstein, a friend of his, republished the theory on March 25, 2004, with much more mathematical support for the calculations. The theory is called MOND, for modified Newtonian dynamics.
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- Astronomers are pursuing both theories. Trying to find Dark Matter and trying the math of MOND on gravitational lensing and other gravity effects that must explain theory with evidence.
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- You do not modify Newton’s laws that have lasted 300 years with out extraordinary evidence. We have more to learn. Funny how that happens.
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- A redshift of z indicates the Universe has expanded by 1+z since the radiation was emitted. z = dw/Wo. If z=2, 1+z = 3, the Universe has grown by a factor of 3 times.
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- Gravity is a weak force compared to the other three forces. A good illustration is to observe that it takes 200 feet for gravity to pull a falling man off a 200 foot building, but, the electromagnetic force at ground level can stop him in less than a tenth of an inch.
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- See Review #373 “How to Weigh a Galaxy”
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- August 21, 2019 662
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--------------------- Thursday, August 22, 2019 --------------------
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