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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. - PowerPoint PPT Presentation
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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
• Gravitational potential energy increases as distance increases
• Kinetic energy decreases as distance increases• So, why do higher orbitals have more energy?
rGMmE
rGMm
rGMm
rGMmmvE
UKE
2
221 2
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
Escape velocity
• Minimum velocity needed to “escape” the gravitational force
RGMv
RGMmmv
UUKKE
i
i
ifif
2
0)0()210(
0)()(
2
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. Butthe kinetic energy does. Thus, a more massive rocketrequires more fuel.
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!
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’srotational velocity. Also want to launch along Earth’s orbitalpath, as well.
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!
Discovery Launch
• http://www.youtube.com/watch?v=4FROxZ5i67k
http://www.intothemusic.biz/wp-content/uploads/2010/04/space_shuttle_launch.jpg
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
Earth above km 36,000
km 000,424
4
32
2
2
3
2
GMTr
GMrT
Which satellites would you want to be geostationary?
• Spy satellites• Television satellites• GPS satellites• Cell phone satellites• Weather forecasting satellites
Kepler’s Laws
Orbits are elliptical
• Eccentricity = 0, then circular
• Eccentricity = 1 then linear
• Most planets have an eccentricity close to 0
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.
constantdtdA
Period-squared is proportional to a3
constant
4
v
3
2
32
2
22
2
aT
rGM
T
rGMr
rGM
Example Question: Earth Speed
• Where is the speed of the earth the greatest?
D
A C
B
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?
A) FasterB) SameC) SlowerD) Not enough information
Winter half is shorter and speed in winter is faster…
Main Points
• Satellites– Escape velocity depends on the gravitational field
of planet– Geostationary orbits 35,000 km from Earth
• Kepler’s Laws– Orbits are elliptical– Orbits sweep out equal area in equal time– Orbital period-squared is proportional at a3
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