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Register a new userSemi-analytical estimates for the orbital stability of Earths satellites
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Normal form stability estimates are a basic tool of Celestial Mechanics for characterizing the long-term stability of the orbits of natural and artificial bodies. Using high-order normal form constructions, we provide three different estimates for the orbital stability of point-mass satellites orbiting around the Earth. i) We demonstrate the long term stability of the semimajor axis within the framework of the $J_2$ problem, by a normal form construction eliminating the fast angle in the corresponding Hamiltonian and obtaining $H_{J_2}$ . ii) We demonstrate the stability of the eccentricity and inclination in a secular Hamiltonian model including lunisolar perturbations (the geolunisolar Hamiltonian $H_{gls}$), after a suitable reduction of the Hamiltonian to the Laplace plane. iii) We numerically examine the convexity and steepness properties of the integrable part of the secular Hamiltonian in both the $H_{J_2}$ and $H_{gls}$ models, which reflect necessary conditions for the holding of Nekhoroshevs theorem on the exponential stability of the orbits. We find that the $H_{J_2}$ model is non-convex, but satisfies a three-jet condition, while the $H_{gls}$ model restores quasi-convexity by adding lunisolar terms in the Hamiltonians integrable part.
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We present and validate a novel semi-analytical approach to study the effect of dynamical friction on the orbits of massive perturbers in rotating stellar discs. We find that dynamical friction efficiently circularises the orbit of co-rotating perturbers, while it constantly increases the eccentricity of counter-rotating ones until their angular momenta reverse, then once again promoting circularisation. Such drag toward circular corotation could shape the distribution of orientations of kinematically decoupled cores in disc galaxies, naturally leading to the observed larger fraction of co-rotating cores.
We revisit the relegation algorithm by Deprit et al. (Celest. Mech. Dyn. Astron. 79:157-182, 2001) in the light of the rigorous Nekhoroshevs like theory. This relatively recent algorithm is nowadays widely used for implementing closed form analytic perturbation theories, as it generalises the classical Birkhoff normalisation algorithm. The algorithm, here briefly explained by means of Lie transformations, has been so far introduced and used in a formal way, i.e. without providing any rigorous convergence or asymptotic estimates. The overall aim of this paper is to find such quantitative estimates and to show how the results about stability over exponentially long times can be recovered in a simple and effective way, at least in the non-resonant case.
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We present a study on the discoverability of temporarily captured orbiters (TCOs) by present day or near-term anticipated ground-based and space-based facilities. TCOs (Granvik et al. 2012) are potential targets for spacecraft ren- dezvous or human exploration (Chyba et al. 2014) and provide an opportunity to study the population of the smallest asteroids in the solar system. We find that present day ground-based optical surveys such as Pan-STARRS and ATLAS can discover the largest TCOs over years of operation. A targeted survey conducted with the Subaru telescope can discover TCOs in the 0.5 m to 1.0 m diameter size range in about 5 nights of observing. Furthermore, we discuss the application of space-based infrared surveys, such as NEOWISE, and ground-based meteor detection systems such as CAMS, CAMO and ASGARD in discovering TCOs. These systems can detect TCOs but at a uninteresting rate. Finally, we discuss the application of bi-static radar at Arecibo and Green Bank to discover TCOs. Our radar simulations are strongly dependent on the rotation rate distribution of the smallest asteroids but with an optimistic distribution we find that these systems have > 80% chance of detecting a > 10 cm diameter TCO in about 40 h of operation.
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