MadSci Network: Astronomy

Re: Why circle of sun on sun-dial vary from South to North between 12/21 & 6/21

Date: Wed Mar 3 22:56:50 1999
Posted By: David Taylor, Staff, programming, Testronics
Area of science: Astronomy
ID: 919877407.As

Why does the sun's midday position in the sky appear to change from Summer 
to Winter?

I'm going to ask you to create some models to help increase your 
understanding of this question. The pencil model is pretty basic, but I 
recommend you actually construct the globe model.


Find a pencil and a bright flashlight and turn the lights out. We'll 
pretend the pencil is a little man standing on the surface of the earth. 
The flashlight is the sun. Hold the pencil vertically on a table top, 
hold the flashlight out to the side of the pencil, and aim 
the flashlight at the pencil and move the flashlight up and down. Notice 
what happens to the shadow. It gets longer and shorter as the flashlight 
moves up and down. The shadow is longer when the flashlight is lower in the 
sky (Winter) and shorter when the flashlight is higher in the sky (Summer).


Now for the really neat model. You will need a circular table and a 
standard globe that has a TIPPED AXIS and the northern hemisphere on top. 
You are almost certain to find both of these in your local library. Another 
globe, or perhaps a drinking glass with a volleyball on top can represent 
the sun. Put your 'sun' in the middle of the circular table, and your earth 
globe on one edge of the circular table. This non-scale model will 
represent the earth-sun system. Our earth orbits the sun in a 3% eccentric 
ellipse. This is really quite close to a circle. The earth is actually 
slightly closer to the sun during the northern hemisphere's winter/southern 
hemisphere's summer. For this exercise, treat the earth's orbit as a 
perfect circle.

In this model of the earth-sun system, the earth will spin on its axis to 
the right, or counter-clockwise when viewed from above. Spin the globe with 
your finger so that it moves in a counter-clockwise direction. Now move the 
entire globe counter-clockwise around the edge of the table. As the globe 
moves around the edge of the table, its axis always points the same 
direction. (The hemicircular bar holding the axis of the earth globe will 
always point towards the same side of the room your model is in.)

The earth rotates around the sun. Its axis does NOT rotate around the sun. 
This is the key to why the sun's midday position in the sky varies to the 
north and south over the year. (I'm intentionally neglecting very small 
effects like precession and nutation.) 

Bordeaux, France (latitude 44 degrees 50 minutes North or approximately 45 
degrees North) is almost exactly halfway between the equator and the north 

Wherever you are on the earth, the sun's elevation in the sky will 
gradually move over a range of 47 degrees (twice the earth's axial tilt of 
23.5 degrees).


Move the globe around the table, keeping the axis pointing in the same 
direction, until the axis is pointing away from the 'sun'. This is winter 
solstice (basically, 'Christmas'), or the peak of the northern hemisphere's 
winter and the southern hemisphere's summer. In Bordeaux, at local noon of 
the winter solstice, the sun will only be about 21.5 degrees above the 
horizon. Why? Turn the globe on it's axis until Bordeaux is pointing as 
close to the sun as it can. This is local noon in Bordeaux (this is 
actually a few minutes away from 12PM, but that's a related but different 
tale.) If you extend a geometric plane tangentially (the horizon) from 
Bordeaux in this position, it will be 21.5 degrees off of the plane of the 
table that earth orbits the 'sun' in. 
90 degrees - ( 45 degree lattitude + 23.5 degree tilt of the earth ) = 21.5 

The sun is hitting the southern hemisphere squarely, and striking a 
glancing blow at the more strongly tilted northern hemisphere. A glancing 
illumination means less energy per area than a perpendicular illumination.


If you move the globe around to the far side of the table, until the 
earth's axis is now pointing at the sun, it is summer solstice (6/21). It's 
now summer in France, and perpetually midnight on the south pole. Spin the 
globe and notice that the south pole is always well in the shadow of the 
earth now. It's as dark as midnight all day long on the south pole this 
time of year. The sun will now rise about 68.5 degrees above the horizon on 
this day of the year. 

90 degrees - ( 45 degrees latitude - 23.5 degrees tilt of the earth ) = 
68.5 degrees.

That's it. With the model, you can make your own coarse predictions of 
where the sun will be in the sky from a given position, date and time.

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