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Explicit relations and criteria for eclipses, transits and occultations
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Veras, Dimitri (2019) Explicit relations and criteria for eclipses, transits and occultations. Monthly Notices of the Royal Astronomical Society, 483 (3). pp. 3919-3949. doi:10.1093/mnras/sty3104 ISSN 1745-3933.
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Official URL: https://doi.org/10.1093/mnras/sty3104
Abstract
Solar system, exoplanet and stellar science rely on transits, eclipses and occultations for dynamical and physical insight. Often, the geometry of these configurations are modelled by assuming a particular viewpoint. Here, instead, I derive user-friendly formulae from first principles independent of viewpoint and in three dimensions. I generalise the results of Veras & Breedt (2017) by (i) characterising three-body systems which are in transit but are not necessarily perfectly aligned, and by (ii) incorporating motion. For a given snapshot in time, I derive explicit criteria to determine whether a system is in or out of transit, if an eclipse is total or annular, and expressions for the size of the shadow, including their extreme values and a condition for engulfment. These results are exact. For orbital motion, I instead obtain approximate results. By assuming fixed orbits, I derive a single implicit algebraic relation which can be solved to obtain the frequency and duration of transit events – including ingresses and egresses – for combinations of moons, planets and stars on arbitrarily inclined circular orbits; the eccentric case requires the solution of Kepler’s equation but remains algebraic. I prove that a transit shadow – whether umbral, antumbral or penumbral – takes the shape of a parabolic cylinder, and finally present geometric constraints on Earth-based observers hoping to detect a three-body syzygy (or perfect alignment) – either in extrasolar systems or within the solar system – potentially as a double annular eclipse.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QB Astronomy | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Physics | ||||||||
Library of Congress Subject Headings (LCSH): | Eclipses, Transits, Occultations | ||||||||
Journal or Publication Title: | Monthly Notices of the Royal Astronomical Society | ||||||||
Publisher: | Oxford University Press | ||||||||
ISSN: | 1745-3933 | ||||||||
Official Date: | March 2019 | ||||||||
Dates: |
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Volume: | 483 | ||||||||
Number: | 3 | ||||||||
Page Range: | pp. 3919-3949 | ||||||||
DOI: | 10.1093/mnras/sty3104 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Reuse Statement (publisher, data, author rights): | This is a pre-copyedited, author-produced PDF of an article accepted for publication in Monthly Notices of the Royal Astronomical Society following peer review. The version of record Veras, Dimitri (2018) Explicit relations and criteria for eclipses, transits and occultations. Monthly Notices of the Royal Astronomical Society . is available online at: https://doi.org/10.1093/mnras/sty3104 | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 16 November 2018 | ||||||||
Date of first compliant Open Access: | 16 November 2018 | ||||||||
RIOXX Funder/Project Grant: |
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