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A local system of bodies in General Relativity whose exterior metric field asymptotically approaches the Minkowski metric effaces any effects of the matter distribution exterior to the Minkowski boundary condition. To enforce to all orders this property of gravity which appears to hold in nature, a method using linear algebraic scaling equations is developed, which generates by an iterative process an Nbody Lagrangian expansion for gravity’s motion-independent potentials, which fulfills the exterior effacement. The algebraic method is then applied in this first of two papers to produce the motion-independent N-body gravity Lagrangian to the 1/c4 order of expansion. A subsequent paper supplements exterior effacement conditions with others—interior effacement and Lorentz time dilation and spatial contraction—to create additional iterative algebraic equations for obtaining the nonlinear, motion-dependent N-body gravity Lagrangian potentials as well. The scaling conditions developed in these papers may also serve as validation checks on more traditional determinations of higher-order gravity which employ perturbative solutions of gravity’s nonlinear field equations.

In the companion paper [1], iterative algebraic scaling equations were developed which yield motion-independent potentials to all non-linear orders for gravity’s N-body Lagrangian which enforce exterior effacement—that local gravity expressed in local proper coordinates is not affected by the distribution of matter in the universe exterior and far from the local system of bodies. This paper deals with determination of the motion-dependent potentials of gravity’s N-body Lagrangian. Additional algebraic scaling conditions are developed for this purpose which exploit other invariances desired for gravity—that a local gravitational system must have dynamics which manifest Lorentz time dilation and spatial contractions upon boosts and does not reveal a preferred inertial frame in the cosmos; and additionally, for composite body sources, interior effacement is enforced in which only a single total mass-energy parameter represents the body in its spherical limit in all N-body Lagrangian potentials. Iterative algebraic equations for enforcing these conditions as well as the exterior effacement condition are applied to obtain a 1/c4 order N-body Lagrangian for gravity.

Few facts in science are more surprising and none has had a longer history than the apparent equivalence of the two kinds of mass in physics, gravitational and inertial. From Galileo and Newton to Eotvos and Einstein, it has been a compelling issue both theoretically and experimentally. Ground-based tests have now a precision of about 1 part in 10 12 . Even with this extraordinary agreement, there are profound theoretical reasons for carrying the measurements further. Our generation has the unique oppurtunity to make an advance of a factor of a million in testing the Equivalence Principle in space.

Equality of the rate of acceleration of Earth and Moon by the Sun is confirmed to 5×10 −13 using laser ranging data. This experiment not only matched those in the laboratory in showing composition-independence of gravity's acceleration, but it also has become the tightest constraint on general relativity's 1/c 2 order, non-linear structure which couples the Sun's accelerating gravity to the Earth's internal gravitational binding energy. But the ability of LLR data to test theory at even higher levels of precision is restrained by presence of systematic range residual signals from unmodeled physics. This suggests the need for a new priority and approach — redesigning the data-fitting hypotheses for mapping out the unmolded signal, whatever its source, rather than simply trying to fit for a pre-defined relativity signal. Initial work in this direction is described. The goal is model improvement and the ability to measure gravity theory signals closer to the inherent noise limits of the data, being in this case a factor 4 or 5 smaller than the present ‘realistic uncertainties’ allowed for incomplete modeling.

Earth-Mars radar ranging data such as produced in the ‘Viking’ mission can be used to measure two effects from relativistic gravity, both comparably sensitive to alternative theory parameters — the radar propagation delay signal proportional to Eddington parameter 1 + γ, and a polarization of the Earth and Mars orbits toward Jupiter proportional to 4β − 3 − γ and indicating anomalous gravitational to inertial mass ratio of the sun. When the two are considered together, inspection of the ranging experiment's covariance matrix finds that well mixed combinations of the two theory parameters γ, β, not the two separate effects, are independent observables. Measurement precision of these parameters are independent observables. Measurement precision of these parameters are tabulated for some past and future cases. A ‘correlated data filter’ is described which can reduce systemic errors in Earth-Mars range produced by unmodeled asteroid perturbations.

We have corrected our calculation of the finite general relativistic contribution to the synodic month period Earth-Moon range oscillation by including previously overlooked terms in the Moon's post-Newtonian equation of motion: the corrected result $x(t)\ensuremath{\simeq}(\frac{3{g}_{S}{r}^{2}}{{c}^{2}})cos(\ensuremath{\omega}\ensuremath{-}\ensuremath{\Omega})t$ agrees with the Shahid-Saless calculation which was performed in the geocentric frame. It is also pointed out that at the level of a few millimeters synodic month period amplitude, the Moon's orbit is polarized by the solar radiation pressure force on the Moon.

