{"id":370264,"date":"2017-02-28T03:00:00","date_gmt":"2017-02-28T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=3284cb849c4d4b06843b38ed7b8b3767"},"modified":"2017-02-28T03:00:00","modified_gmt":"2017-02-28T00:00:00","slug":"exploring-the-orbital-evolution-of-planetary-systems","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=370264","title":{"rendered":"Exploring the orbital evolution of planetary systems"},"content":{"rendered":"<p>The aim of this paper is to encourage the use of orbital integrators in the classroom to discover<br \/>\nand understand the long term dynamical evolution of systems of orbiting bodies. We show how to<br \/>\nperform numerical simulations and how to handle output data in order to reveal the dynamical<br \/>\nmechanisms that dominate the evolution of arbitrary planetary systems in timescales of millions of<br \/>\nyears using a simple but efficient numerical integrator. Through some examples we reveal the<br \/>\nfundamental properties of planetary systems: the time evolution of the orbital elements, the free<br \/>\nand forced modes that drive oscillations in eccentricity and inclination, the fundamental<br \/>\nfrequencies of the system, the role of the angular momenta, the invariable plane, orbital<br \/>\nresonances, and the Kozai\u2013Lidov mechanism.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The aim of this paper is to encourage the use of orbital integrators in the classroom to discover<br \/>\nand understand the long term dynamical evolution of systems of orbiting bodies. We show how to<br \/>\nperform numerical simulations and how to handle output da&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-370264","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/370264","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=370264"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/370264\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=370264"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=370264"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=370264"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}