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Transcript of Copyright © 2012 Pearson Education Inc. Orbital motion, final review Physics 7C lecture 18 Thursday...
![Page 1: Copyright © 2012 Pearson Education Inc. Orbital motion, final review Physics 7C lecture 18 Thursday December 5, 8:00 AM – 9:20 AM Engineering Hall 1200.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649eef5503460f94bffb66/html5/thumbnails/1.jpg)
Copyright © 2012 Pearson Education Inc.
Orbital motion, final review
Physics 7C lecture 18
Thursday December 5, 8:00 AM – 9:20 AMEngineering Hall 1200
![Page 2: Copyright © 2012 Pearson Education Inc. Orbital motion, final review Physics 7C lecture 18 Thursday December 5, 8:00 AM – 9:20 AM Engineering Hall 1200.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649eef5503460f94bffb66/html5/thumbnails/2.jpg)
Copyright © 2012 Pearson Education Inc.
Newton’s law of gravitation
• The gravitational force can be
expressed mathematically as
• Fg = Gm1m2/r2,
• where G is the gravitational
constant. Note G is different from
g.
• G = 6.67 E -11 N m2/kg2
![Page 3: Copyright © 2012 Pearson Education Inc. Orbital motion, final review Physics 7C lecture 18 Thursday December 5, 8:00 AM – 9:20 AM Engineering Hall 1200.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649eef5503460f94bffb66/html5/thumbnails/3.jpg)
Copyright © 2012 Pearson Education Inc.
Gravitation and spherically symmetric bodies
• The gravitational interaction of bodies having spherically symmetric mass distributions is the same as if all their mass were concentrated at their centers.
• This is exact, not approximation! Let’s prove it mathematically.
![Page 4: Copyright © 2012 Pearson Education Inc. Orbital motion, final review Physics 7C lecture 18 Thursday December 5, 8:00 AM – 9:20 AM Engineering Hall 1200.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649eef5503460f94bffb66/html5/thumbnails/4.jpg)
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Gravitational potential energy
• The gravitational potential energy of a system consisting of a particle of mass m and the earth is U = –GmEm/r.
• This assumes zero energy at infinite distance.
![Page 5: Copyright © 2012 Pearson Education Inc. Orbital motion, final review Physics 7C lecture 18 Thursday December 5, 8:00 AM – 9:20 AM Engineering Hall 1200.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649eef5503460f94bffb66/html5/thumbnails/5.jpg)
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The motion of satellites
• The trajectory of a projectile fired from A toward B depends on its initial speed. If it is fired fast enough, it goes into a closed elliptical orbit (trajectories 3, 4, and 5 in Figure 13.14 below).
![Page 6: Copyright © 2012 Pearson Education Inc. Orbital motion, final review Physics 7C lecture 18 Thursday December 5, 8:00 AM – 9:20 AM Engineering Hall 1200.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649eef5503460f94bffb66/html5/thumbnails/6.jpg)
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Circular satellite orbits • For a circular orbit, the speed of a satellite is just right to keep its distance
from the center of the earth constant. (See Figure 13.15 below.)
• A satellite is constantly falling around the earth. Astronauts inside the satellite in orbit are in a state of apparent weightlessness because they are falling with the satellite. (See Figure 13.16 below.)
• Follow Example 13.6.
![Page 7: Copyright © 2012 Pearson Education Inc. Orbital motion, final review Physics 7C lecture 18 Thursday December 5, 8:00 AM – 9:20 AM Engineering Hall 1200.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649eef5503460f94bffb66/html5/thumbnails/7.jpg)
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Kepler’s laws and planetary motion
• Each planet moves in an elliptical orbit with the sun at one focus.
![Page 8: Copyright © 2012 Pearson Education Inc. Orbital motion, final review Physics 7C lecture 18 Thursday December 5, 8:00 AM – 9:20 AM Engineering Hall 1200.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649eef5503460f94bffb66/html5/thumbnails/8.jpg)
Copyright © 2012 Pearson Education Inc.
Kepler’s laws and planetary motion
• A line from the sun to a given planet sweeps out equal areas in equal times (see Figure at the right).
![Page 9: Copyright © 2012 Pearson Education Inc. Orbital motion, final review Physics 7C lecture 18 Thursday December 5, 8:00 AM – 9:20 AM Engineering Hall 1200.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649eef5503460f94bffb66/html5/thumbnails/9.jpg)
Copyright © 2012 Pearson Education Inc.
Kepler’s laws and planetary motion
• The periods of the planets are proportional to the 3/2 powers of the major axis lengths of their orbits.
![Page 10: Copyright © 2012 Pearson Education Inc. Orbital motion, final review Physics 7C lecture 18 Thursday December 5, 8:00 AM – 9:20 AM Engineering Hall 1200.](https://reader030.fdocuments.in/reader030/viewer/2022032805/56649eef5503460f94bffb66/html5/thumbnails/10.jpg)
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Some orbital examples• The orbit of Comet Halley. See Figure below.
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A point mass inside a spherical shell
• If a point mass is inside a spherically symmetric shell, the potential energy of the system is constant. This means that the shell exerts no force on a point mass inside of it.
what is the motion of the small ball?
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Copyright © 2012 Pearson Education Inc.
A point mass inside a spherical shell
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Black holes • If a spherical nonrotating body has radius less than the Schwarzschild radius,
nothing can escape from it. Such a body is a black hole. (See Figure 13.26 below.)
• The Schwarzschild radius is RS = 2GM/c2.
• The event horizon is the surface of the sphere of radius RS surrounding a black hole.
• Follow Example 13.11.
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Detecting black holes
• We can detect black holes by looking for x rays emitted from their accretion disks. (See Figure below.)
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Review for final exam