No Frills Help!

Graph This!

 

Yes!  Yes! Quickly before the dullnamic duo, Dick and Jane, arrive.  They don't know I'm here and I'd like to have just one No Frills Help edition without their characterless chatter.  So, what exactly does the graph like the following represent?

 

Wonderfully Dull Graphic Number 1

You should know that when we try to map things here on earth we use latitude and longitude.  To map things in the sky, you should also know by now that we use declination and right ascension.  You may have noticed that declination and right ascension are very similar to latitude and longitude – if you haven't noticed this, they are very similar.  So in the graph above, right ascension (RA) for any object in the sky is listed across the top – the X axis.  On the right side you see degrees marked out which is the declination.  With that said, let's look at the next graphic.

Boring Graphic Number 2

In the same way we "flatten" the spherical earth onto a flat surface to create a map, Boring Graph Number 2 is just a projection of the celestial sphere onto a two dimensional surface.  In the case of our moving graphic, we are looking at the position of the sun on the celestial sphere during certain times of the year.

In my usual brilliant manner, I'll give you some graphing examples to help you along.

In this example we will be graphing the sun throughout the year.  You should recall that on March 21 of each year, the sun reaches the Vernal Equinox, which is 0h RA.  If we have equal amounts of day and night this day, then the sun's declination is at 0 degrees.  So when we graph the sun at that time, we get the graph above.

Still Boring Graphic Number 3

To continue with the example, the above graph is the sun for the first day of summer. The blue dot is where the sun was at the Vernal Equinox, the yellow is its present position - the first day of summer.  If you think it through you will remember that the sun is at the highest point above the horizon on this day (compared to all other days in the year) for the Northern Hemisphere.  This means that the sun has to have the highest declination on this day.  The largest declination possible due to the tilt of the earth's axis relative to the plane of the ecliptic is 23.5 degrees.

You might ask yourself, "Gee, Mr. Brisban, how do I find the right ascension (RA)?"  The graph that I drew here is for one year.  By moving from spring to summer, we should have traversed one quarter of the graph.  One quarter of 24 hours is 6 hours.  That is the RA for the sun on June 21, as plotted above.

Somewhat Interesting Graphic Number 4

Again, the graph above is where the sun will be at another time of the year.  This time it is the first day of fall, September 21.  We know that on this day, everyone on earth will see the same amount of sunlight as darkness.  This means that we are at another equinox.  The Vernal Equinox had a declination of 0 degrees, so that also applies to the Autumnal Equinox.  We have now gone half a year since we started tracing the graph.  This means that the RA now has to be at 12 hours RA (half of 24 hours).

Much More Interesting Graphic Number 5

Continuing on to the first day of winter, December 21, we receive the least amount of sunlight, and we have now gone three-quarters of the way in RA on the graph.  Therefore, the sun's declination is –23.5 (the exact opposite of the summer) and the RA is 18.

Good Graphic Number 6

To finish the example, (as shown above) I will back us up to the Vernal Equinox.  The Vernal Equinox is at both 24 hours RA or 0 hours RA.  They are one in the same.  And the sun is at 0 degrees declination.

Brisban's Brilliant Graphic Number 7

Finally, if you could apply more points of where the sun is on different days of the year, you would see that the sun follows a gentle curve.

That's it for this edition of No Frills Help.  And to think, no Dick and Jane for the entire session – Oh! Sweet miracle!