Isaac Newton and Gravity COSMOS 2007

Information about Isaac Newton and Gravity COSMOS 2007

Published on January 16, 2008

Author: Marietta1

Source: authorstream.com

Content

COSMOS – Cluster 6: The physics of Waves and Stars – July 11, 2007:  COSMOS – Cluster 6: The physics of Waves and Stars – July 11, 2007 Newton’s Laws of Motion Newtonian Gravity Sir Isaac Newton:  Sir Isaac Newton Born 1642 (or 1643 according to the modern calendar) Woolsthorpe, England Lucasian Professor of Mathematics at Cambridge University at age 27 Warden of the Mint 1696, Master 1699 Died 1727 London Newton’s first law of motion:  Newton’s first law of motion A body at rest remains at rest and a body in constant motion remains in constant motion unless an external force is applied. This is often called the law of inertia. Note: the motion continues in a straight line – both the direction and speed of the motion are constant. Why is Newton’s first law not intuitive?:  Why is Newton’s first law not intuitive? Friction Drag Forces Newton’s second law of motion:  Newton’s second law of motion 2. The acceleration of an object depends directly on the force applied and inversely on the object’s mass. Newton’s Second Law:  Newton’s Second Law If you push with twice the force, you will have twice the acceleration If the mass increases by a factor of two you will have one half the acceleration for the same push The acceleration is inversely proportional to the mass. This can be used to define mass Newton’s third law of motion:  Newton’s third law of motion 3. Forces come in pairs, a force applied to an object results in the object applying an equal but opposite force on the source of the force Newtons are the units scientists use for force in the SI system – the English unit, pound is not used very much Newton’s Law of Gravity:  Newton’s Law of Gravity Two bodies attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them G is the universal gravitational constant Newton’s Universal law of Gravity:  Newton’s Universal law of Gravity The force is directed along the line that connects the two objects An equal but opposite force is applied to the other object The force applied by gravity is called weight The force falls off as one over the square of the distance Newton’s universal law of gravity:  Newton’s universal law of gravity Applies to everything – hence “universal” Only attractive, there is no anti-gravity Weight versus Mass:  Weight versus Mass Mass is what determines your inertia – it is measure of the matter content of an object According to Newton’s second law, a fixed force will accelerate you more if your mass is less and vice versa Your weight on the Earth is the gravitational force applied by the Earth on you at the surface of the Earth What is your weight on Mars? Free Fall:  Free Fall When you are falling in an elevator with the cable cut, you don’t feel your apparent weight, you are “weightless” (but your weight is still the same!) – a better term is that you are in “free fall” Airplanes flying along a special path can produce short periods of free fall. A Russian cargo plane version of the vomit comet. Weightless in space:  Weightless in space The Shuttle orbits near the surface of the Earth The weight (gravitational force) of the astronauts is nearly the same in the space shuttle as on the Earth The shuttle astronauts do not feel their apparent weight – the force holding them up because they are falling at the same rate as the shuttle Free Fall is a better description of this. Newton’s laws of motion plus the universal law of gravity explain orbital motion:  Newton’s laws of motion plus the universal law of gravity explain orbital motion If an object above the Earth moves parallel to the surface at the right speed, the falling toward the center of the Earth produced by gravity is exactly matched by the curvature of the Earth - the object stays in orbit with no propulsion needed Univ. of Virginia Applet - Newton's Mountain From Newton’s A Treatise of the System of the World Transfer Orbits:  Transfer Orbits Typically rockets are designed to burn a lot of fuel in a short amount of time Most of the time, spacecraft are moving without power in an elliptical orbit Halley’s Comet:  Halley’s Comet Edmond Halley (a friend of Isaac Newton) believed that comets had elliptical orbits He recognized that the comet of 1682 was the comet of 1531 and 1607 He predicted a return in December of 1758 including a correction for the gravitational effect of Jupiter The comet was spotted 25 December 1758 Edmond Halley 1656-1742 Halley’s Comet 1986 The Discovery of Neptune:  The Discovery of Neptune Uranus was discovered accidentally by William Herschel in 1781 The position of Neptune was predicted by John Couch Adams (England) and Urban-Jean-Joseph Leverrier in the the 1840’s Newton’s laws of motion and universal law of gravity were used to make the predictions Neptune was discovered on September 23, 1846 within a degree of the predicted position Newtonian gravity produces paths that are conic sections:  Newtonian gravity produces paths that are conic sections Newton’s modifications to Kepler’s Laws:  Newton’s modifications to Kepler’s Laws 1. The planetary orbits are ellipses with the barycenter (the center of mass) at one of the foci. If two equally massive objects orbit each other, they move about a point half way between the two. 2. The planets sweep out equal areas in equal time (this is the same). 3. (M1 + M2) P2 = a3 (where M1 is the mass of the Sun and M2 is the mass of the planet and P is the period and a is the semi-major axis of the orbit. This is also true for binary stars and can be used to find the masses of the stars. A Newtonian Interpretation of Kepler’s Laws:  A Newtonian Interpretation of Kepler’s Laws Kepler found such good ellipses assuming the Sun was stationary because the mass of Jupiter, the most massive planet, is about 1/1000 th the mass of the Sun – so the wobble about the barycenter is small. Kepler’s 1st and 3d laws are a direct consequence of the laws of motion and an inverse square law gravitational force. Kepler’s 2nd law would be true for any central force law when angular momentum is conserved. Kepler’s 3d law can be used to measure the mass of the central object if G, the universal constant of gravitation can be measured. Or without G, we can find the ratio of the mass to the sun’s mass. Edmund Halley and Isaac Newton:  Edmund Halley and Isaac Newton Halley visited Newton in 1684 – he told Newton that he could show that the predicted orbits were ellipses but that he had mislaid his proof Halley, Robert Hooke, and Sir Christopher Wren were working on a mechanical theory for planetary orbits in competition with Isaac Newton Edmond Halley Principia by Isaac Newton:  Principia by Isaac Newton Newton expanded his studies on celestial mechanics (i.e. the motion of planets) into what was to become the “Principia” or more formally “Philosophiae naturalis principia mathematica (The Mathematical Principles of Natural Philosophy)” Halley saw the “Principia” through the printing process – including correspondence about Hooke’s claim to having discovered the inverse square law nature of gravitational force. The “Principia” was published in 1687. Halley and the scale of the solar system:  Halley and the scale of the solar system Halley’s idea (1716) was to use the transit of Venus (predicted for 1761 and 1769) across the disk of the Sun to triangulate an accurate, absolute distance scale in the solar system. We now know that the mean Earth-Sun distance (called the Astronomical Unit or A.U. by astronomers) is 1.496 x 108 km. 1 A. U. = 1.496 x 108 km = 1.496 x 1011 m Or about 93,000,000 miles

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