The process of capture in the coorbital region of a solar system planet is studied. Absolute capture likelihood in the 1:1 resonance is determined by randomly constructed statistical ensembles numbering $7.24\times 10^5$ of massless asteroids that are set to migrate radially from the outer to the inner boundaries of the coorbital region of a Jupiter-mass planet. Orbital states include coorbital capture, ejection, collisions with the Sun and the planet and free-crossing of the coorbital region. The relative efficiency of retrograde capture with respect to prograde capture is confirmed as an intrinsic property of the coorbital resonance. Half the asteroids cross the coorbital region regardless of eccentricity and for any inclination less than $120^\circ$. We also find that the recently discovered retrograde coorbital of Jupiter, asteroid 2015 BZ509, lies almost exactly at the capture efficiency peak associated with its orbital parameters.Comment: 8 pages. 2 figures. Submitted to Journal of Computational and Applied Mathematic
The discovery of almost two thousand exoplanets has revealed an unexpectedly diverse planet population. We see gas giants in few-day orbits, whole multi-planet systems within the orbit of Mercury, and new populations of planets with masses between that of the Earth and Neptune-all unknown in the Solar System. Observations to date have shown that our Solar System is certainly not representative of the general population of planets in our Milky Way. The key science questions that urgently need addressing are therefore: What are exoplanets made of? Why are planets as they are? How do planetary systems work and what causes the exceptional diversity observed as compared to the Solar System? The EChO (Exoplanet Characterisation Observatory) space mission was conceived to take up the challenge to explain this diversity in terms of formation, evolution, internal structure and planet and atmospheric composition. This requires in-depth spectroscopic knowledge of the atmospheres of a large and well-defined planet sample for which precise physical, chemical and dynamical information can be obtained. In order to fulfil this ambitious scientific program, EChO was designed as a dedicated survey mission for transit and eclipse spectroscopy capable of observing a large, diverse and well-defined planet sample within its 4-year mission lifetime. The transit and eclipse spectroscopy method, whereby the signal from the star and planet are differentiated using knowledge of the planetary ephemerides, allows us to measure atmospheric signals from the planet at levels of at least 10 −4 relative to the star. This can only be achieved in conjunction with a carefully designed stable payload and satellite platform. It is also necessary to provide broad instantaneous wavelength coverage to detect as many molecular species as possible, to probe the thermal structure of the planetary atmospheres and to correct for the contaminating effects of the stellar photosphere. This requires wavelength coverage of at least 0.55 to 11 μm with a goal of covering from 0.4 to 16 μm. Only modest spectral resolving power is needed, with R~300 for wavelengths less than 5 μm and R~30 for wavelengths greater than this. spectroscopy technique means that no spatial resolution is required. A telescope collecting area of about 1 m 2 is sufficiently large to achieve the necessary spectro-photometric precision: for the Phase A study a 1.13 m 2 telescope, diffraction limited at 3 μm has been adopted. Placing the satellite at L2 provides a cold and stable thermal environment as well as a large field of regard to allow efficient time-critical observation of targets randomly distributed over the sky. EChO has been conceived to achieve a single goal: exoplanet spectroscopy. The spectral coverage and signal-to-noise to be achieved by EChO, thanks to its high stability and dedicated design, would be a game changer by allowing atmospheric composition to be measured with unparalleled exactness: at least a factor 10 more precise and a factor 10 to 1000 more accurate tha...
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