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---------------------------- - 2356 - The Gravity of It All
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- Gravity has been around for a long time but there is still a lot we do not understand about it. Gravity accelerates things. It accelerates you at 32 feet per second per second towards the center of the Earth.
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- Our Sun and all the other stars accelerate towards the center of the Milky Way Galaxy. But, gravity acceleration powers decrease as the square of the distance, so the Sun’s acceleration toward the center of the Milky Way is only the width of an atom per second per second. The Sun only feels the gravity of the Milky Way 100 billionth as strong as you feel gravity on the surface of the Earth.
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- What would happen if you drilled a hole from the North Pole to the South Pole and dropped a bowling ball into the hole?
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- If you drilled a hole from the North Pole to the South Pole and dropped a bowling ball into the hole, the bowling ball would accelerate to the center, then it would slow down until it reached the South Pole, then it would turn around and fall to the center again, and again, and again.
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- Isaac Newton developed the three laws of motion and the theory of gravity. In Newton’s universe space and time were absolute, regardless of the motion of the observer and the mass contained within space.
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- Newton found the force of gravity depends on the size of the masses and is inversely proportional to the square of the distance between them.
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- In 1905, Albert Einstein changed all that. His universe described gravity as the warping of space-time, not a force acting at a distance. He had space and time as relative to the observer and both are altered as motion approaches the speed of light, distances appear to stretch and time slows down. He also predicted the gravity waves distorting space-time travel at the speed of light.
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- We are just beginning to detect gravity waves. LIGO detectors are getting close to routine detection. Gravity waves are traveling through you and the Earth all the time. They are ripples in space-time. These ripples actually cause wobbles in mass and material. The whole Earth is wobbling all the time due to passing gravity waves.
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- For example, when a gravity wave of 200 cycles per second travels through the Earth the distance between the North Pole and the South Pole increases and the Earth’s diameter at the equator decreases. (Assuming a north - south orientation of the gravity wave in this case.)
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- A half-cycle later the opposite wobble occurs causing the distance between the North and South poles to shorten and the diameter at the equator to lengthen. This wobbling, or oscillation, goes on at 200 cycles per second until the gravity wave passes through the Earth.
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- The wave is traveling at the speed of light, but one cycle of the gravity wave lasts 5 thousandths of a second (the reciprocal of the 200 cycles per second frequency).
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- Why is it so hard to measure such a wave?
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- There are two projects called LIGO and LISA that are using laser interferometers to measure the changes in length caused by such gravity waves. The changes are actually stretches and contractions in space itself. It is not the mass that is stretching but the space the mass occupies is stretching.
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- These ripples in the geometry of space-time are caused whenever a massive object is moving rapidly, near the speed of light.
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- Such a massive object could be a pulsar, neutron star, supernovae, or black hole moving rapidly. We can see the results of gravity waves by observing these pulsars. Several binary pulsars are being studied today. Binary pulsars are two neutron stars orbiting each other.
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- Astronomers have observed that there orbits are speeding up and getting closer together with time. It is believed that this is due to the fact that they are emitting gravity waves and losing energy.
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- This loss of energy is compensated for in order to maintain the law of Conservation of Momentum ( Momentum is mass times velocity, or times distance per unit time). As the orbit decays the stars velocity is increasing.
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- Several binary pulsars have been observed demonstrating this behavior.PSR1913+16 is a binary pulsar that has been studied since 1975. The stars are spinning at 17 times per second and orbiting each other in 8 hours and they are 1,000,000 miles apart. The predicted rate of inward spiral from the equations of general relativity are 3 millimeters per orbit. To date the inward spiral and increased speed of orbit has exactly matched this. The orbital times have decreased ( speed increased ) 30 seconds over a 27 year period.
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- LIGO and LISA are projects designed to detect and measure waves emanating from binary pulsars. It is not easy. The changes in lengths that we have been talking about are very, very small. The wobble in the diameter of the Earth would be the size of a nucleus, about 10^-15 meters.
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- If we used a laser interferometer between Earth and the Sun we would only see a change in distance the diameter of an atom, about 10^-10 meters. So, gravity waves have massive scales and distort space only a tiny bit.
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- You are thinking, “ How could you ever detect a change in length that small occurring over a distance as long as that between the North and South Poles?”
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- Well, with laser interferometers astronomers are getting powerfully close for routine detections. Believe it or not.
