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------------------- 2175 - Why is Gravity so Small?
- If you read Review 43 “ The Gravity of it All”, you probably were asking the question, “Why is gravity so small?”. You would not have come up with this question naturally because we think of gravity is being big. A big powerful force.
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- Just try to lift 100 pounds. But, you have to realize the other part of gravity is the mass of the Earth and it is very, very big, 13,200,000,000,000,000,000,000,000 pounds. Yet, a small magnet will pick up a paper clip that the entire Earth can not hold on to.
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- Compared with the other forces in nature gravity is small. It is 10^29 times weaker than the Weak Nuclear Force. If we set the electromagnetic force equal to 1:
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-------------------------- Strong Force ------------------------ 20
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-------------------------- Electromagnetic Force ------------ 1
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-------------------------- Weak Force ------------------------- 0.0000001
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-------------------------- Gravity Force ----------------------- 10^-36
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- The Strong Nuclear Force is 20 times stronger than the magnet. The Weak Nuclear Force is 10,000,000 time weaker than the magnet. The force of gravity is 10^36 times weaker than the magnet.
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- The Strong Force actually gets stronger with distance. That is how it holds protons, neutrons, quarks together in the nucleus. If their distance separates the Strong force increases. That is, if the quarks try to get farther apart the Strong Force gets ever stronger and pulls them back together.
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- The Weak Nuclear Force only operates over a very short distance, the dimensions of the atom, 2*10^-18 meters. It holds the elementary particles together inside the atom but not as strongly as the Strong Force. The Weak Force is what allows beta decay to occur in the nucleus if radioactive elements. It is beta decay that changes uranium into lead over time.
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- The electric and magnetic force as well as gravity force decrease with the square of the distance. This is simply like light radiation decreasing as the surface area of a sphere as the radius increases. So these forces are inversely proportional to distance squared.
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- The electric force is directly proportional to the two charges. The gravity force is directly proportional to the two masses. Isaac Newton’s equation for the gravity force: (Charles Coulomb’s equation is the same except the constant is “k” = 9*10^9 kg * m^3/sec^2/coulomb^2 and the two electric charges are weighed in Coulombs of charge instead of kilograms of mass.)
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----------------------- Gravity force = - G * m * M / r^2
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------------------------ “m” and “M” are the two masses.
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------------------------ “ r” is the distance between them
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------------------------ “G” is the gravity constant of proportionality for the units of measurement.
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------------------------ G = 6.7 *10^-11 meters^3/kilogram/ second^2
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------------------------ G = 0.000,000,000,067 meters^3/kilogram/ second^2
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- If gravity decreases with the square of distance it must increase as distances decrease. Gravity increases as distances decrease. What happens to gravity at atomic distances? Isaac Newton’s simple equation does not work at atomic distances. You have to use Quantum Mechanics formulas. His simple equation does not work at high speeds or high masses either. You have to use Einstein’s Theory of Relativity formulas in those situations.
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- The shortest distance we can get to is 10^-35 meters. This is called Planck’s length. The shortest time we can get to is 10^-43 seconds. That is called the Planck time. The speed of light is 3*10^8 meters / second. In 10^-43 seconds light travels 3*10^-35 meters.
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- The largest mass that can exist with a diameter of the shortest distance is 2.2 *10^-8 kilograms. Anything larger with that radius would turn into a miniature Black Hole. So, although the math is incorrect, let’s put two of theses small masses together separated by the shortest distance and see what happens. What is the force of gravity?
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-------------- Gravity Force = G*m*m/r^2
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-------------- Gravity Force = 6.7*10^-11 * 2.2*10^-7 * 2.2*10^-7 / 10^-35^2
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-------------- Gravity Force = 32.4 * 10^-25 * 10^70
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-------------- Gravity Force = 3.2 * 10^44 kg * m/sec^2
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-------------- Gravity Force = 0.73 * 10^44 pounds
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-------- Gravity Force = 73000000000000000000000000000000000000000000 pounds
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- No wonder it turns into a Black Hole. And, gravity is supposed to be the smallest force. What’s with that?
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- Energy goes up in direct proportion to radiation frequency. E = h*f
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----------------- Energy = 6.6 * 10^-34 * frequency.
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----------------- Wavelength * frequency = speed of light
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----------------- Energy = 6.6*10^-34 * speed of light / wavelength.
