{"id":4420,"date":"2015-04-13T08:51:58","date_gmt":"2015-04-13T12:51:58","guid":{"rendered":"http:\/\/pages.vassar.edu\/magnes\/?p=4420"},"modified":"2015-05-13T23:06:59","modified_gmt":"2015-05-14T03:06:59","slug":"preliminary-results-precession-of-mercurian-planets","status":"publish","type":"post","link":"https:\/\/pages.vassar.edu\/magnes\/2015\/04\/13\/preliminary-results-precession-of-mercurian-planets\/","title":{"rendered":"Preliminary Results: Precession of Mercurian Planets"},"content":{"rendered":"

This week I worked on the modeling of Mercury’s orbital motion around the Sun. Using the Euler-Chromer Method\u00a0and the general relativistic force law (see previous post for a more quantitative description) I was able to create a code that shows Mercury’s movement over several orbits. The value for alpha was used at 0.01 (very much greater than the true value) and that the initial conditions used were when \" r_{I}=0.47 AU \",\u00a0and \" V_{I}=8.2 \" \" \frac{AU}{year} \". It is clear over several orbits that the location of Mercury’s perihelion is changing.<\/p>\n

In the following plot, the different positions for the\u00a0aphelion (chosen for clarity)\u00a0are clearly\u00a0shown by lines connecting the origin (or the Sun) to the aphelion.<\/p>\n

\"MercuryPeri3\"<\/a><\/p>\n

It is my next goal to determine the amount of degrees by which\u00a0the orientation of this orbit changes over time. I have run into the issue\u00a0that Matlab’s acos and asin (arccos and arcsin) functions\u00a0give imaginary values if their inputs are\u00a0not with the range of -1<x<1. When this issue is resolved, I will be able to\u00a0finish deriving the precession rate of Mercury, and will proceed to experimenting with\u00a0the eccentricity of Mercurian planet orbits and their resulting\u00a0rates of precession.<\/p>\n

Here is a link to my Matlab code: https:\/\/docs.google.com\/a\/vassar.edu\/document\/d\/1fw8L5ZvhqMMVMYltkJH6Ac425KrmnbbDUJs_6GV7aPI\/edit?usp=sharing<\/p>\n","protected":false},"excerpt":{"rendered":"

This week I worked on the modeling of Mercury’s orbital motion around the Sun. Using the Euler-Chromer Method\u00a0and the general relativistic force law (see previous post for a more quantitative description) I was able to create a code that shows Mercury’s movement over several orbits. The value for alpha was used at 0.01 (very much […]<\/p>\n","protected":false},"author":2308,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-4420","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/4420","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/users\/2308"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/comments?post=4420"}],"version-history":[{"count":9,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/4420\/revisions"}],"predecessor-version":[{"id":5053,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/4420\/revisions\/5053"}],"wp:attachment":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/media?parent=4420"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/categories?post=4420"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/tags?post=4420"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}