We provide in this paper the discrete equations of motion for the newtonian n-body problem deduced from the quantum calculus of variations (Q.C.V.) developed in [3, 4, 7, 8]. These equations are brought into the usual lagrangian and hamiltonian formulations of the dynamics and yield sampled functional equations involving generalized scale derivatives. We investigate especially homographic solut...

The goal of this paper is to demonstrate how the internal symmetry of the N-body celestial-mechanics problem can be exploited in orbit calculation. We start with summarising research reported in (Efroimsky 2002, 2003; Newman & Efroimsky 2003; Efroimsky & Goldreich 2003) and develop its application to planetary equations in non-inertial frames. This class of problems is treated by the variationo...

We consider the classical three-dimensional motion in a potential which is the sum of n attracting or repelling Coulombic potentials. Assuming a non-collinear configuration of the n centres, we find a universal behaviour for all energies E above a positive threshold. Whereas for n = 1 there are no bounded orbits, and for n = 2 there is just one closed orbit, for n ≥ 3 the bounded orbits form a ...

Applying the recently developed dynamical perturbation formalism on cosmological background to scalar-tensor theory, we provide a solid theoretical basis and a rigorous justification for phenomenological models of orbital dynamics that are currently used to interpret experimental measurements of the timedependent gravitational constant. We derive the field equations for the scalar-tensor pertur...

A high-school exercise is used to get an insight into planetary motion.