How much does the setting Sun move on horizon?

[CT2MEwoodnutt]

Hi Group,

I'm a 'Sunset Nut' and try to watch the Sun set everyday that I can.
We live up on a hill, with a clear view towards the West, so every day that is relatively clear, I watch it.

I watch the Sun's movement to the left, or South, from the week after June 21st, until the week after December 21st, then it moves to the right or North and repeats.

I'm wondering, about how much does it move from one day until the next?
One 'Sun's width' (as viewed when it is on the horizon) per day, perhaps?

It has moved 'three fist widths', as viewed with an out streched arm, since December 21st, at it's most southerly position.

Just curious as to how much movement each day?

Does anyone know?

Thanks!

CTwood Nutt

[303Guy]

That would be 23.5° north to south but the daily rate of change will vary from zero at the solstices to a maximum at the equinox. It would be interesting to learn just what the change is.

[harry chickpea]

Here ya go:

Beginner's Guide to Equatorial Sundials

Table of the Declination of the Sun

[Ericthebean]

On the equator, the setting sun moves on the horizon 23.44 degrees to the north of west June 21st (or 293.44), 23.44 degrees to the South of west on December 21st (or 246.55), and is straight west on equinoxes (270)
(That assumes no atmospheric refraction. Atmospheric refraction throws this off from being exact because in actuality the sun doesn't set on the horizon, it appears to set when a tad below the horizon (about -.83 degrees below the horizon) due to appearance of sun above its true position and that the top of the sun's disc, not middle of the sun's disc, marks true sunrise/sunset.)

Now, the farther from the equator you go, the more north of west the sun appears to set in June and the more South of west it appears to set in December

In the Southern Hemisphere mid-latutudes, the June sun rises in the Northeast, moves counterclockwise around the northern sky, then sets in the Northwestern sky. This is a short day.

In the Northern Hemisphere mid-latutudes, the June sun rises in the Northeast, but moves clockwise around the southern sky, then sets in the Northwestern sky. This is a long day.

December it's vice versa and it's the long day Southeast sunrise looped around northern sky for the Southern Hemisphere, and the short version for the Northern Hemisphere around the southern sky

On the June solstice at latitude 40 degrees north, the formula for whete the sun's azimuth angle AKA Compass direction will be when on the horizon Is simply

360 minus

arc cosine of
[Sin(23.44-degrees) - sin(40-degrees)*sin(-0.83-degrees)]/[cos(40-degrees)*cos(-0.83-degrees)]

Where 0=North 90=East 180=South. 270=West. In between these angles you get your NE, NW, SW, SE etc

For sunrise you would do the same thing but not take 360 minus the arc cosine....you would just take the arc cosine. But since the declination angle changes continuously, for better precision you should not use exactly the same declination angle you used for sunset as the one you use for sunrise. But around the solstice it's safe to do it this way because there's hardly a change in declination angle for days at a times around solstices.

A quicker equation if you don't care about atmospheric refraction is just take for June 21 on 40 degrees north

360 minus. Arc cosine of (sin(23.44) / cos(40))
In excel it would be this formula
=360-((acos(sin(23.44*(3.1415/180))/(cos(40*(3.1415/180)))/(3.1415/180))

This comes to 301.28. In other words 31.28 angular degrees farther north from 270-west is roughly where the sun will set on Latitude 40 (Close to say Philadelphia Pennsylvania on June 21st. It's more than the 23.44 as it's farther from the equator.

About The pi/180 in the excel formula: it is to convert degrees to radians for sines and cosines. MS Excel defaults to using radians and so if you don't include pi/180 you will not get the correct formula outputs.

Hope this helps!

Also, there is a roughly similar relationship between length of day and how far from West the sun sets. It is not exact though so you can't blindly measure length of day by position of the sunset proportionately but it's a good ballpark rule of thumb for middle and higher latitudes. Doesn't work in the tropics because the sun paths closer to the equator, throughout the day, do not align smoothly around compass degree angles. Instead the sun moves across the sky in a vertical motion. As a result, time in hours correlates less to compass angles being connected to times of the day.

The fluctuation in compass angles at times of the day phenomenon in the tropics, is closely analogous with the variation in "lengths of day" in the arctic/antarctic. In fact, these are completely tied together.