{"id":2822,"date":"2013-12-12T23:56:01","date_gmt":"2013-12-12T23:56:01","guid":{"rendered":"http:\/\/thetravellerslastjourney.com\/shai\/?p=2822"},"modified":"2019-08-25T07:56:34","modified_gmt":"2019-08-25T07:56:34","slug":"astronomy","status":"publish","type":"post","link":"https:\/\/thetravellerslastjourney.com\/shai\/2013\/12\/12\/astronomy\/","title":{"rendered":"Astronomy"},"content":{"rendered":"<p style=\"text-align: justify;\">Meta: Writing this note during week one: My plan is to complete week one (i.e. first) and then try to use a holistic perspective to see if I can get some sort of MM-type [<span style=\"font-size: 8pt;\">Mind Map<\/span>] notes going. The final goal by the end of this course will be to have an <em>intellectual framework<\/em> for astronomy.<\/p>\n<p style=\"text-align: justify;\"><strong>2: The Celestial Sphere<\/strong><\/p>\n<ul style=\"text-align: justify;\">\n<li>Modern astronomy recognizes 88 constellations as areas (with defined boundaries) that cover the sky, and can be used as points of reference (e.g. <em>alpha Aries<\/em>\u00a0is the primary star within that constellation).<\/li>\n<li>Stars located in terms of a <strong>celestial sphere<\/strong>, being an imaginary enormous sphere with the Earth at its centre.<\/li>\n<li><strong>Declination<\/strong> = Measure of celestial latitude (marked as <em>lines of declination<\/em>), measured as degrees from <strong>celestial equator<\/strong> (corresponding to the Earth&#8217;s equator).<\/li>\n<li><strong>Right ascension<\/strong> = Measure of celestial longitude (marked as <em>hour circles<\/em>), measured in hours to east from the <strong>prime celestial meridian<\/strong> (being at right angle to the\u00a0vernal equinox; the place where the sun passes celestial equator moving south-north, in the constellation Pisces*.\u00a0Vernal equinox is the northern hemisphere&#8217;s spring equinox). It corresponds with the rotation of the earth, such that an object at 30-degrees longitude is measured as 2 hours RA, that being how far the sky rotates in that time.\n<ul>\n<li>*This had historically been called the <em>first point of Aries<\/em>, but due to the procession of equinoxes, the position has moved to within Pisces.<\/li>\n<li>Cf. A <strong>terrestrial meridian<\/strong>\u00a0is a line of longitude.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">[<a href=\"http:\/\/astro.wsu.edu\/worthey\/astro\/html\/lec-celestial-sph.html\">Via<\/a>\u00a0<em>The Celestial Sphere\u00a0<\/em>@\u00a0<em>Astronomy WI<\/em>]\n<ul style=\"text-align: justify;\">\n<li>The path traced by the sun over a 1-year cycle is called the <strong>ecliptic<\/strong>\u00a0&#8211; the height of the sun (maximum at summer) moves W-E by 1-degree\/day. (For heaps more see Wikipedia\u00a0<a href=\"http:\/\/en.wikipedia.org\/wiki\/Ecliptic\">article<\/a>).<\/li>\n<li>The <strong>sidereal month<\/strong>\u00a0for the moon is the time taken to rotate the Earth relative to fixed stars (27.3 days), which is shorter than the\u00a0<strong>synodic month<\/strong>, which is the time between identical phases of the moon (29.5 days), due to the displacement of the Earth over the period requiring further movement to achieve the same relative geometries. (More at Wikipedia <a href=\"http:\/\/en.wikipedia.org\/wiki\/Orbit_of_the_Moon\">article<\/a>).<\/li>\n<li>[Might read more from this source, but am realizing that at this stage of the course, these facts are not yet directly relevant]<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><strong>3: The Local View<\/strong><\/p>\n<ul style=\"text-align: justify;\">\n<li>A star&#8217;s position above the horizon is given as <strong>altitude<\/strong> in degrees above the <em>horizon<\/em>, which can also be measured in relation to my\u00a0<strong>zenith<\/strong> (directly overhead)\u00a0altitude (<em>equals<\/em> 90 degrees <em>minus<\/em> altitude).<\/li>\n<li>The <strong>celestial north\/south poles<\/strong>\u00a0correspond with the zenith above the respective poles of the Earth&#8217;s axis of rotation.<\/li>\n<li>Position around the horizon is given relative to the <strong>local meridian<\/strong>*\u00a0(in terms of the north\/south line it offers), given in degrees. Often given as\u00a0<strong>azimuth<\/strong>, which is the angle from north.\n<ul>\n<li>*The <em>local meridian<\/em>\u00a0is a circle passing through the celestial poles and the zenith (i.e. of my location).