<body bgcolor="#ffffff" text="#000000" link="#0000ff" vlink="#0000ff"> <BODY> <P> <center> <h2> CONSEQUENCES OF THE ORBITAL MOTION OF THE EARTH </h2> </center> <P><br> <h2> The annual variations (seasonal variations and changing constellations in the night sky) are caused by the orbital motion (revolution) of the Earth around the Sun. <i><font color="magenta"> The Earth moves from the west-to-east around the Sun (i.e., in the CCW-sense as viewed from the NCP--the Earth rotates and revolves in the same sense, west-to-east).</i></font> As a result of the orbital motion of the Earth, the <a href="http://pages.uoregon.edu/~imamura/121/images/Ecliptic2.jpg"> Sun moves slowly through the stars</a> on the Celestial Sphere from <font color=magenta>west-to-east</font>. The path it traces out is referred to as the <font color=magenta><i>Ecliptic</i></font> and the constellations through which it passes are referred to as the <a href="http://pages.uoregon.edu/~imamura/121/images/zodiac_ecliptic.gif"> Zodiac Constellations</a>. The Sun takes one <font color="magenta"><i> sidereal</i> year (roughly 365.2564 days)</font> to make one complete trip around the Celestial Sphere with respect to the stars. <a target="_blank"href="https://www.youtube.com/watch?v=EoFct5WwVys">Helpful video</a>. <P> <center> Equinoxes and Solstices </center> <p> To define positions of objects on the Celestial Sphere, we use a system analogous to <i> longitude</i> and <i> latitude</i>. The rotation axis of the Earth and the orbital axis of the Earth are not parallel (they form an angle = 23.5<sup>o</sup>). <center> <img src="http://pages.uoregon.edu/~imamura/121/images/ecliptic_plane.jpg"> </center> <p> As a result, the <font color="magenta">Ecliptic </font> and the <font color="magenta">Celestial Equator</font> are inclined with respect to each other. Because of this, the Sun is sometimes <font color=aqua> <i>above the Celestial Equator</i></font> and sometimes <font color=aqua><i>below the Celestial Equator</i></font>. This gives us some natural checkpoints on the sky (spheres have no ears to grab). We define the following points on the Celestial Sphere; <center> <p> <img src="http://pages.uoregon.edu/~imamura/121/images/ecliptic.jpg"> </center> <p> <b> Vernal (Mar 19, 2020 UTC) and Autumnal (Sep 22, 2020 UTC) Equinoxes and Winter (Dec 21, 2020 UTC) and Summer (June 20, 2020 UTC) Solstices</b> <P> The two equinoxes occur when the Sun passes through the Celestial Equator and the two solstices occur when the Sun is at its greatest distance north and south of the Celestial Equator. <P> <p> <p> <center> <br> The Seasonal Variations </center> <P> The seasons change on a period of 365.2422 days (the <font color=magenta><i> Tropical year</i></font>); an interval slightly shorter than the <font color=magenta>sidereal year</font>. The cause of the changing of the seasons is the misalignment between the rotation axis and orbital axis of the Earth coupled with the orbital motion of the Earth. Huh? The question is then <p><center><font color="green"> <i> How do the axis misalignment and orbital motion lead to seasonal variations on the Earth?</i></font> <P></center> There are two primary effects: <P> <ul> <li>the Solar heating depends on the <a href="http://pages.uoregon.edu/~imamura/121/images/insolation.jpg"> angle at which the sunlight strikes particular locations on the Earth</a>, <P><center><img width=600 src="SunRayAngles.png"></center><p> The heating (angle), for a particular location, <a href="http://pages.uoregon.edu/~imamura/121/images/season.jpg"> varies over the course of a year</a>. This is the main effect. <li>The Solar heating depends on the amount of time the Sun spends above the horizon on a given day (hours of daylight per day).