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------------ 2746 - ASTRONOMICAL LADDER - How far does it reach?
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- Eratosthenes was in the town of Syene, now called Aswan. He noted that on the 1st day of summer, June 21st, every year, the Sun shined to the bottom of a deep well. He discovered that at the same time of year in the town of Alexander a 10 foot pole cast a 16 inch shadow on the ground. Using this ratio 16 / 120 he determined the angle of the Sun’s rays to be 7 1/2 degrees. The distance between Aswan and Alexander was 50 days travel by camel. A camel’s speed is about 10 1/2 miles per day.
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--------------- 10 1/2 * 50 = 525 miles
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--------------- 525 miles would correspond to the 7 1/2 degrees as the circumference of the Earth would correspond to 360 degrees.
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----------------- 360 /7.5 = Circumference / 525 miles.
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----------------- Circumference = 25,200 miles.
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- The camels must have been carrying lighter loads because today’s most scientific measurement is 24,900 miles. 99% accuracy 300 B.C. Amazing.
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- Once we knew the Earth was round, and the diameter is 24,900 / pi = 7,926 miles, we could us parallax to measure the distance to the planet Mars. This is the next rung in the ladder. We line up Mars with a straight line to distance stars. We wait 12 hours and do it again.
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- The parallax angle is the small angle the target moves compared with the distant stars. It moves 0.0092 degrees. The tangent of the right triangle for this small angle is 0.00016057. The tangent = Distance / diameter of Earth.
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------------ Distance = 0.00016057 * 7,926 miles = 49,360,000 miles.
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------------ Today’s science has the Earth at 227.9 million kilometers, Mars at 149.6 million kilometers from the Sun, making the Earth - Mars distance of 78.3 million kilometers, or 48,634,000 miles. Again, 99% accuracy using trigonometry.
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- To get the next rung in the ladder astronomers used the discovery that the planet’s period of orbit squared is proportional to the radius of orbit cubed. They used this formula to estimate the distance to Jupiter. Jupiter’s period of orbit was measured to be 11.83 years. The Earth’s orbit is one year had a radius of 93 million miles.
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------------ (11.83 years )^2 / 1 year^2 = (Jupiter’s orbit)^3 / (93 million miles)^3.
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------------- 141 = (Jupiter’s orbit)^3 / 8.04*10^23
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------------- Jupiter’s orbit = 483,300,000 miles.
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- Today’s science puts Jupiter’s orbit at 483,416,000 miles.
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- Now that astronomer’s had the Earth’s orbit at 93,000,000 miles they could wait 6 months between sightings and get a far bigger parallax angle. To calculate the distance to the stars they picked the brightest star Sirius, figuring that must be the closest. They got a parallax angle of 0.002075 degrees.
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------------- Tangent 0.0020975 = 93,000,000 miles / Distance to Sirius.
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------------ Distance to Sirius = 50,570,000,000,000 miles.
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------------ A lightyear is 5,880,000,000,000 miles
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------------- Distance to Sirius = 8.6 lightyears.
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- By 1900 astronomers had calculated the distances for 100 stars. Parallax measurements had reached their limits, so, another method was needed for the next rung on the ladder.
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- The brightness of stars varies inversely proportional to the square of the distance. By knowing the intrinsic brightness of Sirius and the distance to Sirius astronomers could calculate the distance to similar stars that were further away. Their brightness falls off as the square of the distance. If a similar star is 1% as bright it must be 10 times further away, 10 * 8.6 = 86 lightyears.
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- To calculate distances out to 1,000 lightyears astronomers used a special kind of pulsating star called a Cepheid. These stars pulsate their brightness inversely proportional to the rate of the pulsations. The bigger the Cepheid star the more slowly it pulsates. And, the bigger the Cepheid star the brighter it shines.
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- Polaris, the North Star, is the nearest Cepheid and its distance was determined to be 466 lightyears away. Cepheid stars have been used to take the astronomical ladder out to 60 million lightyears.
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- To get the astronomical ladder out to 300 million lightyears astronomers used the light spectrum of hydrogen gas. Hydrogen gas emits a wavelength of 21 centimeters. Observing the 21 centimeter wavelength emitted from a rotating galaxy the discovered the Doppler effect.
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- The wavelength was blue shifted on the side of the galaxy rotating towards us, and, the wavelength was redshifted on the side of the galaxy rotating away from us. The rotation speed of galaxies could be calculated. And, the rotation speed was proportional to the galaxy’s brightness. Knowing the brightness we could calculate the distance.
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- Gravitational Lensing was used for the next rung on the astronomical ladder. Immense gravity can bend light. If there is a galaxy cluster of immense gravity between our line of sight and a distance Quasar we can use the lensing to calculate the distance to the Quasar.
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- The Quasar is a super massive Blackhole in the center of a distant galaxy that emits pulsating jets. The light from these jets travels different paths through the gravitational lens. The same event on the Pulsar can be viewed months apart because of the different paths each light beam travels through the Gravitational Lens.
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- The gravity caused space to curve and each light beam follows the shortest path through curved space. Measuring how much longer a second path has taken allows the distance the light traveled to be calculated.
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- A star survives against gravity as long as its hydrogen fuel is burning. When the fuel runs out the star collapses under the force of gravity. The burn rate for a star is the cube of its size. A star 10 times bigger than the Sun will burn 1000 times faster. The Sun will burn for 10 billion years. The star 10 times larger will burn out living only 10 million years before it explodes as a supernova.
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- If the core of the collapsing star is less than 1.4 Solar Mass it will collapse into a White Dwarf star, a Neutron Star, about 100 miles in diameter. If the mass at the core is greater than 1.4 Solar Mass it collapses into a Blackhole. Nothing can escape the gravity of a Blackhole.
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- To escape the Earth’s gravity from the surface you need a rocket that can achieve a velocity of 24,000 miles per hour. The surface of the Earth is 3,963 miles above its center. If the Earth was 1/2 that size, 4 G’s, the escape velocity would be 1.4 times , or 33,600 miles per hour. If we collapsed the Earth down to a radius of 0.35 inches the escape velocity would be 186,000 miles per second. The Earth at that density would be a Blackhole.
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- As an objects velocity approaches the speed of light, 186,000 miles per second, the mass increases, the length shortens, and the time slows down. At near light speeds mass is infinite, length is zero, and time stops.
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- Obviously, only massless light can travel that fast. So, a super massive Blackhole presents us with physics we do not understand. But, we humans have only been working on these problems for a short time.
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- If the age of the World were a calendar year, vertebrates did not appear until November 21st, primates did not show up until Christmas day and us Homo Sapiens got here just 3.5 minutes before New Year’s Eve. That is not much time to figure all this stuff out.
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- But, we keep working at it and once the mind is stretched it never returns to its original shape. The astronomical ladder has stretched us out to 12.8 billion lightyears, where we see galaxies 12.8 billion lightyears distant.
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- We need to discover another rung on the ladder.
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- May 25, 2020 1108 2746
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--------------------- Monday, May 25, 2020 -------------------------
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