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.

Newtonian View vs. Fields Newtonian MechanicsAction 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.

Gravitational Field Now we can use Gauss’s Law to calculate g.

Gauss’s Law Spherically symmetric system:

Gravity Field Density Field Inside constant density: Decreases like r Outside: Increases like 1/r 2

Constant Density Sphere Density Field Inside:Outside:

Wall A A A gg

Field from Direct Integration R z0z0

Limits R z0z0 If z 0 >> R: If z 0 << R: Like a point mass! Like a wall of mass!