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---------------- Energy of the smallest wavelength of radiation = to a Planck length
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---------------- Energy = 6.6*10^-34 * 3.10^8 / 1.6*10^-35
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--------------- Energy = 12.4 * 10^9 kg*m^2/sec^2
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---------------- Energy = 12,400,000,000 joules
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---------------- Energy = 3,444 kilowatt hours.
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- 3,444 kilowatt hours does not seem like very much energy. My electric bill consumes 500 kilowatt hours each month. At 12 cents per Kwh that is $60 per month. So the energy in the smallest wavelength of radiation is a little over $400 worth of electric power. However, you have to remember that this amount of energy is concentrated in a very, very small space.
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- Energy is directly proportional to frequency and is indirectly proportional to wavelength. To see small distances we need lots of energy in a very small space. That is what particle accelerators are all about.
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- The force of gravity is also equal to mass times acceleration, F = m*a.
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- The acceleration of gravity can be measured at Earth’s surface. Regardless of their mass all objects fall at the same rate, assuming there is no air resistance.
The acceleration = 9.81 m/sec^2. Let’s calculate the force of gravity of Planck’s mass at the surface of Earth.
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---------------- Gravity Force = m * a
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---------------- Gravity Force = 2.2 *10^-8 kg * 9.81 m/sec^2
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---------------- Gravity Force = 21.6 * 10^-8 kg*m/sec^2
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---------------- Gravity Force = 4.85 * 10^-8 pounds.
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---------------- Gravity Force = 0.0000000485 pounds
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- This small mass 2.2 * 10^-8 kilograms, 0.000000022 kilograms, is about the weight of an amoeba bacteria, or the weight of the period at the end of this sentence, experiences a change in weight from the surface of the Earth to the smallest distance before it becomes a Black Hole of 10^53 times, just due to the decrease in distance. The radius of the Earth is 6,474,000 meters.
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------------- The radius of a Black Hole, called the Accretion Disk, = 2*G*M/c^2
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------------- The Planck length squared = r^2 = G*h/2*pi*c^3.
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-------------- If you set these two equations equal to each other:
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-------------- G*h / 2*pi*c^3 = 4*G^2 * M^2 / c^4
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-------------- M ^2 = h* c / 8*pi*G
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--------------- A Black Hole’s mass squared that has a radius equal to a Planck length = h*c / 8*pi*G
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--------------- M^2 = 1.2 * 10^-16 kilograms^2
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--------------- M = 1.1*10^-8 kilograms
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- Although the math is this review “does not work in reality” it was fun playing around with these classical formulas used in the macroworld. You can still learn something from them. Gravity does not seem small at all but compared to the other forces in nature it is.
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- Footnotes:
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- (1) ------------ G = 6.674215*10^-11 m^3/kg/sec^2
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- (2) --------- Planck length^2 = G*h/2*pi*c^3 = 1.61599*10^-35 meters
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----------------- r^2 = 6.7*10^-11* 6.610^-34 / 6.28 * 27 * 10^24 meters^2
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-------------- Planck mass^2 = h*c/2*pi*G = 2.17684 *10^-8 kilograms
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------------------ m^2 = 6.6*10^-34 * 3*10^8 / 25 * 6.7*10^-11 kilograms^2
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----------------- Planck time^2 = G * h / 2*pi* c^5 = 10^-43 seconds
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----------------- t^2 = 6.7*10^-11 * 6.6*10^-34 / 6.28 * 243*`10^40 seconds^2
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- (3) --------- Kg*m/sec^2 = 1 Newton = 1/ 4.448 pounds
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- (4) ---------- h = Planck’s Constant = 6.626076 * 10^-34 kilogram*meters^2 / second
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- (5) ----------- Joule of Energy = kg * m^2/sec^2
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------------------ 1 Kilowatt-hour = 3.6*10^6 joules.
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- Other reviews available:
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- 2174 - Gravity - what is it really?
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- 2170 - Gravity - measuring with gravity waves/
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- 2127 - Einstein’s ring
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- 2089 - The gravity of he details
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- 2014 - Gravity a property of pace and time. Lists 12 more reviews on this subject.
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- 1913 - Is gravity a universal force?
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- 43 - “ The Gravity of it All”
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- 368 - Time Comes to Us in Particles - Planck Time
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- 6 - Big Bang’s First Creations, the 4 forces”
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- November 23, 2018 816
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--- Some reviews are at: -------------- http://jdetrick.blogspot.com -----
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-------------------------- Friday, November 23, 2018 --------------------------
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