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PHYS16 – Lecture 27

PHYS16 – Lecture 27. Gravitation November 10, 2010. This Week. Newton’s law of Gravity Gravitational Potential Energy Satellites Kepler’s Laws of Planetary Motion Orbital Shape Orbital Areas Orbital Period. Satellites. Orbital Energy.

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PHYS16 – Lecture 27

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  1. PHYS16 – Lecture 27 Gravitation November 10, 2010

  2. This Week • Newton’s law of Gravity • Gravitational Potential Energy • Satellites • Kepler’s Laws of Planetary Motion • Orbital Shape • Orbital Areas • Orbital Period

  3. Satellites

  4. Orbital Energy • Gravitational potential energy increases as distance increases • Kinetic energy decreases as distance increases • So, why do higher orbitals have more energy?

  5. Example Question: Satellite • A Satellite orbiting the Earth wants to go to a lower orbit. What should the satellite do? A) Nothing. It is falling toward the earth. B) Turn on rocket thrusters to accelerate, moving to lower orbital. C) Turn on rocket thrusters to decelerate, moving to a lower orbital

  6. Escape velocity • Minimum velocity needed to “escape” the gravitational force

  7. Trivia: Launching Rockets • When launching a rocket to escape the Earth’s gravity, does the mass of the rocket matter? Why or why not? The escape velocity does not depend on mass. But the kinetic energy does. Thus, a more massive rocket requires more fuel.

  8. Trivia: Launching Rockets • When launching a rocket to escape the Earth’s gravity, does the mass of the rocket matter? Why or why not? • Which planet has the smallest escape velocity? Mercury!

  9. Trivia: Launching Rockets • When launching a rocket to escape the Earth’s gravity, does the mass of the rocket matter? Why or why not? • Which planet has the smallest escape velocity? • Does the direction of launch from the earth matter? Why or why not? Want to launch eastward to take advantage of the Earth’s rotational velocity. Also want to launch along Earth’s orbital path, as well.

  10. Trivia: Launching Rockets • When launching a rocket to escape the Earth’s gravity, does the mass of the rocket matter? Why or why not? • Which planet has the smallest escape velocity? • Does the direction of launch from the earth matter? Why or why not? • What would be the escape velocity of a black hole? Infinity!

  11. Discovery Launch • http://www.youtube.com/watch?v=4FROxZ5i67k http://www.intothemusic.biz/wp-content/uploads/2010/04/space_shuttle_launch.jpg

  12. Geostationary Satellites • Satellites that have an orbital radius such that their period is the same as the period of the earth http://www.splung.com/kinematics/images/satellites/geostationary.png

  13. Which satellites would you want to be geostationary? • Spy satellites • Television satellites • GPS satellites • Cell phone satellites • Weather forecasting satellites

  14. Kepler’s Laws

  15. Orbits are elliptical • Eccentricity = 0, then circular • Eccentricity = 1 then linear • Most planets have an eccentricity close to 0

  16. Equal areas in equal times • The area of the triangle swept out by the object is equal for equal amounts of time • The further the object is from the sun the lower the speed.

  17. Period-squared is proportional to a3

  18. Example Question: Earth Speed • Where is the speed of the earth the greatest? B A C D

  19. Example Question: Seasons • If the earth spends two less days in the winter half of the orbit than the summer half of the orbit (for N. hemisphere), what is its speed in winter vs. summer? • Faster • Same • Slower • Not enough information Winter half is shorter and speed in winter is faster…

  20. Main Points • Satellites • Escape velocity depends on the gravitational field of planet • Geostationary orbits 35,000 km from Earth • Kepler’sLaws • Orbits are elliptical • Orbits sweep out equal area in equal time • Orbital period-squared is proportional at a3

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