{"id":231696,"date":"2025-06-11T10:11:16","date_gmt":"2025-06-11T10:11:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=231696"},"modified":"2025-06-11T10:11:18","modified_gmt":"2025-06-11T10:11:18","slug":"earth-sun-geometry-for-example-on-april-20-n-30-number-of-days-from-the-closest-equinox-march-21-and-subsolar-point-23-5-cdot-sin-30-23-5-cdot-0-5-11-75-or-11-4","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/11\/earth-sun-geometry-for-example-on-april-20-n-30-number-of-days-from-the-closest-equinox-march-21-and-subsolar-point-23-5-cdot-sin-30-23-5-cdot-0-5-11-75-or-11-4\/","title":{"rendered":"Earth-Sun Geometry For example, on April 20, N = 30 (number of days from the closest equinox, March 21), and Subsolar point = 23.5 \\cdot sin (30\u00b0) = 23.5 \\cdot (0.5) = 11.75\u00b0 or 11\u00b0 45&#8242; N On December 9"},"content":{"rendered":"\n<p> Earth-Sun Geometry For example, on April 20, N = 30 (number of days from the closest equinox, March 21), and Subsolar point = 23.5 \\cdot sin (30\u00b0) = 23.5 \\cdot (0.5) = 11.75\u00b0 or 11\u00b0 45&#8242; N On December 9, N = -78 (number of days from September 22, negative since it is between the September and March equinoxes), and Subsolar point = 23.5 \\cdot sin (-78\u00b0) = -22.90\u00b0 or 22\u00b0 53&#8242; S Notice that we use negative values for the South- ern Hemisphere and positive ones for the Northern Hemisphere&#8211;again by convention. 4. Calculate the subsolar point on: a. March 21 b. June 21 c. September 22 d. December 22 e. Today&#8217;s date 5. Calculate the noon Sun angles for New Orleans, USA (30\u00b0 N), and Helsinki, Finland (60\u00b0 N), on each of the following dates: a. March 21 b. June 21 c. September 22 d. December 22 e. Today&#8217;s date New Orleans Helsinki Compare the declination values for the three additional dates you calculated in question 4 with those on the analemma. 6. What are the zenith and solar elevation angles for your city today? Optional Exercise: Measuring Solar Elevation Angle (Sun Angle) d. Using a calculator or table of tangent values,<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Analyzed<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonAlways show detailsCopy<code>from datetime import datetime\nimport math\n\n# Constants\nlatitude_new_orleans = 30  # degrees North\nlatitude_helsinki = 60     # degrees North\ndeclination_max = 23.5     # maximum declination in degrees\n\n# Date info\ntoday = datetime.today()\nmarch_21 = datetime(today.year, 3, 21)\njune_21 = datetime(today.year, 6, 21)\nsept_22 = datetime(today.year, 9, 22)\ndec_22 = datetime(today.year, 12, 22)\n\n# Days from equinoxes\ndef days_from_march_21(date):\n    return (date - march_21).days\n\n# Subsolar point calculation\ndef subsolar_point(N):\n    # Convert N to degrees and find declination using sine\n    declination = declination_max * math.sin(math.radians(N))\n    return declination\n\n# Noon Sun angle = 90\u00b0 - |latitude - declination|\ndef sun_angle(latitude, declination):\n    return 90 - abs(latitude - declination)\n\n# Dates to evaluate\ndates = {\n    \"March 21\": march_21,\n    \"June 21\": june_21,\n    \"September 22\": sept_22,\n    \"December 22\": dec_22,\n    \"Today\": today\n}\n\n# Prepare results\nresults = {}\nfor label, date in dates.items():\n    N = days_from_march_21(date)\n    decl = subsolar_point(N)\n    angle_nola = sun_angle(latitude_new_orleans, decl)\n    angle_helsinki = sun_angle(latitude_helsinki, decl)\n    results[label] = {\n        \"N\": N,\n        \"Declination (\u00b0)\": round(decl, 2),\n        \"New Orleans Noon Sun Angle (\u00b0)\": round(angle_nola, 2),\n        \"Helsinki Noon Sun Angle (\u00b0)\": round(angle_helsinki, 2)\n    }\n\nresults\n<\/code><\/pre>\n\n\n\n<p>Result<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">{'March 21': {'N': 0,\n  'Declination (\u00b0)': 0.0,\n  'New Orleans Noon Sun Angle (\u00b0)': 60.0,\n  'Helsinki Noon Sun Angle (\u00b0)': 30.0},\n 'June 21': {'N': 92,\n  'Declination (\u00b0)': 23.49,\n  'New Orleans Noon Sun Angle (\u00b0)': 83.49,\n  'Helsinki Noon Sun Angle (\u00b0)': 53.49},\n 'September 22': {'N': 185,\n  'Declination (\u00b0)': -2.05,\n  'New Orleans Noon Sun Angle (\u00b0)': 57.95,\n  'Helsinki Noon Sun Angle (\u00b0)': 27.95},\n 'December 22': {'N': 276,\n  'Declination (\u00b0)': -23.37,\n  'New Orleans Noon Sun Angle (\u00b0)': 36.63,\n  'Helsinki Noon Sun Angle (\u00b0)': 6.63},\n 'Today': {'N': 82,\n  'Declination (\u00b0)': 23.27,\n  'New Orleans Noon Sun Angle (\u00b0)': 83.27,\n  'Helsinki Noon Sun Angle (\u00b0)': 53.27}}<\/pre>\n\n\n\n<p>Here are the calculated results for the <strong>subsolar point<\/strong> and <strong>noon Sun angles<\/strong> on key dates, including today:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>4. Subsolar Point (Solar Declination)<\/strong><\/h3>\n\n\n\n<p>Calculated using