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Information Exchange on Newtonian Gravity and Einstein's Theory of General Relativity 1 Information Exchange on Newtonian 1: Newton develops his gravity and Einstein's Theory of General theory Relativity Newton wasn't hit on the head It is 1918, Einstein published his General by an apple, but he may have Theory of Relativity just a couple years ago, watched one fall from an and has yet to test it in a regime that will set apple tree near his window. When he saw it apart from Newtonian Gravity. the apple fall, the light bulb that went off in his head was not that gravity existed – he We want to exchange information on these and his contemporaries already knew that. two theories, especially in regards to how Instead, Newton realized that gravity might they account for the orbits of the planets in extend so far above the Earth that it could be our Solar System. To that end, we will the force holding the moon in its orbit. attempt to answer the following questions for each of the theories: Newton published his law of universal gravitation on July 1687 in the Principia. With 1. How was the theory developed? the Principia, Newton became internationally 2. Give a description of the theory. recognized. 3. How does it explain the motions of the planets? 4. How does it solve the problem of Mercury's orbit? 5. What prediction does it make for the bending of light and the upcoming eclipse in 1919? 2: How Newton's gravity 3: Newton's gravity predicts works the planet, Neptune Newton showed that if the Since ancient times, people force of gravity decreased as have known about the planets the inverse square of the Mercury, Venus, Earth, Mars, distance, that he could calculate the Moon's Jupiter and Saturn. In 1781, William orbital period. He postulated that this same Herschel, a comet hunter, discovered Uranus force was responsible for other orbital in 1781. In 1821, Alexis Bourvard published motions, and so it was called "universal detailed tables of Uranus' orbit. However, gravitation". observations showed deviations from these tables, leading Bouvard to hypothesize a Newton's equation describing the perturbing body gravitational attraction of two objects of mass m1 and m2 separated by a distance, d, Independently, John Couch Adams (1845) is given by: and Urbain Le Verrier (1846) calculated an m m orbit for an 8th planet that would account for FG= 1 2 Uranus' motions. G d 2 The night in 1846 that Johann Gottfried Galle where FG is the force of gravity and G is the gravitational constant. began observations to search for this new planet he found it! The planet was within 1° Newton's laws of motion have stood up to of where Le Verrier had predicted (and 10° of intense scrutiny and testing for over 200 where Adams predicted). Observations over years. the next few nights confirmed that this new object was a planet, which was later named Neptune. 4b: How Newton's gravity 4a: Mercury's orbit explains Mercury's orbit All planets orbit the Sun in an Newton's theory of universal oval, as described by Kepler's gravitation has had wonderful Laws, so there is a point in that success in explaining the orbit that is closest to the Sun, motions of the planets in our called the perihelion. Solar System, even leading to the discovery of Neptune. However, given the known We observe that as Mercury orbits the Sun, planets in our Solar System, Newton's theory the perihelion advances by a small amount. does not fully explain the precession of Newton's theory does not fully explain this Mercury's orbit. precession of Mercury's perihelion. There is a 43 arcsecond per century discrepancy Some astronomers theorize that another between the Newtonian prediction (resulting planet, inside the orbit of Mercury, could from the gravitational tugs of the other account for the odd behavior of Mercury. planets) and the observed precession. This position is bolstered by the success in finding Neptune using the perturbations of Uranus' orbit to calculate an orbit of the undiscovered planet. The proposed planet between the Sun and Mercury has been named Vulcan, but has yet to be observed. 