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Universal Gravitation Physics Mr. Padilla Falling Apple hits Newton on the head. According to the law of inertia, it would not fall unless acted upon by an outside force. If the moon did not fall, it would move off in a straight line and leave orbit. The moon is, therefore just a projectile circling Earth under the attraction of gravity Newton & Gravity Newton did not discover gravity. Newton showed that the gravity of a regular sphere is the same as if the mass were concentrated at its center. Developed the law of universal gravitation. This theory confirmed the Copernican theory of the solar system. Law of Universal Gravitation Everything pulls on everything else. This pull involves only an objects mass and their distance apart. Law of universal gravitation – every object acts on every other object with a force that for any two objects is proportional to the mass of each object. Law of Universal Gravitation The force decreases as the square of the dist. between objects increases. The greater the distance the less the force. Universal Gravitational Constant – G Force of gravity between two objects Fg = G m1m2 r2 Gravitational Constant The gravitational constant was first calculated by Henry Cavendish, 150 years after Newton’s discovery, and then again later by Phillip von Jolly G 6.67 10 11 2 Nm 2 kg Example Problem The Earth has a mass of 5.98x1024 kg and rotates around the Sun at a distance of 1.50x1011 m. If the sun has a mass of 1.99x1030 kg, what is the force of gravity the Sun exerts on the Earth? Force of gravity = 3.53x1022 N Sample Problem 7I Find the distance between a 0.300 kg billiard ball and a 0.400 kg billiard ball if the magnitude of the gravitational force is 8.92 x 10-11 N. Gravity and you Estimate your mass. If the radius of the Earth is 6.67x106 m, can you calculate the force of gravity exerted on you by the Earth? (Do it) Is there another way to do it? Gravity Gravity is considered to be a very weak force. We sense gravity only when large masses like the Earth are involved. Is your mass the same at sea level as it is on a high mountain? Is your weight the same? Inverse Square Law This law applies to the weakening of gravity with distance The quantity varies as the inverse square of its distance from its source. Inverse Square The greater the distance from the Earth the less it will weigh. No matter how great the distance Earth’s gravity does not drop to zero. The gravitational influence of every object is exerted through all space. Universal Gravitation Particles exerting gravity on each other created round planets. Planets exert gravity on each other. When these planets are close enough, they can disturb each others orbits. This deviation is called a perturbation. Gravity in the Universe The perturbations of Uranus led to other planets being discovered. Neptune in 1846 Pluto in 1930 The universe may have been created 10-15 bill. years ago (big bang) Since then its been constantly expanding Gravity may stop, or even reverse this expansion Gravitational Interactions Gravitational field – force field that surrounds massive objects = gravity Outside the planet Inside the planet Weight and weightlessness Ocean Tides Orbits Circular – A satellite in a circular orbit, always moves perpendicular to the force of gravity, so it always moves at a constant speed The time it takes for a satellite to complete one orbit is called the period. Not all satellites follow a circular orbit. Some will travel along an oval path called an ellipse. Ellipse A closed path taken by a point (satellite) that moves in such a way that the sum of it distances from two fixed points is constant. These points are called foci Ellipse Satellite speed varies in an ellipse. Satellites speed up as they approach and slow as they go away. The satellite will continue to orbit unless it reaches escape speed Planetary motion is caused by, yes you guessed it, gravity. Tycho Brahe (15461601) was one if the first to make exact measurements of the position of the planets and stars. He still believed that the Earth was the center of the solar system Johannes Kepler, one of his assistants, used Brahe’s data and with the sun as the center of the solar system, and was able to explain the behavior of every satellite and planet. Kepler’s Laws of Planetary Motion 1. The paths of the planets are ellipses, with the sun at one focus. 2. An imaginary line from the sun to a planet sweeps out equal areas in equal time intervals. (Planet travels faster when closer to the sun) Kepler’s Laws 3. The square of the ratio of the periods of any two planets revolving around the sun is equal to the cube of the ratio of their average distances from the sun. 2 TA rA TB rB 3 Escape Speed: Take off… Speed necessary for an object to escape gravity and not come crashing back down. Escape velocity varies from planet to planet because each planet has a different amount of gravity. Here are some escape velocities Earth – 11.2 km/s Moon – 2.4 km/s Mars – 5.0 km/s Jupiter – 60.2 km/s Sun’s gravity from Earth – 42.2 km/s Sun – 620 km/s Stars Produce energy through fusion of Hydrogen The more fusion, the bigger and hotter the star Less fusion, smaller and cooler When a star runs out of fuel, gravity will dominate and the start will collapse Sun After Hydrogen is gone Helium will fuse into carbon Causes sun to expand into a red giant It will expand beyond Earth’s orbit Won’t take place for about 5 billion years When Helium is used up… Red Giant will collapse into a black dwarf It will no longer give off heat and light. Black Holes Happens for stars at least twice as big as ours When gravitational collapse takes over it doesn’t stop. Density becomes infinite Gravity is so great that nothing can get out. Gravitational field does not change. Black Holes can not be seen