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![Page 1: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/1.jpg)
-Energy Considerations in Satellite and Planetary Motion
-Escape Velocity-Black Holes
AP Physics CMrs. Coyle
![Page 2: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/2.jpg)
Tangential Velocity of an Orbiting Tangential Velocity of an Orbiting SatelliteSatellite
2
2
GmM mv
r r
GMv
r
![Page 3: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/3.jpg)
SatellitesSatellites
• At a certain r the speeds of the satellites are the same.
• Geosynchronous: satellite that have the same period as earth.
![Page 4: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/4.jpg)
Escape VelocityEscape Velocity
• The minimum speed required to launch an object from the earth’s surface in order for it to escape the earth’s pull.
![Page 5: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/5.jpg)
To find the escape velocity of an object use conservation of energy
Energy at Earth's surface= Energy at Infinity
i fE E
![Page 6: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/6.jpg)
For a Earth-Satellite System For a Earth-Satellite System
• Total energy E = K + U
• Note: in a bound system, E < 0
21
2
MmE mv G
r
![Page 7: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/7.jpg)
Escape VelocityEscape Velocity
2 2
2
1 1
2 2
10
2
i f
i fi f
ii
E E
GMm GMmmv mv
r r
GMmmv
r
esc
2GMv
R
![Page 8: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/8.jpg)
Escape VelocityEscape Velocity
• For any planet:
esc
2GMv
R
![Page 9: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/9.jpg)
Note:Note:–According to Newton’s Law of Universal
Gravitation the gravitational field even at infinity is does not equal to zero but approaches zero.
–Some planets have atmospheres and others do not because their escape velocities vary and some gas molecules have high enough speeds to escape.
![Page 10: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/10.jpg)
Two Particle Two Particle Bound SystemBound System
2 21 1
2 2
i f
i fi f
E E
GMm GMmmv mv
r r
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Energy in a Circular Orbit Energy in a Circular Orbit
21
2
MmE mv G
r
2
GMmE
r
Tangential GM
vr
![Page 12: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/12.jpg)
Note: Note: Energy in a Circular Orbit
• K>0 and is equal to half the absolute value of the potential energy.
• |E| = binding energy of the system.
• The total mechanical energy is negative.
![Page 13: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/13.jpg)
Energy in an Elliptical OrbitEnergy in an Elliptical Orbit• r= 2a=the
semimajor axis
2
GMmE
a
• The total mechanical energy,E is negative.
• E is constant if the system is isolated.
![Page 14: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/14.jpg)
Example #63a) Determine the amount of work (in Joules)
that must be done on a 100kg payload to elevate it to a height of 1,000km above the earth’s surface.
b) Determine the additional work required to put the payload into circular orbit at this elevation(The radius of the earth is 6.37x106 m, G=6.67x10-11 Nm2 / kg2)
Ans: a)8.50x108 J, b) 2.71x109 J
![Page 15: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/15.jpg)
Note: For a Two Particle Bound System
• Both the total energy• and
• the total angular momentum are constant.
![Page 16: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/16.jpg)
Compare the Kinetic Energy and Angular Momentum of a Satellite
at orbit 1 and 2
21
Earth
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How does the speed of a satellite at position 2 compare to the speed at
position 1. The distance r2 =2r1. (Hint: Use conservation of angular
momentum)
Earth 12
![Page 18: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/18.jpg)
Black HolesBlack Holes
• A black hole is the remains of a star that has collapsed under its own gravitational force
• The escape speed for a black hole is very large due to the concentration of a large mass into a sphere of very small radius– If the escape speed exceeds the speed of
light, radiation cannot escape and it appears black
![Page 19: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/19.jpg)
Black HolesBlack Holes• The radius at which the
escape speed equals the speed of light, c, is called the Schwarzschild radius, RS
• An imaginary surface of a sphere with this radius is called the event horizon.
• If an object is not closer than the Rs , it can still escape the black hole.
![Page 20: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/20.jpg)
Accretion DisksAccretion Disks Material from a nearby
star (in a binary system) can be pulled into the black hole and forms an accretion disk around the black hole.
![Page 21: -Energy Considerations in Satellite and Planetary Motion -Escape Velocity -Black Holes AP Physics C Mrs. Coyle.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649e895503460f94b8e839/html5/thumbnails/21.jpg)
Black Hole Video Clip
http://www.youtube.com/watch?v=hoLvOvGW3Tk&feature=player_embedded#!