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-------------------------- 2431 - COSMIC LADDER - the distance to the stars
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- The farthest astronomers can reach is the “ Observable Universe”. That is a distance of 13.7 billion lightyears in any direction. Which is as far as light has traveled since the beginning of the Universe. Since the beginning of time. Beyond that distance the light has not had time to reach us yet. And, if the expansion of the Universe is truly accelerating than that light at the edge never will reach us.
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- The stepping stones in measuring astronomical distances are these five: (There are many, many more methods being tried, but, these are considered the most reliable today.)
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-------------- (1) Radar
-------------- (2) Parallax
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-------------- (3) Main - Sequence Fitting
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-------------- (4) Cepheid Variables
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-------------- (5) White Dwarf Supernovae
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-------------- (1) Radar is no different than the radar gun the Highway Patrol officer is using except we bounce the radar beam off the planet instead of your car.. We measure the time for the radar beam to make the round trip and multiply by the speed of light to get the distance.
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- Once we know the exact orbits we can calculate the distance each planet is from the Sun. The Earth to Sun distance is 93 million miles. It is called one Astronomical Unit.
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-------------- (2) Parallax - Once we know the exact distance of the diameter of Earth’s orbit around the Sun we can use parallax to measure the distance to the stars. Parallax is no different than the Boy Scout measuring the distance across the river.
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- The Boy Scout sights a tree on the shore of the other side. He measures the angle between the line of sight to the tree and along the river bank. He then steps off a measured distance along the river bank, one step is one yard. He measures the angle again between his new line of sight to the tree.
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- Now, he has two angles and one side of a triangle and he can use simple trigonometry to calculate the perpendicular distance across the river. Astronomers have to wait 6 months to make their same measurement to the star. Astronomers measure the angle to the line of sight to the target star with reference to the background stationary stars that are much further away. Then, 6 months later you measure the angle again.
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- The Earth has moved 2 times 93 million miles and the new line of sight shows the target star has shifted in the sky relative to the background stars. The parallax angle is half the angle of the annual back and forth shift of the target star. The distance is 3.26 lightyears * 1 / the angle in arc seconds.
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- Again, it is simple trigonometry except in this case the sine of a very small angle is equal to the angle. The hypotenuse of the right triangle is the distance to the star.
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- For example: The parallax angle for the star, Sirius, is 0.379 arc seconds. The distance is 1/.379 = 2.64 parsecs. 1 parsec = 3.26 lightyears. So the distance to Sirius is 8.6 lightyears.
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-------------- (3) “Main - Sequence Fitting” is the method of finding a star that is very similar to our Sun located in another galaxy. Since we know the luminosity of our Sun, we measure it. And, we measure the Apparent Luminosity of the far away star. We calculate the distance based on the dimness resulting from the star being farther away. Brightness falls off as the inverse square of the distance.
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-------------------- Apparent Brightness = Actual Luminosity / 4*pi* Distance^2
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-------------------- Apparent Brightness = 1.0 * 10^-12 watts / m^2
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-------------------- Actual Luminosity = 3.8*10^26 watts
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-------------------- Distance^2 = 3.8*10^26 / 12.6 * 1.0*10^-12 meters^2
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-------------------- Distance^2 = .30*10^38 m^2
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-------------------- Distance = .55*10^19 meters
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-------------------- One lightyear = 9.5*10^16 meters
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-------------------- Distance = 580 lightyears
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- So, taking the square root of the ratio of Actual to Apparent Brightness will give us the distance.
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- For example: Main Sequence Stars are those ranging in mass to be bright , hot, blue stars to dimmer, cooler, red stars. They plot on a temperature versus luminosity diagram in a straight line with a constant slope. So, instead of measuring the dimness of just one star like our Sun we measure the dimness of the whole range of stars in a galaxy where we know the distance against a range of stars in a galaxy where we are trying to find the distance.
