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Chapter 7 Gravity

Chapter 7 Gravity. Planetary Motion based on Kepler’s Laws First Law- all the planets orbits are ellipses with the sun at one focus http://zebu.uoregon.edu/~soper/Orbits/kepler1.html. Con. Second Law- a line joining a planet to the sun sweeps out equal areas in equal times

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Chapter 7 Gravity

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  1. Chapter 7 Gravity Planetary Motion based on Kepler’s Laws • First Law- all the planets orbits are ellipses with the sun at one focus http://zebu.uoregon.edu/~soper/Orbits/kepler1.html

  2. Con. • Second Law- a line joining a planet to the sun sweeps out equal areas in equal times http://csep10.phys.utk.edu/astr161/lect/history/kepler.html

  3. Con. • Third Law- the square of the ratio of the periods of any two planets is equal to the cube of the ratio of the average distances from the sun. (TA/TB)2 = (rA/rB)3 T= period r= average distance http://jersey.uoregon.edu/vlab/kepler/Kepler.html

  4. Example The moon has a period of 27.3 days and a mean distance of 3.9x105 km from the center of the Earth. • Find the period of a satellite in orbit 6.70x103 km from the center of the Earth. • How far above the Earth’s surface is this satellite?

  5. Newton’s Law of Universal Gravitation • Gravitational Force-force of attraction between 2 objects is proportional to the objects’ masses • Law of Universal Gravitation- objects attract other objects with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them or

  6. Con. F= Gm1m2 r2 where r=distance between the centers of objects G= universal gravitation constant = 6.67x10-11 N•m2/kg2 http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/circles/u6l3c.html

  7. How does the Law of Universal Gravitation and Kepler’s Third Law relate to each other? F=ma  Fnet= mpac Force is gravitational force ac is the centripetal acceleration of a planet Remember ac = 42r/T2  Fnet= mp(42r/T2 )

  8. Con. Gmsmp = mp42r r2 T2 T2 = 42r3 Gms so T =  42r3 Gms T= 2  r3/Gms

  9. Using the Law of Universal Gravitation Fnet= mac Fnet= mv2/r Plug in G for Fnet GmEm = mv2 r2 r Solve for v so v= GmE/r And T= 2r3/GmE

  10. Example A satellite orbits the Earth 225 km above its surface. Given the mass of the Earth equals 5.97x1024 kg and the radius equals 6.38 x106 m, what are the satellite’s velocity and period?

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