<\/li>\n<li>*Cf. For terrestrial geography, a meridian is a <em>line of latitude<\/em> (i.e. connecting the poles along the planet&#8217;s surface).<\/li>\n<\/ul>\n<\/li>\n<li>It can be shown (by drawing triangles on an appropriately labelled celestial sphere) that one&#8217;s latitude will correspond with the altitude of the visible pole in the sky (e.g. at the north pole I am at 90 degrees latitude, and that is the position of the <em>celestial north pole<\/em> in my sky; similarly if I am at latitude 35 degrees, that is the hight of my CNP). Thus can measure position.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">[Via <em>Astronomy without a telescope<\/em>\u00a0@ <em>Astronomy Note<\/em>]\n<ul style=\"text-align: justify;\">\n<li>The stars rotate in the sky in a path that is parallel to the celestial equator.<\/li>\n<li>The passing of a star through the local meridian marks the highest altitude it reaches during that day-night cycle.<\/li>\n<li>The angle of stars&#8217; rotation in the sky can be measured as an angle relative to the horizon, which is obviously the same for the entire sky at any location. It can be given as <em>equals<\/em> 90-degrees <em>minus<\/em>\u00a0the observer&#8217;s latitude. Thus (as said) at the poles the stars never set, and the angle becomes steeper the closer to the equator.<\/li>\n<li>During daylight, the meridian separates the morning (AM, Latin. <em>antemeridiem<\/em>) and afternoon (PM,\u00a0<em>post-meridiem<\/em>) positions of the sun. At noon, in the southern hemisphere, the sun is due north (and vice versa).<\/li>\n<li>As I move north from the south pole, with every degree: (1) the position of the SCP moves 1-degree away from (i.e. my) zenith southwards (nb. the SCP&#8217;s position on the celestial sphere, which is theoretically infinite in diameter, is easily visualized by giving it a proxy, e.g. using a star); (2) the highest point of the celestial equator moves 1-degree higher from the northern horizon.<\/li>\n<li>Nb. It follows that at the Earth&#8217;s equator, the SNP is on the southern horizon, the celestial equator is at 90-degrees, and thus directly overhead E-W, and the stars rise\/set perpendicular to the horizon (i.e. straight up\/down). This last point means that we see half of the stars&#8217; full rotation around the Earth, similar to the rotation of the sun we see during the day.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><strong>4: Sidereal Time<\/strong><\/p>\n<ul style=\"text-align: justify;\">\n<li>Stars around the celestial pole that are <strong>circumpolar<\/strong>, those in the midst of summer\u00a0never set and rotate around the pole, and in the midst of winter at the opposite pole, they never rise.\u00a0Stars\u00a0in between\u00a0the two circumpolar regions rise, move west, and set.<\/li>\n<li>Note that our <strong>zenith<\/strong>&#8216;s declination is equal to our latitude. And vice versa.\n<ul>\n<li>In other words, the position of the zenith&#8217;s degrees perpendicular, i.e. declination, away from the celestial equator, is the same as our position in degrees perpendicular, i.e. latitude, away from the terrestrial equator. This is easy to see in the case of the north pole, when I&#8217;m at 90-degrees latitude north, and my zenith is at 90-degrees declination, i.e. at the celestial pole).<\/li>\n<\/ul>\n<\/li>\n<li>Note that our <strong>zenith<\/strong>&#8216;s right ascension (in other words the celestial, corresponding to the terrestrial, meridian above our location) is thus also our sidereal time.<\/li>\n<li><strong>Sidereal time<\/strong>\u00a0is the name of the\u00a0<strong>prime meridian<\/strong>\u00a0(cf. terrestrial) which corresponds to the local celestial meridian.\n<ul>\n<li>Nb. Proceeds with time. Similarly moves forward by moving east.<\/li>\n<li>Thus 24-sidereal hours correspond to a 360-degree rotation of the Earth around its axis.<\/li>\n<li>Thus can measure time, as in 1-(sidereal) hour, the celestial sphere shifts by 1-hour of right ascension.<\/li>\n<li>Thus the position of stars in my sky varies with my location, and every 15-degrees latitude corresponds to the 1-sidereal hour (nb. in a continuous manner).<\/li>\n<\/ul>\n<\/li>\n<li>A star is highest at its meridian crossing, in other words, when sidereal time is its RA.