the formula:<br><strong>Subsolar Point (\u00b0) = 23.5 \u00d7 sin(N\u00b0)<\/strong><br>where <strong>N<\/strong> is the number of days from <strong>March 21<\/strong>:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th><strong>Date<\/strong><\/th><th><strong>N (days from Mar 21)<\/strong><\/th><th><strong>Declination (\u00b0)<\/strong><\/th><\/tr><\/thead><tbody><tr><td>March 21<\/td><td>0<\/td><td>0.00\u00b0<\/td><\/tr><tr><td>June 21<\/td><td>92<\/td><td>23.49\u00b0<\/td><\/tr><tr><td>September 22<\/td><td>185<\/td><td>-2.05\u00b0<\/td><\/tr><tr><td>December 22<\/td><td>276<\/td><td>-23.37\u00b0<\/td><\/tr><tr><td>Today (June 11)<\/td><td>82<\/td><td>23.27\u00b0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>5. Noon Sun Angles<\/strong><\/h3>\n\n\n\n<p>Formula:<br><strong>Noon Sun Angle = 90\u00b0 &#8211; |latitude \u2212 declination|<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th><strong>Date<\/strong><\/th><th><strong>New Orleans (30\u00b0N)<\/strong><\/th><th><strong>Helsinki (60\u00b0N)<\/strong><\/th><\/tr><\/thead><tbody><tr><td>March 21<\/td><td>60.00\u00b0<\/td><td>30.00\u00b0<\/td><\/tr><tr><td>June 21<\/td><td>83.49\u00b0<\/td><td>53.49\u00b0<\/td><\/tr><tr><td>September 22<\/td><td>57.95\u00b0<\/td><td>27.95\u00b0<\/td><\/tr><tr><td>December 22<\/td><td>36.63\u00b0<\/td><td>6.63\u00b0<\/td><\/tr><tr><td>Today (June 11)<\/td><td>83.27\u00b0<\/td><td>53.27\u00b0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>6. Zenith and Solar Elevation Angles (Today)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Zenith angle<\/strong> = angle between the Sun and the vertical direction =<br><strong>Zenith = 90\u00b0 \u2212 Solar Elevation<\/strong><\/li>\n\n\n\n<li>From today\u2019s results:\n<ul class=\"wp-block-list\">\n<li><strong>New Orleans<\/strong>: Zenith = 90\u00b0 \u2212 83.27\u00b0 = <strong>6.73\u00b0<\/strong><\/li>\n\n\n\n<li><strong>Helsinki<\/strong>: Zenith = 90\u00b0 \u2212 53.27\u00b0 = <strong>36.73\u00b0<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcd8 <strong>300-word Explanation (Textbook Style)<\/strong><\/h3>\n\n\n\n<p>The Earth-Sun geometry determines the solar declination\u2014the latitude where the Sun is directly overhead at solar noon, also called the <strong>subsolar point<\/strong>. This point shifts between 23.5\u00b0N and 23.5\u00b0S due to the Earth\u2019s axial tilt. The declination angle follows a sinusoidal pattern throughout the year, and is calculated as:<br><strong>\u03b4 = 23.5 \u00d7 sin(N\u00b0)<\/strong>,<br>where <strong>N<\/strong> is the number of days from the spring equinox (March 21), and the angle is measured in degrees.<\/p>\n\n\n\n<p>On equinoxes (March 21 and September 22), the Sun is directly overhead at the equator, so the declination is 0\u00b0. On solstices, declination reaches its extreme: about +23.5\u00b0 on June 21 (Tropic of Cancer) and \u221223.5\u00b0 on December 22 (Tropic of Capricorn).<\/p>\n\n\n\n<p>The <strong>solar elevation angle<\/strong> at local noon is the angle of the Sun above the horizon. It depends on both the observer\u2019s latitude and the solar declination and is calculated using:<br><strong>Noon Sun Angle = 90\u00b0 \u2212 |Latitude \u2212 Declination|<\/strong><\/p>\n\n\n\n<p>For example, in New Orleans (30\u00b0N), the Sun reaches 83.3\u00b0 above the horizon near the June solstice, meaning the Sun is nearly overhead. In contrast, Helsinki (60\u00b0N) experiences a much lower noon Sun even on June 21, peaking at 53.5\u00b0, and drops dramatically to only 6.6\u00b0 by December 22, contributing to short, dim winter days.<\/p>\n\n\n\n<p>The <strong>zenith angle<\/strong> is the complement of the solar elevation and describes how far the Sun is from being directly overhead. It is smallest when the Sun is highest in the sky. Today, June 11, the subsolar point is near the Tropic of Cancer, so Northern Hemisphere cities like New Orleans and Helsinki receive strong midday sunlight.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-949.jpeg\" alt=\"\" class=\"wp-image-231697\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Earth-Sun Geometry For example, on April 20, N = 30 (number of days from the closest equinox, March 21), and Subsolar point = 23.5 \\cdot sin (30\u00b0) = 23.5 \\cdot (0.5) = 11.75\u00b0 or 11\u00b0 45&#8242; N On December 9, N = -78 (number of days from September 22, negative since it is between the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-231696","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/231696","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=231696"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/231696\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=231696"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=231696"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=231696"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}