Estimation of the Yarkovsky effect on the example of the asteroid 1685 Toro (1948 OA)

On the example of 1685 Toro, secular drifts of orbital elements and the displacement from the unperturbed position were obtained using the analytical solution of the averaged equations of motion of the asteroid in the central gravitational field and additional perturbing acceleration, inversely proportional to the square of the distance to the Sun, in the frame of reference associated with the radius vector. The components of this acceleration are calculated based on the thermophysical characteristics of 1685 Toro within the framework of the Yarkovsky acceleration linear model for spherical asteroids.

Oscillating Cosmological Force Modifies Newtonian Dynamics

In the Newtonian limit of general relativity a force acting on a test mass in a central gravitational field is conventionally defined by the attractive Newtonian gravity (inverse square) term plus a small repulsive cosmological force, which is proportional to the slow acceleration of the universe expansion. In this paper we considered the cosmological-force correction due to fast quantum oscillations of the universe scale factor as a potential solution of the cosmological constant problem. These fast fluctuations of the cosmological scale factor violate Lorentz invariance at the Planck scale, and they induce strong changes to the current sign and magnitude of the average cosmological force, thus making it one of the potential probable causes for the modification of Newtonian dynamics in galaxy-scale systems. The modified cosmological force may be responsible for the recently discovered “cosmic-clock” behavior of disk galaxies in the low-redshift universe. The obtained results have strong implications for astroparticle physics since they demonstrate that typical galaxy rotation curves may be obtained without (or almost without) dark-matter particles.

TRANSLATIONAL-ROTATIONAL MOTION OF THE TRIAXIAL BODY WITH VARIABLE COMPRESSIONS IN THE PRESENCE OF REACTIVE FORCES AND MOMENTS

In this paper we investigated the translational-rotational motion of a triaxial body of constant dynamic shape and variable mass and size in a non-stationary Newtonian central gravitational field. Differential equations of the translationalrotational motion of the triaxial non-stationary body in the relative coordinate system with the origin at the center of a non-stationary spherical body are derived. The axes of the own coordinate system of the non-stationary triaxial body are directed along the principle axes of inertia of the body and we assumed that in the course of evolution their relative orientation remains unchanged. An analytical expression for the force function of the Newtonian interaction of the triaxial body of variable mass and size with a spherical body of variable size and mass is given. In the presence of reactive forces and moments the equations of translational-rotational motion of a triaxial non-stationary body in osculating elements are obtained in the presence of reactive forces and moments.

On the motion of bodies based on changes in the kinetic moment

The controlled motion of a body in a central gravitational field without mass flow is considered. The possibility of moving the body in the radial direction from the center of attraction due to changes in the kinetic moment relative to the center of mass of the body is shown. A scheme for moving the body using a system of flywheels located in the same plane in near-circular orbits with different heights is proposed. The use of the spin of elementary particles is considered as flywheels. It is proved that using the spin of elementary particles with a Compton wavelength exceeding the distance to the attracting center is energetically more profitable than using the momentum of these particles to move the body. The calculation of motion using hypothetical particles (gravitons) is presented. A hypothesis has been put forward about the radiation of bodies during accelerated motion, which finds indirect confirmation in stellar dynamics and in an experiment with the fall of two bodies in a vacuum. The results can be used in experiments to search for elementary particles with low energy, explain cosmic phenomena and to develop transport objects on new physical principles.

Testing the \(f(R)\)-theory of Gravity

A procedure of testing the \(f(R)\)-theory of gravity is discussed. The latter is an extension of the general theory of relativity (GR). In order this extended theory (in some variant) to be really confirmed as a more precise theory it must be tested. To do that we first have to solve an equation generalizing Einstein's equation in the GR. However, solving this generalized Einstein's equation is often very hard, even it is impossible in general to find an exact solution. It is why the perturbation method for solving this equation is used. In a recent work \cite{Ky:2018fer} a perturbation method was applied to the $f(R)$-theory of gravity in a central gravitational field which is a good approximation in many circumstances. There, perturbative solutions were found for a general form and some special forms of \(f(R)\). These solutions may allow us to test an \(f(R)\)-theory of gravity by calculating some quantities which can be verified later by the experiment (observation). In \cite{Ky:2018fer} an illustration was made on the case \(f(R)=R+\lambda R^2\). For this case, in the present article, the orbital precession of S2 orbiting around Sgr A* is calculated in a higher-order of approximation. The $f(R)$-theory of gravity should be also tested for other variants of $f(R)$ not considered yet in \cite{Ky:2018fer}. Here, several representative variants are considered and in each case the orbital precession is calculated for the Sun--Mercury- and the Sgr A*--S2 gravitational systems so that it can be compared with the value observed by a (future) experiment. Following the same method of \cite{Ky:2018fer} a light bending angle for an $f(R)$ model in a central gravitational field can be also calculated and it could be a useful exercise.