\n<ul>\n<li>At this time its ZA (<strong>zenith angle<\/strong>, i.e. degrees from zenith) <em>equals<\/em>\u00a0its declination\u00a0<em>minus<\/em> the latitude. (Nb. this follows from the fact that our zenith is equivalent to our latitude)&#8230;<\/li>\n<li>&#8230;Furthermore: Since the altitude (i.e. local view) of the zenith is 90-degrees, then the altitude of a star at the meridian crossing <em>equals<\/em>\u00a090-degrees <em>minus<\/em>\u00a0ZA. However, see next point&#8230;<\/li>\n<li>&#8230;Nb. ZA must be given an absolute form, so if the declination is greater than the latitude then the azimuth must be made to zero degrees, and otherwise to 180 degrees. In other words, in the former case the meridian crosses north of the zenith, and in the latter case, south.<\/li>\n<li>To find the star earlier\/later, rotate east\/west by 15 degrees.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><strong>5: Where is the sun?<\/strong><\/p>\n<ul style=\"text-align: justify;\">\n<li>The sun&#8217;s right ascension makes a full cycle (i.e. a sidereal day) over the course of a year.<\/li>\n<li>Because the Earth is moving along its orbit as well as rotating, therefore once it&#8217;s completed a complete rotation it must still turn a little further in order to be the same relative angle (i.e. the sun&#8217;s RA) to the sun.\n<ul>\n<li>Therefore a <em>solar day<\/em>, as timed by our clocks (aka <em>local time<\/em>), is longer than a <strong>sidereal day<\/strong>\u00a0(thus 24 sidereal hours <em>equals<\/em> 23h-56m-4s).<\/li>\n<\/ul>\n<\/li>\n<li>On September 21, <em>sidereal time<\/em> is roughly equal to <em>local time<\/em>\u00a0(ignoring the conventions of time zones, etc). Obviously, after this date, sidereal time can be estimated by adding 4min per day (and vice versa too). Also, on the 21 of December\/March\/June sidereal time can be estimated by adding 6\/12\/18hrs (and obviously by next September, another whole day has been added, etc).<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">An example that makes use of this:\u00a0<em>When is Vega&#8217;s RA 18h 36m at midnight?<\/em><\/p>\n<ol style=\"text-align: justify;\">\n<li>Since a star is highest at its meridian crossing, i.e. when its sidereal time is its RA&#8230;<\/li>\n<li>&#8230;therefore we want Vega when sidereal time (ST) is 18:36. But we want this to occur at a local time (LT) of 24:00&#8230;<\/li>\n<li>&#8230;therefore we want ST to equal LT + 18hr&#8230;<\/li>\n<li>&#8230;which occurs on June 21. To get the extra 36m we calculate at 4m per day (i.e. the change between ST and LT) to get 9 days&#8230;<\/li>\n<li>&#8230;therefore the answer is June 30.<\/li>\n<\/ol>\n<p style=\"text-align: justify;\">[Via Analemma @ Wikipedia]: Although it can technically refer to the relationship between any two celestial bodies, it is generally used to mean that of the sun as seen from Earth. It can be drawn based on the position of the sun as seen from a fixed location at the same local time every day.<\/p>\n<p style=\"text-align: justify;\"><strong>6: Tilt and seasons<\/strong><\/p>\n<ul style=\"text-align: justify;\">\n<li>The Earth is 23.5 degrees tilted relative to the plane of orbit around the sun. Alternatively, the Earth is straight but moving around a tilted orbit.<\/li>\n<li><strong>Obliquity<\/strong> (or <em>axial tilt<\/em>) is the angle between the equatorial plane and the orbital plane.<\/li>\n<li>It follows that the <strong>ecliptic<em>\u00a0<\/em><\/strong>(or sun&#8217;s movement around the celestial sphere) is at 23.5 degrees, and the two points when the ecliptic meets the celestial equator are called the <em>vernal<\/em> (March 21)\u00a0<em>and autumnal<\/em> (September 21) <em>equinox<\/em>. The former by definition is the prime meridian, thus the sun is overhead at 0hr RA. The sun&#8217;s declination varies between these points to achieve a maximum declination of 23.5 degrees (i.e. south or north at the 12-month interval).<\/li>\n<li>E.g. after the vernal equinox, the ecliptic moves on the celestial sphere north away from the celestial equator, so that the latitude from which the sun is overhead moves north. During these 6-months, the declination of the sun is also the degrees of latitude away from the north pole which is always exposed to the sun.<\/li>\n<li>At <strong>equinox<\/strong>\u00a0day the day\/night is 12\/12 hours everywhere.