Unit 4 : Activity 4 : Apparent Motions of the Sun : Sidereal Time : Unit Exam

# Apparent Motions of the Sun

During the year the earth moves around the sun.  As a result, the sun appears to move around the sky once with respect to the stars as seen from Earth.

Earth takes about 365 and a quarter days to travel once around the sun.  Since the earth moves around the sun and we are resident on the earth, it means that the sun appears to shift in the sky about 1 degree per day.  This number is calculated by taking the total degrees in a circle (360 deg, since the earth moves 360 degrees around the sun) and dividing that amount by the total number of days in a year (365.2422).  The result is 360 deg / 365.2422 days to equal about 1 degree per day.

The plane of the earth's orbit is called the ecliptic.  Since the earth orbits the sun, the sun is also on the ecliptic.  As a result, the sun appears to us to move around the sky on the ecliptic.

Please note that the ecliptic is not the same thing as the earth's extended equator, the celestial equator.  The earth's axis (and hence also the celestial equator) is actually tilted by 23.5 degrees with respect to the plane of the earth's orbit, or the ecliptic.

Still don't understand what the ecliptic is?
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If we consider the celestial equator as the reference circle, the ecliptic appears to be inclined, or tilted, 23.5 degrees from the plane of the earth's equator, as demonstrated above.  This orientation means that the sun appears to transit the sky north of the eelestial equator during part of the year and south of the eelestial equator the other part of the year.  The interactive graphic below illustrates this point.

Interactive Graphic 4-1-1

For details on the tilted figure-eight motion of the sun, you can visit the non-ISU web site http://www.analemma.com

On the illustration below, click on the Play button towards the bottom right.  Each time you click on play, a new step will be shown.  After you click on Play enough times, the pattern will repeat.

Please note: The label for the Winter Solstice in this animation contains an error - this is the shortest, not the longest, day of the year. We will fix it as soon as we find the flash file for it.

In the plot above, declination is on the Y axis (or vertical axis) and right ascension (measured in hours) is across the top.  You can take this sky plot and wrap it around a sphere, with the two points at the edges labeled "vernal equinox"just touching.   Both the celestial equator (the straight line with dec = 0 deg) and the Ecliptic (the sun's apparent path) would be circles on the surface of the Celestial Sphere.  Click on the silver play button above to watch the successive steps.  The interactive graphic will repeat itself after you pass through all the season.

The maximum declination that the sun achieves is +23.5 degrees.  This number naturally corresponds to the tilt of the Earth's axis.  The sun reaches this declination at the summer solstice around June 21.  This day is also called "midsummer" or "the first day of summer".  The sun reaches a declination of -23.5 degrees at the winter solstice, about Dec. 21.

Don't have a clue what these graphs mean?
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Interactive Graphic 4-1-2

So, around December 21, the sun has a declination of –23.5 degrees.  As the months pass, the sun gradually moves higher in sky (northward if you are in the northern hemisphere) as it gains declination (greater than –23.5 degrees).  Around March 21, the Sun crosses the celestial equator.  This moment and the date are both called the vernal equinox.  The day is also called "the first day of spring."  To make things even a little more confusing, the position in the sky where the sun passes the celestial equator heading north is also called the vernal equinox.  Don't let this confuse you, it is no worse than knowing three people who are all named "Tom."

Remember! We are talking about the gradual shift in the sky over the course of a year, not the sun's daily transit from east to west.