相关论文: Hill's Lunar Equations, Series, Convergence, Motio…
A simple and clear method is proposed to calculate the averaged motion of the apsis line in the Moon orbit. The obtained result is $3^{\circ}1'12''$ for the starry period of the Moon revolution around the Earth or $40^{\circ}22'48''$ per…
We consider the planar Hill's lunar problem with a homogeneous gravitational potential. The investigation of the system is twofold. First, the starting conditions of the trajectories are classified into three classes, that is bounded,…
In his study of periodic orbits of the 3 body problem, Hill obtained a formula relating the characteristic polynomial of the monodromy matrix of a periodic orbit and an infinite determinant of the Hessian of the action functional. A…
The perturbation of the lunar motion caused by a hypothetical violation of the equivalence principle is analytically worked out in terms of power series \`a la Hill-Brown. The interaction with the quadrupolar tide is found to amplify the…
The motion of a satellite around a planet can be studied by the Hill model, which is a modification of the restricted three body problem pertaining to motion of a satellite around a planet. Although the dynamics of the circular Hill model…
In this paper we represent a different approach to the calculation of the perihelion shift than the one presented in common text books. We do not rely on the Schwarzschild metric and the Hamilton Jacobi technique to obtain our results.…
Prior to the invention of the telescope many astronomers worked out theories of the motion of the Moon. The purpose of such theories was to be able to predict the position of the Moon in the sky. These geometrical models implied a certain…
We derive Copernicus's epicycles from Newton's gravitational force law by assuming that a planet's orbit is a perturbed circular orbit, with the perturbation defined to be co-rotating with the said orbit. We substitute this orbit expression…
For a family of second-order elliptic systems in divergence form with rapidly oscillating almost-periodic coefficients, we obtain estimates for approximate correctors in terms of a function that quantifies the almost periodicity of the…
We solve the geodesic deviation equations for the orbital motions in the Schwarzschild metric which are close to a circular orbit. It turns out that in this particular case the equations reduce to a linear system, which after…
We deduce a new formula for the perihelion advance of a test particle in the Schwarzschild black hole by applying a newly developed non-linear transformation within the Schwarzschild space-time. By this transformation we are able to apply…
In this work, we study the continuation of a periodic orbit on a relatively large scale and discover the existence of convergence under certain conditions, which has profound significance in research on asteroids and can provide a total…
By applying Monte-Carlo method, the Moon radius is obtained by counting craters in a spherical square over the surface of it. As it is well known, approximate values for $\pi $ can be obtained by counting random numbers in a square and in a…
I derived an equation to describe the dependence of Moon orbit radius around the Earth. I obtained the radius changes with time according to a scaling equation, Moon orbit radius is proportional to power 2/5 of the Moon age. Using the…
The non-integrability of the Hill problem makes that its global dynamics must be necessarily approached numerically. However, the analytical approach is feasible in the computation of relevant solutions. In particular, the nonlinear…
In this work we study the geodesic motion on a noncommutative space-time. As a result we find a non-commutative geodesic equation and then we derive corrections of the deviation angle per revolution in terms of the non-commutative parameter…
The equations of motion of a secularly precessing ellipse are developed using time as the independent variable. The equations are useful when integrating numerically the perturbations about a reference trajectory which is subject to secular…
Lam\'e's differential equation is a linear differential equation of the second order with a periodic coefficient involving the Jacobian elliptic function ${\rm sn}$ depending on the modulus $k$, and two additional parameters $h$ and $\nu$.…
In this article we consider the existence of a family of doubly-symmetric periodic orbits in the spatial circular Hill's lunar problem, in which the secondary primary at the origin is oblate. The existence is shown by applying a fixed point…
Einstein's perihelion advance formula can be given a geometric interpretation in terms of the curvature of the ellipse. The formula can be obtained by splitting the constant term of an auxiliary polar equation for an elliptical orbit into…