Wave Physics PHYS2023phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_15.pdf•Nevil Maskelyne...
Transcript of Wave Physics PHYS2023phyweb.phys.soton.ac.uk/quantum/lectures/cm/cm20_15.pdf•Nevil Maskelyne...
PHYS 2006
Tim Freegarde
Classical Mechanics
15 Gravitation2020-21
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Classical Mechanics
LINEAR MOTION OF
SYSTEMS OF PARTICLESNewton’s 2nd law for bodies (internal forces cancel)
rocket motion
ANGULAR MOTION
rotations and infinitessimal rotations
angular velocity vector, angular momentum, torque
centre of mass
parallel and perpendicular axis theorems
rigid body rotation, moment of inertia, precession
GRAVITATION &
KEPLER’S LAWS
conservative forces, law of universal gravitation
2-body problem, reduced mass
NON-INERTIAL
REFERENCE FRAMES
centrifugal and Coriolis terms
Foucault’s pendulum, weather patterns
NORMAL MODESboundary conditions, Eigenfrequencies
coupled oscillators, normal modes
planetary orbits, Kepler’s laws
energy, effective potential
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Newton’s law of Universal Gravitation
• Exact analogy of Coulomb electrostatic interaction
• gravitational force between two masses and
• gravitational field
• gravitational potential • gravity is a CENTRAL FORCE (acts along line joining masses)
• spherically-symmetric central forces are CONSERVATIVE
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Gravitational PE near the Earth’s surface
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Inverse-square law forces
Coulomb Gravity
charge mass
coupling coupling
potential potential
electric field gravitational field
charge density mass density
Gauss’s law Gauss’s law
Gauss’s law Gauss’s law
potential energy per unit mass
potential energy per unit charge
force per unit mass
force per unit charge
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Gravity anomaly
•
• local depends upon • altitude
• latitude (spheroid, centrifugal force)
• local material density
• tides
• phase of Moon
• gravity map typically shows Bouguer anomaly
• difference from value expected for uniform smooth ellipsoid
• corrected for altitude
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Gravity anomaly
• gravity anomaly = variation from uniform solid
•
NASA/JPL/University of Texas Center for Space Research
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Schiehallion – estimate of mass of the Earth
WalkHighlands
Wikipedia
• Nevil Maskelyne (Astronomer Royal) 1774
• 11.6” difference between north & south
• concluded Earth density 4,500 kg m-3 (20% low)
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Gravimetry
MuquansWikipedia
• quartz spring balance
• 5 μGal
• atom matterwave interferometry
• 1 μGal
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Newton’s law of Universal Gravitation
• Exact analogy of Coulomb electrostatic interaction
• gravitational force between two masses and
• gravitational field
• gravitational potential
SCALAR
VECTOR
• scalar addition may be simpler than vector addition
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Gravitational attraction of a spherical shell
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Gravitational attraction of a spherical shell
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Gravitational attraction of a spherical shell
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Gravitational attraction of a spherical shell
• Exact analogy of Coulomb interaction
• gravitational field
• gravitational potential
• gravitational force between two masses
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Galilean equivalence principle
inertial mass
• gravitational field
• gravitational motion of mass
Apollo 15, David R Scott (7 August 1971) www.youtube.com/watch?v=MJyUDpm9Kvk
history.nasa.gov/alsj/a15/a15.clsout3.htmlnssdc.gsfc.nasa.gov/planetary/lunar/apollo_15_feather_drop.html
the trajectory of a point-like mass in a gravitational field is independent of the composition and structure of the mass
gravitational mass
• equivalence principle
inertial mass = gravitational mass
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Newton’s law of Universal Gravitation
• Exact analogy of Coulomb electrostatic interaction
• gravitational force between two masses and
• gravitational field
• gravitational potential
• a spherically-symmetric mass distribution will have the same external field as a point mass of equal magnitude at the sphere’s centre
• inertial mass = gravitational mass
PHYS 2006
Tim Freegarde
Classical Mechanics