<p><center> <font color=green>How and Why does this vary? </font></center> <P> <ul> <table> <tr><th width="20%"></th><th></th></tr> <td bgcolor=white valign=top> <p> <p> <p> <img src="http://pages.uoregon.edu/~imamura/121/images/sunalt.jpg"> <br> <p> <p> <p> </td> <td bgcolor="#ffffff"> <h2> On June 22 (or so), the Sun reaches its farthest point north of the Celestial Equator, the <b> Summer Solstice</b>. The Sun then moves toward the Celestial Equator, passing through the Celestial Equator on around September 22, the <b> Autumnal Equinox</b>. The Sun reaches its maximum distance south of the Celestial Equator on around December 22, the <b> Winter Solstice</b>, passing through the Celestial Equator, heading north, on around March 21, the <b> Vernal Equinox</b>. <P> How do the diurnal circles for the Sun vary over a year in Eugene, OR (latitude ~ 45<sup>o</sup> N, longitude ~ 123<sup>o</sup> W). In Eugene, the altitude of the NCP above the north point on the horizon is ~ 45<sup>o</sup>. <font color="red"> [<i> How far is the Celestial Equator above the south point on the horizon?</i> Answer: ~ 45<sup>o</sup>.] </font> So, what is the altitude of the Sun above the (South/North?) point on the horizon at roughly noon on the equinoxes and solstices? <P> <i><font color="magenta"> So, in Eugene, the maximum altitude of the Sun above the horizon is: <p> <ul> Equinoxes -- 45<sup>o</sup> (Sun is on the Celestial Equator).<br> Winter Solstice -- 45<sup>o</sup>-23.5<sup>o</sup>=21.5<sup>o</sup> (Sun is 23.5<sup>o</sup> below the Celestial Equator).<br> Summer Solstice -- 45<sup>o</sup>+23.5<sup>o</sup>=68.5<sup>o</sup> (Sun is 23.5<sup>o</sup> above the Celestial Equator).<br> <P> </ul></font></i> <table><tr> <td><h2>On the <i> Summer Solstice</i> more than 1/2 of the Sun's diurnal circle</a> is above the hoizon and the hours of daylight exceed the hours of darkness. The opposite is true around the Winter Solstice. On the Equinoxes, half of the Sun's diurnal circles are above the horizon and the hours of daylight and darkness are the same.</td><td> <img src="http://pages.uoregon.edu/~imamura/121/images/sunday.jpg"> </td></tr></table><p><table><tr> <td><img src="cel-sph-sun.jpg"></td><td><h2>For an observer at mid-northern latitudes (say in Eugene), the Sun spends a larger fraction of its diurnal motion above the horizon than below for a given day. The opposite is true on the winter solstice. The Sun spends nearly equal amounts of time above and below the horizon on the equinoxes. This is true for an observer at any latitude. </td></tr></table><p> <p><font color="magenta"> <i> The Arctic circle is the region on the Earth where the Sun can be above the Horizon for longer than 24 hours, i.e., where the Sun is circumpolar.</font><p><font color=green><center> Above what latitude is the Sun circumpolar during the summer in the northern hemisphere?</center></font><p></i> </font> </h2> </td> </tr> </table> <p> <p> <h2> </ul> </ul> <ul> <li>The year of the seasons, the <font color="magenta"><i>Tropical year,</i> </font> is a little shorter than the <font color="magenta"><i>sidereal year.</i></font> <a href="http://pages.uoregon.edu/~imamura/121/lecture-2/precession.html"> Why?</a><p> <li>Because the Tropical Year is 365.2422 d long which is around 1/4 of a day longer than the <font color=magenta>calendrical year</font>, the calendar and the seasons would get out of sync if nothing was done to correct for this mismatch. To correct for this, <i><font color="magenta">Leap Years</i></font> are inserted periodically (usually every fourth year). If we always added a day every fourth year, we would still run into trouble because 4 x 0.2422 d = 0.9688 d and an extra 0.0312 d would be added every 4 years. This would again cause the calendar to get out of sync with the seasons. <p> Consequently, further rules concerning leap years are formulated: <p><ul> <li>there are no leap years for the years that are multiples of 100 (i.e., 100, 200, 300, and so on). <p> <li> However, there are leap years if the year is a multiple of 400 (i.e., 400, 800, and so on). </ul> <p> Unfortunately, this still isn't quite right and it was decreed that there would be no leap years for the years 4000, 8000, and so on. <p> <p> <P> <p> <br> <br> <p> <p> <center> <a href="http://pages.uoregon.edu/~imamura/121/lecture-2/lecture-2.html"> <img width=100 src="http://pages.uoregon.edu/~imamura/122/images/ shinkansen-back.jpg"></a> </center>