- 3342 - GRAVITY - have we figured it out? Newton's major goal was to explain planetary motion. Johannes Kepler had devised three laws of planetary motion without the use of Newton's law of gravity. They are fully consistent and one can prove all of Kepler's Laws by applying Newton's theory of universal gravitation.
--------------------- 3342 - GRAVITY - have we figured it out?
- Gravity is one of the most pervasive behaviors that we experience, it's no wonder that even the earliest scientists tried to understand why objects fall toward the ground.
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- Aristotle, the Greek philosopher, believed that objects fall at a speed that is proportional to their weight. In other words, if you took a wooden object and a metal object of the same size and dropped them both, the heavier metal object would fall at a proportionally faster speed.
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- Aristotle's philosophy about motion toward a substance's natural place held sway for about 2,000 years, until the time of Galileo Galilei. Galileo conducted experiments rolling objects of different weights down inclined planes (not dropping them off the Tower of Pisa, despite the popular apocryphal stories), and found that they fell with the same acceleration rate regardless of their weight.
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- Sir Isaac Newton recognized that falling motion observed on Earth was the same behavior of motion that the Moon and other objects experience, which holds them in place within relation to each other.
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- This insight from Newton was built upon the work of Galileo, but also by embracing the heliocentric model and Copernican principle, which had been developed by Nicholas Copernicus prior to Galileo's work.
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- Newton's development of the law of universal gravitation brought these two concepts together in the form of a mathematical formula that seemed to apply to determine the force of attraction between any two objects with mass. Together with Newton's laws of motion, it created a formal system of gravity and motion that would guide scientific understanding unchallenged for over 200 years.
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- The next major step in our understanding of gravity comes from Albert Einstein, in the form of his general theory of relativity, which describes the relationship between matter and motion through the basic explanation that objects with mass actually bend the very fabric of space and time.
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- This changes the path of objects in a way that is in accord with our understanding of gravity. Therefore, the current understanding of gravity is that it is a result of objects following the shortest path through spacetime, modified by the warping of nearby massive objects.
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- However, there are some cases where not even general relativity can quite give us meaningful results. Specifically, there are cases where general relativity is incompatible with the understanding of “quantum physics“.
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- One of the best known of these examples is along the boundary of a blackhole, where the smooth fabric of spacetime is incompatible with the granularity of energy required by quantum physics. This was theoretically resolved by the physicist Stephen Hawking, in an explanation that predicted blackholes radiate energy in the form of Hawking radiation.
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- What is needed is a comprehensive theory of gravity that can fully incorporate quantum physics. Such a theory of ‘quantum gravity” would be needed in order to resolve these questions.
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- Physicists have many candidates for such a theory, the most popular of which is “string theory“, but none which yield sufficient experimental evidence or even sufficient experimental predictions to be verified and broadly accepted as a correct description of physical reality.
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- In addition to the need for a quantum theory of gravity, there are two experimentally-driven mysteries related to gravity that still need to be resolved. Scientists have found that for our current understanding of gravity to apply to the universe, there must be an unseen attractive force (called dark matter) that helps hold galaxies together and an unseen repulsive force (called dark energy) that pushes distant galaxies apart at faster rates.
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- How did we get here? Johannes Kepler (German physicist, 1571-1630) had developed three laws governing the motion of the five then-known planets. He did not have a theoretical model for the principles governing this movement, but rather achieved them through trial and error over the course of his studies.
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- Newton's work was to take the laws of motion he had developed and applied them to planetary motion to develop a rigorous mathematical framework for this planetary motion.
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- Newton eventually came to the conclusion that the apple and the moon were influenced by the same force. He named that force gravitation (or gravity) after the Latin word gravitas which literally translates into "heaviness" or "weight."
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- Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.
