Gravitational Fields Research Papers - Academia.edu (original) (raw)

Economical recursion formulas for the earth's gravitational potential and its partial derivatives with respect to the Cartesian coordinates, and time are established for any number and any type of the harmonic coefficients. General... more

Economical recursion formulas for the earth's gravitational potential and its partial derivatives with respect to the Cartesian coordinates, and time are established for any number and any type of the harmonic coefficients. General computational algorithms are also given for their implementations on digital computers.

Since more than a decade, a bi-scale, unified approach to strong and gravitational interactions has been proposed that uses the geometrical methods of general relativity, and yielded results similar to 'strong gravity' theories. We fix... more

Since more than a decade, a bi-scale, unified approach to strong and gravitational interactions has been proposed that uses the geometrical methods of general relativity, and yielded results similar to 'strong gravity' theories. We fix our attention on hadron structure, and show that also the strong interaction strength alpha(sub S), ordinarily called the '(perturbative) coupling-constant square', can be evaluated within our theory, and found to decrease (increase) as the 'distance' r decreases (increases). This yields both the confinement of the hadron constituents (for large values of r) and their asymptotic freedom (for small values of r inside the hadron), in qualitative agreement with the experimental evidence. In other words, our approach leads us, on a purely theoretical ground, to a dependence of alpha(sub S) on r which had been previously found only on phenomenological and heuristic grounds. We expect the above agreement to be also quantitative, on the basis of a few checks performed in this paper, and of further work of ours about calculating meson mass-spectra.

Development of a new approach to the solution of the coplanar problem of a satellite orbiting two primaries. First, the stability of the libration points is discussed, by examining weak variations of a topological surface. Collinear... more

Development of a new approach to the solution of the coplanar problem of a satellite orbiting two primaries. First, the stability of the libration points is discussed, by examining weak variations of a topological surface. Collinear points are shown to reside on local maxima, while triangular points reside on local minima of this surface. Second, a conjecture is made concerning the correctness of the gravity potential, and canonical classification is discussed from the viewpoint of simplifying the governing partial differential equations. A transformation is constructed which reduces these equations to an inhomogeneous Laplace equation describing the satellite's motion. An inverse procedure, coupled with this approach, generates an unknown gravity potential for a known satellite trajectory. This potential must solve an inhomogeneous wave equation.

: Gravity field approximation using the predictors of Bjerhammer and Hardy is investigated. In the Bjerhammar method, a finite number of observations is given and it is required to compute a disturbing potential which is harmonic down to... more

: Gravity field approximation using the predictors of Bjerhammer and Hardy is investigated. In the Bjerhammar method, a finite number of observations is given and it is required to compute a disturbing potential which is harmonic down to a sphere fully internal to the Earth, regular at infinity and it satisfies all the observations. In the Hardy method, a particular family of density anomaly functions is selected which, together with its normal derivatives, vanishes at the boundary. The resulting disturbing potential is non-singular at points that induce potential. Both methods can use any linear functional of the disturbing potential as observation and/or quantity to be predicted. Both predictors were tested with the White Sands test data. Reference field and residual terrain model effects were removed from the observations and they were restored at the control stations after the predictions were performed. The best gravity anomaly predictions with both methods were performed with ...

The relative velocity between objects with finite velocity affects the reaction between them. This effect is known as general Doppler effect. The Laser Interferometer Gravitational-Wave Observatory (LIGO) discovered gravitational waves... more

The relative velocity between objects with finite velocity affects the reaction between them. This effect is known as general Doppler effect. The Laser Interferometer Gravitational-Wave Observatory (LIGO) discovered gravitational waves and found their speed to be equal to the speed of light c. Gravitational waves are generated following a disturbance in the gravitational field; they affect the gravitational force on an object.

Two approaches to the study of cosmological density perturbations in modified theories of Palatini gravity have recently been discussed. These utilize, respectively, a generalization of Birkhoff's theorem and a direct linearization of the... more

Two approaches to the study of cosmological density perturbations in modified theories of Palatini gravity have recently been discussed. These utilize, respectively, a generalization of Birkhoff's theorem and a direct linearization of the gravitational field equations. In this paper these approaches are compared and contrasted. The general form of the gravitational Lagrangian for which the two frameworks yield identical results in the long-wavelength limit is derived. This class of models includes the case where the Lagrangian is a power-law of the Ricci curvature scalar. The evolution of density perturbations in theories of the type f(R) = R - c/Rb is investigated numerically. It is found that the results obtained by the two methods are in good agreement on sufficiently large scales when the values of the parameters (b, c) are consistent with current observational constraints. However, this agreement becomes progressively poorer for models that differ significantly from the standard concordance model and as smaller scales are considered.

Astron. Astrophys. 230, 55-66 (1990) ASTRONOMY AND ASTROPHYSICS Stability of the Lagrangian points in stellar bars Daniel Pfenniger Geneva Observatory, CH- 1290 Sauverny, Switzerland Received October 9; accepted November 28, 1989... more

Astron. Astrophys. 230, 55-66 (1990) ASTRONOMY AND ASTROPHYSICS Stability of the Lagrangian points in stellar bars Daniel Pfenniger Geneva Observatory, CH- 1290 Sauverny, Switzerland Received October 9; accepted November 28, 1989 Abstract. The stability of the Lagrangian points is examined in the context of barred galaxies, and more generally, of asymmetric gravitational potentials. The stability conditions can be stated by three criteria, each one having a distinct physical meaning, involving the local second derivatives of the potential. A diagram (Fig. 1) shows ...

We analyze the temperature three--point correlation function and the skewness of the Cosmic Microwave Background (CMB), providing general relations in terms of multipole coefficients. We then focus on applications to large angular scale... more

We analyze the temperature three--point correlation function and the skewness of the Cosmic Microwave Background (CMB), providing general relations in terms of multipole coefficients. We then focus on applications to large angular scale anisotropies, such as those measured by the {\em COBE} DMR, calculating the contribution to these quantities from primordial, inflation generated, scalar perturbations, via the Sachs--Wolfe effect. Using the techniques of stochastic inflation we are able to provide a {\it universal} expression for the ensemble averaged three--point function and for the corresponding skewness, which accounts for all primordial second--order effects. These general expressions would moreover apply to any situation where the bispectrum of the primordial gravitational potential has a {\em hierarchical} form. Our results are then specialized to a number of relevant models: power--law inflation driven by an exponential potential, chaotic inflation with a quartic and quadratic potential and a particular case of hybrid inflation. In all these cases non--Gaussian effects are small: as an example, the {\em mean} skewness is much smaller than the cosmic {\em rms} skewness implied by a Gaussian temperature fluctuation field.