Abstract
Orbital resonances continue to be one of the most difficult problems in celestial mechanics. They have been studied in connection with the so-called Kirkwood gaps in the asteroid belt for many years. On the other hand, resonant trans-Neptunian objects are also an active area of research in Solar System dynamics, as are the recently discovered resonances in extrasolar planetary systems. A careful monitoring of the trajectories of these objects is hindered by the small size of asteroids or the large distances of the trans-Neptunian bodies. In this paper, we propose a mission concept, called CHRONOS (after the greek god of time), in which a spacecraft could be sent to with the initial condition of resonance with Jupiter in order to study the future evolution of its trajectory. We show that radio monitoring of these trajectories could allow for a better understanding of the initial stages of the evolution of resonant trajectories and the associated relativistic effects.
Highlights
In recent years, the interest in spacecraft missions to study orbital dynamics in general relativity and other effects has soared, in part due to the discovery of some possible astrometric anomalies that challenge our current understanding of gravity [1,2]
One of the main predictions of the theory, i.e., gravity waves, have only been directly detected very recently [45,46], just a century after general relativity was cast into its final form by Einstein
It is surprising, in a certain sense, that even in the local environment of the Solar System there are tests that have not been completed to the precision required
Summary
The interest in spacecraft missions to study orbital dynamics in general relativity and other effects has soared, in part due to the discovery of some possible astrometric anomalies that challenge our current understanding of gravity [1,2]. But improved, have been used in subsequent versions [27] Another important issue concerning highly-accurate orbital integration over prolonged periods of time is the incorporation of relativistic corrections. This is a challenging problem that has pervaded the history of general relativity since its 1915 formulation. The paper is organized as follows: In Section 2, we propose a simple geometric model for the study of perturbations of a major planet on a spacecraft orbiting around the Sun. we consider the classical Newtonian effects and compare several methods of integration. The paper ends with a discussion on the interest of a mission designed to study celestial mechanics resonances
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