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Gravity. Gravitational Field. Interpretation: Gravitational Field is the force that a test particle would feel at a point divided by the mass of the test particle. Why bother?. Newtonian View vs. Fields. Newtonian Mechanics. Action at a Distance. Fields. Local interactions.
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Gravitational Field Interpretation: Gravitational Field is the force that a test particle would feelat a point divided by the mass of the test particle. Why bother?
Newtonian View vs. Fields Newtonian Mechanics Action at a Distance Fields Local interactions All particles generate fields; test particle interacts with local field.
Fields Fields: • Can have finite propagation speeds (static fields are long time consequences of dynamics fields). • Can store and transmit energy and momentum. • Are needed for relativistic quantum mechanics and dynamics. • Are needed for general relativity and gravitational radiation.
Now we can use Gauss’s Law to calculate g. Gravitational Field
Gauss’s Law Spherically symmetric system:
Gravity Field Field Density Inside constant density: Decreases like r Outside: Increases like 1/r2
Constant Density Sphere Field Density Inside: Outside:
Wall g g A A A
z0 R Field from Direct Integration
z0 R Limits If z0 >> R: Like a point mass! If z0 << R: Like a wall of mass!