The general possibilities for cosmological time evolution in the Newtonian dynamics of compact celestial bodies - bodies with significant gravitational self-energy (binding energy) - are developed. In the momentum-conserving cases the general form of the Newtonian-level equation of motion is d/dt[m i (t)dr i /dt]=G(t)Σ j¬=i K ij (t)m i (t)m j (t)r ji /r 3 ij with three possible time-evolving entities: (1) a universal coupling parameter G(t); (2) compact body inertial masses; (3) a body-dependent coupling parameter. Only G(t) persists as a significant time-evolving factor in the dynamics of noncompact bodies such as the solar system planets

In the 'fourth test of general relativity' the gravitational acceleration of celestial bodies-the Earth and the Moon-were experimentally compared in the gravitational field of the Sun. Because such bodies obtain an appreciable fraction of their total mass-energy from their internal gravitational self-energy (5*10-10 for the Earth), this comparison of free-fall rates measures, among other things, how gravity pulls on gravitational energy and how gravitational energy contributes to the inertial mass of celestial bodies. Using high-precision laser ranging between Earth and reflectors on the Moon's surface, it was found that the Earth and Moon's acceleration in the Sun's gravitational field are the same to one part in 1011. Hypothesising that the gravitational to inertial mass ratio of a celestial body may differ from one by the order of the gravitational self-energy content of the body divided by the total mass-energy: MG/MI=1+ eta (UG/Mc2) eta being a dimensionless constant determined by gravitational theory, the lunar laser ranging experiment limits mod eta mod to less than 1.4*10-2. This experiment is consistent with general relativity which predicts eta =0, but scalar-metric tensor theories, such as the Brans-Dicke theory, vector-metric tensor theories and two-tensor theories of gravity are inconsistent with this experiment unless sufficient adjustable parameters are used.

This work develops a straightforward technique for giving an upper bound to any eigenvalue of the one dimensional Sturm‐Liouville problem. It is shown that any trial function that fulfills the proper boundary condition of the problem and possesses the same number of nodes as an exact eigenfunction of the problem can provide an upper bound to that eigenfunction's eigenvalue. Application of the above technique is made to provide a one‐sided bound to quantum mechanical scattering phase shifts.

Exact solutions of the general relativistic field equations of Einstein and Maxwell have been found for a general static distribution of massive charged particles. As in the Newtonian case, the particles must have unit charge to mass ratioe2/m2=1. The active gravitational mass of the system of particles is precisely the sum of individual masses of the constituent particles.

Quantum-electrodynamic renormalization for electron charge in metal environment, using solid state many-body techniques

If cosmological structure is the result of two metrical tensor fields, causal structure is surprisingly modified with signals traveling faster than light and effects preceding causes when viewed by certain inertial observers. Metrical structure is seen to be a property of matter rather than an attribute of the “space‐time” four‐dimensional event continuum.

The post-Newtonian, relativistic (1/c/sup 2/) tidal force is calculated within the general PPN framework of all metric theories of gravity. There are no relativistic tides in general relativity, but they are generally nonzero in other metric theories of gravity, including scalar-tensor theories. In close binaries (GM/c/sup 2/Rroughly-equal10/sup -6/), such as the binary pulsar system PSR 1913+16, the relativistic tides can be orders of magnitude larger than Newtonian tides. In ''preferred frame'' theories of gravity in which the PPN coefficient ..cap alpha../sub 1/ is nonzero, the relativistic tidal field is not the gradient of a scalar potential, but includes also a circulating, nonconservative field in a body.

If anisotropic post-Newtonian metric potentials exist, celestial bodies will possess anisotropic inertial and/or gravitational masses. The binary pulsar system PSR 1913+16 puts stringent limits on such anisotropies through its observable perihelion precession rate and hence offers a Hughes-Drever-type experiment for massive celestial bodies. (AIP)

Le formalisme lagrangien a plusieurs corps developpe par Nordtvedt (1985, Ap. J., 297) est utilise pour developper une extension du premier lagrangien post-newtonien pour les corps celestes compacts en interaction via une theorie metrique de la gravite. Le lagrangien est etendu au second ordre dans le mouvement des corps mais est lineaire dans les potentiels. Une hierarchie d'invariances de Lorentz est ensuite imposee sur ce lagrangien a «champ lineaire» et le lagrangien resultant ne depend que de la structure du premier lagrangien post-newtonien