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- First, we have to learn a little about a laser interferometer, if you want to believe it. Think of the interferometer instrument to be in the form of a giant plus sign. The laser source is at the beginning of one arm, there is a half mirror at 45 degree angle at the center, there are full mirrors at the ends of the 90 degree arms, and the receiving detector at the end of the last arm.
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- The laser source is emitting coherent light at a single frequency. LIGO uses infrared light at 640 nanometers. When the laser light hit’s the half mirror it splits into two beams at 90 degree angles. With the half silvered mirror half the light is reflected at 45 degrees and the remaining half is transmitted through the glass. The transmitted light is traveling in the same direction it had been traveling in originally. The reflected light moves off at right angles to that direction. Their amplitudes are reduced by 1 / square root of 2.
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- Both light beams are reflected by a full mirror and travel back to the mirror splitter. These mirrors are polished to have a uniform surface to within one nanometer. The originally reflected light beam passes through while the originally transmitted light beam is now reflected. In this way the two light beams join back together again.
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- A single beam of coherent light is split in two. The two halves are sent in directions at right angles to each other. The two beams are returned and join into a combined beam again.
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- If the two beams are not exactly aligned and in phase at the point of rejoining then interference patterns are generated. The word interferometer means to measure interference. It the beams travel the exact same distances on their separate trips then they recombine in phase. If one beam travels a half wavelength further, then when the beams recombine out of phase and they cancel each other. The detector output is zero.
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- The idea of the LIGO interferometer is to set the two beams to exactly cancel to zero then when a gravity wave comes through first one beam then the other beam will experience the change in length and the detector will see a ringing interference pattern.
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- The wave length of the infrared laser is 0.64 * 10^-6 meters . The distances LIGO is trying to measure is 10^-18 meters.
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----------------------------- Frequency = speed of light / wavelength
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----------------------------- Frequency = 299.8 * 10^6 meters / second / 640 * 10^-9 meters
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----------------------------- Frequency = 468,000,000,000,000 cycles per second.
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----------------------------- How small is 10^-18 meters?
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----------------------------- Start with one meter:
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---------------- Divide by 10,000 and you get 100 microns the diameter of human hair.
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---------------- Divide by 100 = 1 micron = wavelength of light. Micron = 10^-6 meters.
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----------------------------- Divide by 10,000 = 10^-10 = diameter of an atom.
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----------------------- Divide by 100,000 = 10^-15 = diameter of the nucleus of the atom.
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---------------------- Divide by 1,000 = 10^-18 meters which is what LIGO is measuring.
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- The length change they are trying to detect is much smaller than the wavelength used to measure it. Much more has to be done to optimize these measurements. (I will not go into these technical details here but check out www.ligo.org to learn how they are doing this optimization at Caltech).
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- LIGO stands for Laser Interferometer Gravity-wave Observatory. Each arm is 4 kilometers long. There are two sites. One at Hanford, Richland, Washington. The other at Livingston, Louisiana. They are 3002 kilometers apart and will be able to tell if they both are detecting the same gravity wave.
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- LISA stands for Laser Interferometer Space Antenna. It is going to be 5,000,000 kilometers in each arm. One big advantage of a space interferometer is that it is free from the vibrations of Earth. Earth is always ringing like a big bell and these vibrations must be isolated from the measurement or it interferes with the interference measurements.
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- Due to these Earth vibrations and cosmic noise LIGO is limited to measure waves in the frequency range of 40 to 2000 cycles per second. This is the low end of the audio range so you can actually listen to the output detector in the interference arm.
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- If a gravity wave comes through it would sound like a “chirp”. This chirp could be a very old gravity wave. Today the Universe is 13.7 billion years old. Light, or photon, did not appear until 100,000 years after the Big Bang. Neutrinos appeared one second after. But gravity started at the first instant, 10^-43 seconds after the beginning. Studying gravity waves will allow us to peer far back in to the beginning of time and space.
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- Gravity is not always intuitive. Here are some examples for thought:
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- If you fired two bullets, one straight up, the second at 45 degrees from horizontal, which would hit the ground first?
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- The bullet fired at an angle. Gravity has less vertical acceleration to overcome.
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- If the Earth were spinning 5 times faster what would happen to gravity?
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- Nothing. Gravity is a function of mass and distance, not rotation.
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- If you dropped a bowling ball off a 10 foot ladder and fired a bullet horizontally at the same time and same height, which would hit the ground first?
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- They both hit at the same time.
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- Seeing with gravity is new learning never experienced before and not without the ingenuity of these scientists and engineers.
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- May 6, 2019. 43
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--------------------- Monday, May 6, 2019 -------------------------
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