Newtonian Gravitation  

Theory > s.a. equivalence principle; models of spacetime structure.
* Idea: Bodies interact through a gravitational force Fg = G mg m'g/r2 acting at a distance, and accelerations are proportional to forces with proportionality constant equal to the inertial mass, a = F/mi.
* Masses: The force is proportional to the gravitational masses, but as Newton knew mg mi, which makes gravitation similar to "inertial" forces, in that the acceleration is independent of each body's individual characteristics.
* Potential: If we define (r) = U(r)/r for a test body, then the potential satisfies 2 = 4G ,

(r) = –G dM |rr'|–1 = –GM/rG D · r/r3 G Qij ri rj / r5 + ... ,

where D = dM r' is the dipole moment of the mass distribution (always zero wrt the center of mass), and Qij = dM [3 ri'rj'r' 2ij] the quadrupole moment (vanishes for a spherical mass distribution).
* Potential energy: For an extended body in an external field, U = (r) (r) d3r; The self-energy is

Uself =   (r) (r) d3r = (1/8G) ()3 d3r +  (r) (r) d3r .

@ References: in Ohanian & Ruffini 94; Deser AJP(05)gq/04 [from field theory]; Counihan EJP(07) [basic principles].

Special Topics > s.a. cosmology; gravitational constant; Newton's Theorem; teaching [weightlessness, tides].
* Tidal force: A mass m located at (x, y, z) with respect to a frame centered at a point a distance r0 away from a center of attraction of mass M, feels a tidal force

Fx = –x (GMm/r03) ,   Fy = –y (GMm/r03) ,   Fz = 2z (GMm/r03) ;

In general relativity the expression is more complicated, uses the equation for geodesic deviation.
* Other formulations: A (slightly generalized) geometric version is the Newton-Cartan theory.
@ N-body problem: Volchan a0803 [Sundman-Weierstrass theorem of total collapse].
@ Other situations: Odagaki & Kawai AJP(98) [many-particle statistics]; Beig & Schmidt PRS(03)gq/02 [self-gravitating extended bodies]; Teixeira phy/03 [infinite straight line of mass]; Buchert PLA(06)gq/05 [self-gravitating dust]; Masi AJP(07) [compressive radial tidal forces].
@ Other formulations and issues: De Pietri et al gq/92, CQG(95)gq/94, CQG(95)gq/94 [generalization]; Nardone JPA(98) [regularization]; Natario GRG(06)gq/04 [initial value form, and warp drive].

Phenomenology > s.a. cosmological models; phenomenology of gravity; modifications and tests of newtonian gravity.
@ Effects: Abramowicz et al GRG(97) [curvature of space and perihelion precession].
@ Measurement: Kulikov qp/05 [transparency of cold atoms]; > s.a. Eötvös Experiment; fifth force.
> Other: see critical collapse; orbits in newtonian gravity.


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