<\/li>\n<li><strong>Tropics<\/strong>\u00a0are limited by 23.5 degrees latitude north\/south from the equator, which corresponds to the areas which see the sun reach at least one <strong>subsolar point<\/strong> (i.e. perceiving the sun to be at my zenith).<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">An example that makes use of this: <em>How high is the sun at noon at (Athens) latitude 37.7 degrees north?<\/em><\/p>\n<ol style=\"text-align: justify;\">\n<li>At the equinox: This is when the sun is 0 degrees declination everywhere, thus ZA (equals RA minus declination, or latitude minus declination) is 37.7 degrees, and altitude (equals 90 degrees minus ZA) is 52.3 degrees.<\/li>\n<li>At the summer solstice: This is when the declination is at its maximum, 23.5 degrees, thus ZA equals 14.2 degrees, and altitude 75.8 degrees.<\/li>\n<li>At the winter solstice: When the declination is at <em>negative<\/em> 23.5 degrees, thus ZA equals 61.2 degrees and altitude 28.8 degrees.<\/li>\n<\/ol>\n<p style=\"text-align: justify;\"><strong>7: The Age of Aquarius<\/strong><\/p>\n<ul style=\"text-align: justify;\">\n<li>The solar day is only 24h as a mean due to a few factors including:\n<ul>\n<li>Because the ecliptic is parallel to the equator near the solstices, therefore its eastwards motion is then\u00a0the fastest.<\/li>\n<li>Due to the elliptic shape of Earth&#8217;s orbit, it is slightly nearer and therefore moves slightly faster around January.<\/li>\n<li><strong>Precession<\/strong>, i.e. the wobble of the Earth&#8217;s axis in a westward direction. The north pole moves to the west with a radius of 23.5 degrees every 26,000 years relative to the stars.<\/li>\n<li><strong>Precession of the equinoxes<\/strong>\u00a0follows from the precession causing the points of the equinoxes along the equator to move. From this it follows that the coordinates of the stars move, leading to a system of giving coordinates relative to <strong>epochs<\/strong>\u00a0(generally the epoch J2000, i.e. on January 1 2000).<\/li>\n<\/ul>\n<\/li>\n<li>Age of Aquarius refers to the fact that around 2600CE, the vernal equinox will enter that constellation (from the current Pisces).<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><strong>8: The moon moves too<\/strong><\/p>\n<p style=\"text-align: justify;\">asd<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Meta: Writing this note during week one: My plan is to complete week one (i.e. first) and then try to use a holistic perspective to see if I can get some sort of MM-type [Mind Map] notes going. The final goal by the end of this course will be to have an intellectual framework for [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[159,261,242,128,16],"tags":[],"metadata":[282],"class_list":["post-2822","post","type-post","status-publish","format-standard","hentry","category-all-posts","category-astronomy","category-evernote-entries","category-journal","category-science","metadata-meta"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack-related-posts":[{"id":2557,"url":"https:\/\/thetravellerslastjourney.com\/shai\/2013\/04\/22\/bibliomes-scribbles-2\/","url_meta":{"origin":2822,"position":0},"title":"Bibliomes: Scribbles","author":"Pala","date":"April 22, 2013","format":false,"excerpt":"Editorial notes: For a broader elaboration on Shai's 'Bibliome project' see the Editorial notes to\u00a0'Philosophy Readings Through Time' (Open link in a new tab). Here I start to plan bibliomes - they being organic districts that are fertilized by interest and motivation, and whose seeds can be defined as specifically\u2026","rel":"","context":"In &quot;All Posts&quot;","block_context":{"text":"All Posts","link":"https:\/\/thetravellerslastjourney.com\/shai\/all-posts\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1183,"url":"https:\/\/thetravellerslastjourney.com\/shai\/2016\/12\/05\/some-words-on-descartes\/","url_meta":{"origin":2822,"position":1},"title":"Some words on Descartes","author":"Pala","date":"December 5, 2016","format":false,"excerpt":"Read a biography of Descartes and re-read his Discourse[I] (I\u2019d already read his Methods and excerpts from his scientific slog - optics and harmonics, ergh). So how do I feel about this famous Frenchman, the so-called father of modern philosophy? Philosophy-wise, not that much. His real contribution was to abandon\u2026","rel":"","context":"In &quot;All