5a: Newtonian gravity bends 5b: Newtonian gravity's light eclipse predictions Newton's theory of gravitation On May 29, 1919, there will be a predicts that light will bend total eclipse of the Sun. This when traveling near a massive eclipse is ideal for measuring the object – the larger the mass of the object, bending of starlight by the Sun. the larger the effect of bending. Totality will last for over five minutes – one of the longest eclipses in recent history. Also, the Sun will be directly in front of the Hyades, a In 1801, Johann von Soldner performed 25 bright cluster of stars in the constellation pages of calculations to find that for Taurus. Newtonian gravity the deflection angle of light passing near an object is: Newtonian gravity predicts that the angle of a ≈ 2m/r deflection will be 0.87 arcseconds for the stars where m = GM/c2, M is the mass of the sun near the Sun during this eclipse. r is the closest approach distance of the photon to the sun. This solution is an approximation, since the full solution is an infinite sum of algebraic terms. The equation above gives the first (and largest) term of that series, which is a good approximation. The other terms of the series give small corrections to this solution, but those corrections would be too small to measure at the current time. 1a: Einstein develops his 1b: Einstein on how his theory gravity differs from Newton's From his library in his Berlin From an interview printed in apartment, Einstein saw a the New York Times, Dec 3, man fall from a nearby 1919, page 19: rooftop, fortunately onto a pile of soft [Quoting Einstein] rubbish. When the man described the event "Please imagine the earth removed, and in to Einstein, he said that he did not feel the its place suspended a box as big as a room sensation of gravity as he fell, which he or a whole house, and inside a man would have expected to pull him violently naturally floating in the centre, there being downward. no force whatever pulling him. Imagine, further, that this box begin, by a rope or While Einstein was extending his special other contrivance, suddenly jerked to one theory of relativity, which applies to systems side, which is scientifically termed 'difform undergoing uniform motion, to systems with motion,' as opposed to 'uniform motion.' non-uniform motion (what he calls difform This person would then naturally reach motion), he remembered the falling man, and bottom on the opposite side. The result realized that gravitation might be described would consequently be the same as if he as a "difform motion" (non-uniform motion) obeyed Newton's law of gravitation, while, in fact, there is no gravitation exerted He published his general theory of relativity whatever, which proves that difform motion in 1915. will in every case produce the same effects as gravitation." The concept Einstein describes above is known as the Equivalence Principle. 2: How Einstein's gravity 3: Einstein gravity explains works the planetary motions Einstein's theory proposes The Sun is the largest object in that space and time are one our Solar System, so, according entity – spacetime. Any to Einstein's General Theory of object with mass will curve spacetime, with Relativity, the Sun will "warp" spacetime in the mass of the object determining the the Solar System by the largest amount. The amount of curvature produced. Free-falling planets simply follow the shortest path objects follow "geodesics", or the shortest through spacetime around the Sun, thus path through the curved spacetime. We explaining their orbits. observe objects attracted to massive objects as they follow these paths. We call this gravity. Einstein's gravity becomes evident only in extreme conditions, such as near very massive objects, which cannot be replicated in today's laboratories. Because of this, the theory has yet to be put to any rigorous testing. 4b: How Einstein's gravity 4a: Mercury's orbit explains Mercury's orbit All planets orbit the Sun in an Albert Einstein’s General oval, as described by Kepler's Theory of Relativity provides a Laws, so there is a point in that full explanation for the orbit that is closest to the Sun, called the observed precession of Mercury's perihelion perihelion. without the need for an extra planet We observe that as Mercury orbits the Sun, As Mercury moves toward its perihelion (i.e. the perihelion advances by a small amount. closer to the Sun), it moves deeper into the Newton's theory does not fully explain this Sun's gravity well. Its motion into this region precession of Mercury's perihelion. There is a of greater curvature of space-time causes 43 arcsecond per century discrepancy the perihelion to advance. Einstein's Theory between the Newtonian prediction (resulting of General Relativity predicts exactly the from the gravitational tugs of the other amount of perihelion advance seen in planets) and the observed precession. Mercury. Einstein views this result as the most critical test of his theory to date. 5a: Einstein gravity bends 5b: Einstein gravity's eclipse light predictions Einstein's theory of gravitation On May 29, 1919, there will be a predicts that light will bend total eclipse of the Sun. This when traveling near a massive object – the eclipse is ideal for measuring the larger the mass of the object, the larger the bending of starlight by the Sun.
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