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------------------------ Force of gravity = G * m1 * m2 / r^2
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----------------------- Fg = The force of gravity (typically in newtons)
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----------------------- G = The gravitational constant, which adds the proper level of proportionality to the equation. G = 6.67259 x 10-11 Newtons * m^2 / kg^2
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------------------------- m1 & m1 = The masses of the two particles (kilograms)
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-------------------------- r = The straight-line distance between the two particles ( meters)
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- This equation gives us the magnitude of the force, which is an attractive force and therefore always directed toward the other particle. As per Newton's Third Law of Motion, this force is always equal and opposite.
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- Newton's Three Laws of Motion give us the tools to interpret the motion caused by the force and we see that the particle with less mass (which may or may not be the smaller particle, depending upon their densities) will accelerate more than the other particle.
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- This is why light objects fall to the Earth considerably faster than the Earth falls toward them. Still, the force acting on the light object and the Earth is of identical magnitude, even though it doesn't look that way.
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- It is also significant to note that the force is inversely proportional to the square of the distance between the objects. As objects get further apart, the force of gravity drops very quickly. At most distances, only objects with very high masses such as planets, stars, galaxies, and blackholes have any significant gravity effects.
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- In an object composed of many particles, every particle interacts with every particle of the other object. Since we know that forces (including gravity) are vector quantities, we can view these forces as having components in the parallel and perpendicular directions of the two objects.
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- In some objects, such as spheres of uniform density, the perpendicular components of force will cancel each other out, so we can treat the objects as if they were point particles, concerning ourselves with only the net force between them.
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- The center of gravity of an object ( generally identical to its center of mass) is useful in these situations. We view gravity and perform calculations as if the entire mass of the object were focused at the center of gravity. In simple shapes spheres, circular disks, rectangular plates, cubes, etc., this point is at the geometric center of the object.
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- Sir Isaac Newton's law of universal gravitation can be restated into the form of a gravitational field, which can prove to be a useful means of looking at the situation. Instead of calculating the forces between two objects every time, we instead say that an object with mass creates a gravitational field around it. The gravitational field is defined as the force of gravity at a given point divided by the mass of an object at that point
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- When an object moves in a gravitational field, work must be done to get it from one place to another. Using calculus, we take the integral of the force from the starting position to the end position. Since the gravitational constants and the masses remain constant, the integral turns out to be just the integral of 1 / r^2 multiplied by the constants.
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- On the Earth, since we know the quantities involved, the gravitational potential energy “U” can be reduced to an equation in terms of the mass m of an object, the acceleration of gravity (g = 9.8 m/s), and the distance “y” above the coordinate origin (generally the ground in a gravity problem). This simplified equation yields gravitational potential energy of:
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-------------------------------- Potential energy, U = m *g * y
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- This formula is applied in energy calculations within a gravitational field. As a form of energy, gravitational potential energy is subject to the law of conservation of energy.
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- When Newton presented his theory of gravity, he had no mechanism for how the force worked. Objects drew each other across giant gulfs of empty space, which seemed to go against everything that scientists would expect. It would be over two centuries before a theoretical framework would adequately explain why Newton's theory actually worked.
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- In his Theory of General Relativity, Albert Einstein explained gravitation as the curvature of spacetime around any mass. Objects with greater mass caused greater curvature, and thus exhibited greater gravitational pull.
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- This has been supported by research that has shown light actually curves around massive objects such as the sun, which would be predicted by the theory since space itself curves at that point and light will follow the simplest path through space.
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- Current efforts in “quantum physics” are attempting to unify all of the fundamental forces of physics into one unified force which manifests in different ways. So far, gravity is proving the greatest hurdle to incorporate into the unified theory.
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- Such a theory of quantum gravity would finally unify general relativity with quantum mechanics into a single, seamless and elegant view that all of nature functions under one fundamental type of particle interaction. When we understand it , it will be simple.
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- With quantum gravity, it is theorized that there exists a virtual particle called a “graviton” that mediates the gravitational force because that is how the other three fundamental forces operate. The graviton has not, however, been experimentally observed.
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- November 13, 2021 GRAVITY - have we figured it out? 3342
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