Posts&quot;","block_context":{"text":"All Posts","link":"https:\/\/thetravellerslastjourney.com\/shai\/all-posts\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":40,"url":"https:\/\/thetravellerslastjourney.com\/shai\/2014\/09\/28\/science-news-on-one-foot-circa-september-25\/","url_meta":{"origin":2822,"position":2},"title":"Science News on One Foot (circa September 25)","author":"Pala","date":"September 28, 2014","format":false,"excerpt":"Three headlines selected from this week's Science\/Nature journals: (1) Memory in the innate immune system, (2) water in extrasolar atmospheres, and (3) enhancing photosynthesis in crops. Herein I summarize these, highlighting what makes them interesting to this person.","rel":"","context":"In &quot;All Posts&quot;","block_context":{"text":"All Posts","link":"https:\/\/thetravellerslastjourney.com\/shai\/all-posts\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":2830,"url":"https:\/\/thetravellerslastjourney.com\/shai\/2013\/12\/17\/tuesday-december-17-2013\/","url_meta":{"origin":2822,"position":3},"title":"Tuesday December 17, 2013","author":"Pala","date":"December 17, 2013","format":false,"excerpt":"Meta: Two days previously I had been writing about my study of Bentham. Before continuing I wish to bring attention to two points related to this effort. The first is tangential, and concerns this project perceived from a more generic stance. What I have code-named \"Philosopher Briefs\" is a didactic\u2026","rel":"","context":"In &quot;All Posts&quot;","block_context":{"text":"All Posts","link":"https:\/\/thetravellerslastjourney.com\/shai\/all-posts\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1153,"url":"https:\/\/thetravellerslastjourney.com\/shai\/2017\/05\/11\/r-yona-at-jeta-grove\/","url_meta":{"origin":2822,"position":4},"title":"R Yona at Jeta Grove","author":"Pala","date":"May 11, 2017","format":false,"excerpt":"Editorial notes: The short story below was found in Shai's Google Drive notes and is clearly incomplete. The Brain Storming section at the end of the narrative alludes to the continuation of the story An apocryphal Braisa, non-canonical and existing only in Arabic: \u201cRabbi Yona was lost at sea. Can\u2026","rel":"","context":"In &quot;All Posts&quot;","block_context":{"text":"All Posts","link":"https:\/\/thetravellerslastjourney.com\/shai\/all-posts\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1689,"url":"https:\/\/thetravellerslastjourney.com\/shai\/2010\/09\/30\/the-story-of-thales-2\/","url_meta":{"origin":2822,"position":5},"title":"The story of Thales","author":"Pala","date":"September 30, 2010","format":false,"excerpt":"Editorial notes: In September 2010, Shai begins the first phase of his intellectual journey with an\u00a0essay\u00a0dedicated to the Greek mathematician, astronomer and pre-Socratic philosopher, Thales of Miletus. This the first of\u00a080 essays, written between September 2010 and July 2015, dedicated to analysing the thoughts and writings of the great ancient\u2026","rel":"","context":"In &quot;All Posts&quot;","block_context":{"text":"All Posts","link":"https:\/\/thetravellerslastjourney.com\/shai\/all-posts\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/padotI-Jw","_links":{"self":[{"href":"https:\/\/thetravellerslastjourney.com\/shai\/wp-json\/wp\/v2\/posts\/2822","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thetravellerslastjourney.com\/shai\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thetravellerslastjourney.com\/shai\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thetravellerslastjourney.com\/shai\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/thetravellerslastjourney.com\/shai\/wp-json\/wp\/v2\/comments?post=2822"}],"version-history":[{"count":0,"href":"https:\/\/thetravellerslastjourney.com\/shai\/wp-json\/wp\/v2\/posts\/2822\/revisions"}],"wp:attachment":[{"href":"https:\/\/thetravellerslastjourney.com\/shai\/wp-json\/wp\/v2\/media?parent=2822"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thetravellerslastjourney.com\/shai\/wp-json\/wp\/v2\/categories?post=2822"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thetravellerslastjourney.com\/shai\/wp-json\/wp\/v2\/tags?post=2822"},{"taxonomy":"metadata","embeddable":true,"href":"https:\/\/thetravellerslastjourney.com\/shai\/wp-json\/wp\/v2\/metadata?post=2822"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}