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- The Main Sequence stars in the Hyades Cluster is 7.5 times brighter than the Main Sequence of stars in the Pleiades Cluster. So, Pleiades must be the square root of 7.5, or 2.75 times as far away. Using the parallax method Hyades Cluster is 151 lightyears away. The Pleiades Cluster must be 415 lightyears away.
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-------------- (4) Cepheid Variables stars are stars that pulsate in their brightness. The longer the period of their pulsation the brighter the star. We locate these Cepheid stars in a close in galaxy, like the Large Megellanic Cloud, where we have measured the distance using the above methods.
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- Then, we calculate the Actual Luminosity of the Cepheid star as a function of its period of pulsation. Now, we locate similar Cepheid stars in far away galaxies that we want to know their distance. We use the period of pulsation to calculate the Actual Luminosity, then, we the dimness of their Apparent Brightness to calculate the distance. The same process as the Main-Sequence Fitting.
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-------------- (5) White Dwarf Supernovae are dying, exploding stars of a particular type whereby we know their mass before they explode and we can calculate what the brightness of the explosion should be. After that we use the same ratio of Actual Luminosity to Apparent Brightness to calculate the distance.
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- The White Dwarf Supernovae are binary stars where one of the stars is a White Dwarf. It is pulling mass, gas, from its companion star. When the White Dwarf reaches 1.4 Solar Mass it explodes as a supernova. Astronomers have calculated that when a star reaches the mass 1.4 times the mass of our Sun it’s core burns helium into carbon, into silicon, into iron and collapses into its core rebounding into a supernova explosion of known luminosity.
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-------------- (1) Radar, we can use radar to measure the distances out to 1/3of a lightyear which is inside our solar system.
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-------------- (2) Parallax, we can use parallax on Milky Way stars out to 1000 lightyears.
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-------------- (3) Main - Sequence Fitting , we can use Main-Sequence Fitting to measure nearby galaxies out to 1,000,000 lightyears.
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-------------- (4) Cepheid Variables, we can use Cepheid stars to measure distant galaxies out to 100,000,000 lightyears.
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-------------- (5) White Dwarf Supernovae are much brighter that Cepheids and we can use their standard luminosities to measure distances out to 10,000,000,000 lightyears, 10 billion lightyears, almost to the edge of the Observable Universe.
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- See Review 835 “ The Redshift Explained” to learn how we measure the receding velocities of these far away galaxies. To calculate distances using Redshifts we need to use Hubble’s Constant for the rate of expansion of the Universe. Edwin Hubble measured velocities for several galaxies where distances had been calculated using the above methods.
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------------- Galaxy A distance = 10 million lightyears
------------- Galaxy A velocity = 492,000 miles per hour
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------------- Galaxy B distance = 11 million lightyears
------------- Galaxy B velocity = 541,000 miles per hour
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------------- Galaxy C distance = 700 million lightyears
------------- Galaxy C velocity = 34,400,000 miles per hour
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- So, next we have Galaxy D that is much farther away and we do not know its distance. The Redshift tells us that its receding velocity is 49,000,000 miles per hour. Well, if you take the ratios of the velocity to distance of the other galaxies you get 49,000 miles per hour per million lightyears. If we assume this ratio is constant, Hubble’s Constant, then the Galaxy D must be 1,000 million lightyears away, 1 billion lightyears away.
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--------------------- 49,000,000 miles per hour / 49,000 miles per hour / million lightyears = 1000 million lightyears.
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- The whole accuracy of this distance measurement depends on if Hubble’s constant is truly constant and actually 49,000 miles per hour/ million lightyears. If it really is constant and remained so over the life of the Universe then the reciprocal of Hubble’s Constant is the age of the Universe.
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- 1 million lightyears / 49,000 miles per hour = 13.6 billion years old. I will leave that calculation to the reader who has just climbed the Cosmic Distance Ladder to he farthest stars.
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- August 10, 2019 836
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--------------------- Saturday, August 10, 2019 --------------------
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