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### Gravity_6

Course: ASTR 104, Fall 2008
School: Western Kentucky...
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Word Count: 1676

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of 3/16/09 Conservation Momentum Newtons first law The total momentum of interacting objects cannot change unless an external force is acting on them Interacting objects exchange momentum through equal and opposite forces Conservation of Angular Momentum angular momentum = mass x velocity x radius The angular momentum of an object cannot change unless an external twisting force (torque) is acting on it...

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of 3/16/09 Conservation Momentum Newtons first law The total momentum of interacting objects cannot change unless an external force is acting on them Interacting objects exchange momentum through equal and opposite forces Conservation of Angular Momentum angular momentum = mass x velocity x radius The angular momentum of an object cannot change unless an external twisting force (torque) is acting on it Earth experiences no twisting force as it orbits the Sun, so its rotation and orbit will continue indefinitely Conservation of Angular Momentum Angular momentum = m v r Orbital Keplers 2nd law Conservation of Energy Energy can be neither created nor destroyed. It can change form or be exchanged between objects. The total energy content of the Universe was determined in the Big Bang and remains the same today. Where do objects get their energy? Energy makes matter move. Energy is conserved, but it can: Transfer from one object to another Change in form Basic Types of Energy Kinetic (motion) Radiative (light) Stored or potential Energy can change type but cannot be destroyed. 1 3/16/09 Thermal Energy: the collective kinetic energy of many particles (for example, in a rock, in air, in water) Thermal energy is related to temperature but it is NOT the same. Temperature is the average kinetic energy of the many particles in a substance. Temperature Scales Thermal energy is a measure of the total kinetic energy of all the particles in a substance. It therefore depends both on temperature AND density Example: Gravitational Potential Energy On Earth, depends on: objects mass (m) strength of gravity (g) distance object could potentially fall Gravitational Potential Energy In space, an object or gas cloud has more gravitational energy when it is spread out than when it contracts. A contracting cloud converts gravitational potential energy to thermal energy. Mass-Energy Mass itself is a form of potential energy A small amount of mass can release a great deal of energy Concentrated energy can spontaneously turn into particles (for example, in particle accelerators) 2 3/16/09 A force must pull the Moon toward Earths center According to Newtons 1st Law, the Moon should follow a straight line and leave Earth But, for every 1020m is moves eastward, it falls 1.6mm toward Earth So, there must be a force The Moon can orbit the Earth acting on it only if a force is acting on it Newtons Great Insight The same force makes things fall down on Earth and keeps the planets in their orbits GRAVITY Gravity makes apples fall from trees and keeps the Moon orbiting the Earth The Universal Law of Gravitation Every mass attracts every other mass Attraction is directly proportional to the product of their masses Attraction is inversely proportional to the square of the distance between their centers The Universal Law of Gravitation Strength of gravity vs. distance What does it mean to be inversely proportional to the square of the distance between their centers? 3 3/16/09 Newtons Law and Gravitation Projectile motion Imagine that you throw a ball directly upward. Which of the following statements best describes how Newtons second law accounts for the motion of the ball when it reaches its maximum height? a) The ball has a velocity that is zero and an acceleration that is zero. b) The ball has a velocity that is upward and an acceleration that is downward. c) The ball has a net force that is downward and a velocity that is downward. d) The ball has a net force that is downward and an acceleration of zero. e) The ball has a net force that is downward and an acceleration that is downward. Velocity Acceleration Force In-class Activities: Gravity and Newtons Laws Work with a partner! Read the instructions and questions carefully. Discuss the concepts and your answers with one another. Take time to understand it now!!!! Come to a consensus answer you both agree on. If you get stuck or are not sure of your answer, ask another group. If you get really stuck or dont understand what the question is asking, ask me. Note that position B is at the midpoint between the Moon and Earth. At which location would the net force be least? Moon A Earth B C Note that position B is at the midpoint between the Moon and Earth. If a spaceship is traveling from Earth to the Moon, At which position would the acceleration of the ship be greatest? At which position would the acceleration of the ship be least? Moon Note that position #2 is at the midpoint between the Moon and Earth. If a spaceship was coasting very fast toward the Moon when at position #2, which direction would the acceleration of the ship point? A. toward the moon B. Toward Earth C. the acceleration would be zero Moon A Earth B C 3 1 Earth 2 4 3/16/09 Which of the following correctly describes how the gravitational force exerted by asteroid A on its partner asteroid compares to the gravitational force exerted by asteroid on B its partner asteroid. a) A > B b) B > A c) A = B Acceleration of Gravity The acceleration of a falling object g = 9.8 m/s on earth How is mass different from weight? Mass the amount of matter in an object Weight the force that acts upon an object In which scenario is the weight of the person the greatest? a) b) c) d) e) Elevator stationary Elevator moving at a constant velocity Elevator accelerating upward Elevator accelerating downward Elevator in free-fall You are weightless in free-fall! Mass vs. Weight On Earth, 1 kg of bananas weighs 9.8 Newtons of force On the Moon: A. B. C. D. My weight is the same, my mass is less. My weight is less, my mass is the same. My weight is more, my mass is the same. My weight is more, my mass is less. On the Moon, 1 kg of bananas weighs 1.7 Newtons of force 5 3/16/09 Orbiting Bodies are Falling Bodies An object orbiting Earth is actually falling (being accelerated) toward Earths center An object in a stable orbit continuously misses Earth because of its orbital velocity Why are astronauts weightless in space? There is gravity in space Weightlessness is due to a constant state of free-fall http://www.youtube.com/watch?v=QnB6uYNPia0 Astronauts feel weightless because they are in free-fall! Remember, an astronaut is falling around the Earth So is the spaceship! Both are in free-fall together No force holding the astronaut to the wall of the spaceship Having fun in Zero-G So, they feel weightless! Extending Keplers Laws with Newtons Law Ellipses are not the only orbital paths Orbits can be: Closed (ellipses or circles) Open (parabolas or hyperbolas) NASA uses unbound orbits to slingshot spacecraft to the outer planets Center of Mass Objects orbiting each other actually revolve around their mutual center of mass Objects of equal mass orbit a point halfway between them Objects of unequal mass orbit a point closer to larger object Newtons Version of Keplers 3rd Law Remember Kepler's 3rd Law: Newtons found a general version with his Law of Gravity (P in years, a in AUs, M in solar masses) Kepler's Law works because the mass of the Sun is much larger than the mass of any planet MEarth = 0.000003 MSun, MJup = 0.00096 MSun MSun + MPlanet MSun = 1 6 3/16/09 Use Keplers 3rd Law (modified) to find mass! If we know a moons orbit around its planet, we can find the planets mass! How do gravity and energy together allow us to understand orbits? More gravitational energy; Less kinetic energy Less gravitational energy; More kinetic energy Total orbital energy stays constant Total orbital energy (gravitational + kinetic) stays constant if there is no external force Orbits cannot change spontaneously. Changing an Orbit So what can make an object gain or lose orbital energy? Friction or atmospheric drag A gravitational encounter. Escape Velocity If you want to leave Earth never to return, you must give your spaceship a high enough velocity so it will...

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