Solving problems with a Solar Motion Demonstrator
To study Positional Astronomy each participant will construct his own celestial sphere with the zenith above his head and a horizon N-E-S-W. From a cardboard, glue and brass fastener each one is building his own small, hand-held device, that is to demonstrate the apparent mo-tion of the sun across the sky at any time of the year for any observer at any latitude in the northern hemisphere. The participants are investigating a collection of problems with the instrument's use.
They can research questions like:
Observing, experimenting, predicting and visualising skills are developed. The skills have real-world application. The device is a good preparatory tool for visiting a planetarium, for introducing positional Astronomy, and for working with an armillarsphere in a classroom.
|With scissors cut out the frame along its outline. Fold the frame along the creased lines, so that the month piece swings all the way around. Fold the flap marked „glue" and the quarter-circle below it away from you so that a right angle is formed. The backside of the blank quarter circle hits the backside of the frame. |
Cut a small slot in the horizon disk at north position. Apply glue to the marked portion of the frame. Press the north east quadrant of the disk against the glued proportion. The correct alignment of the frame and the disk is essential to the working of the device.
The head of the brass fastener represents the sun. Bend the fastener tabs over the outside edge of the month piece. The fastener must be able to slide up and down along the month piece.
The Solar Motion demonstrator was designed by Professor Snider of Oberlin College, USA. You may reproduce it for your own classroom or planetarium use (but not for commercial purposes).
- The head of the brass paper fastener represents the sun.
- The latitude part of the frame is used to adjust the horizon disk and to set the observer at any latitude from the Equator (0°) to the North Pole (90°).
- The twisted month arm of the frame has two functions: Setting the sun marker at the desired month adjusts for the time of the year. Swinging it from the east to the west moves the sun in its apparent daily path over the earth.
|N||North Cap||71,175°||most northern point of Conti-nental Europe|
|D||Berlin||52,5°||Bad Honnef 50,6° (5th EAAESS) near Bonn|
|ES||Murcia||38,0°||(equal latitude P: Beja)|
|I||Rome||41,5°||(equal latitude ES:Barcelona)|
Justify your answer using SMD.
Imagine you are standing at the black dot of the horizon disk. A clear horizon around you. With the other hand you pivot the month-semicircle. The paper fastener describes the path of the sun. The angular height of the sun is the angle between your line of sight to a point on the horizon directly beneath the sun and your line of sight to the sun. The sun reaches its greatest height at a time halfway between the sunrise and sunset. By changing the fastener to different months you can get a sense of how large this maximum angular height is for the various times of the year.
If you pivot the fastener over its entire range, this corresponds nearly to one rotation of the Earth, which takes 24 hours. You can determine the relative lengths of day and night by comparing the part of motion above (daytime) and below the horizon.
There are two days called "vernal equinox" (about March 21) and "autumnal equinox" (about September 22).
These days are called the "Summer Solstice" and the "Winter Solstice". On these days the fastener stops and reverses its direction of motion along the month piece. The word "Solstice" means "Sun stands still".
Two factors are responsible for seasons ( referring to the horizontal system ) : the length of the day, and the angle sun's rays strike the ground.
North of the "Arctic Circle" (about 66,5° latitude) the sun will not set at least one day of he year.
Latitude 0°: Vary the time of the year and see how the path of the sun across the sky changes. Notice that the setting sun moves in the same way.
The point straight ahead on the celestial sphere for any observer is called the Zenith and is always 90° from the horizon. The arc that goes through the north point, Zenith, and the south point of the horizon is called Meridian.|
Explore the range of latitude and of times of year for which the sun passes through the zenith. For an observer north of the "Tropic of Cancer" ( at about 23,5° north latitude ) the sun will pass through the zenith. For lower latitudes, it will pass through the zenith at two days of the year only. Which are these days?
The Solar Zenith Angle (Z), which is the angle between the sun's rays and the zenith direction, is the numbers of degrees, that the sun is away from being directly overhead. The complementary angle (90-Z) is the Solar Altitude (or elevation). This is the number of degrees that the sun is above (or below) the local horizon. Solar Noon is that time of day when the sun has reached its highest position in the sky at your location. It does not usually coincide with the noon at your wristwatch.
Set SMD to your latitude and time of the year. Go outside in the sunshine. Hold the horizontal disk of SMD horizontal. Pivot the month part and turn the horizon so that the "N-S" line points in various directions. Hold the device in a way that the shadow of the month part be a thin line as possible, while at the same time the shadow of the paper fastener (=Sun) falls exactly in the middle of the horizon disk, which will show you now the correct geographic directions.
Season Start of the season Length of the sun's path (day/night) Sunrise Azimuth Sunset Azimuth Spring March 21 ... 270° ... Summer ... ... ... ... Autumn ... ... ... ... Winter ... ... ... ...
The apparent motion of the sun results from the rotation of the earth every 24 hours around its axis. Even though it is known that the ancient model of a stationary Earth is incorrect, we will still use it because it is a convenient way to predict the motion of the Sun relative to a location on the Earth. It coincides with the every-day experience of the children.
An old German poem says:
This statement is only correct at the equinoxes. On both days at any point of the earth the sun rises exactly at 6 a.m. in the East and sets at 6 p.m. in the West. At any other day the rising and setting points are shifted to the North and South depending on the latitude.
If you specify the location of the sun in the Altitude - Azimuth System, the observer is located at the centre of his "celestial sphere" with zenith Z above his head and the horizon N-E-S-W .
Select the Java applet "Apparent motion of a star" to show an animation of the celestial sphere changing with latitude.
Download it !
The second way of specifying star positions -preferred by astronomers- is the Equatorial Co-ordinate System. This system is very similar to the Longitude-Latitude System used to specify positions on the Earth's surface. This system is fixed with respect to the stars. A star's position does not depend on the observer's location or time. Fig.4 shows, how in the Equatorial System Right Ascension (RA) and Declination d are defined.
|For the following activities alter the design of SMD. The "month arm" has to be covered with a blank strip of paper. If you put an set square at the horizon, you can determine the solar altitude by measuring the angle.|
At which days sun crosses the meridian at its highest and its lowest point in Helsinki, Bad Honnef and Tavira? How long last those days at the different locations?
By twisting the month arm determine the meridian points, find out the angles and compare the results with the calculated meridian altitudes of Eq. 1.
Using observations of the solar altitude during a midsummer day you get the maximum and minimum elevation at Your location. If hsun,max is the Meridian Passage of the sun in the South and hsun,min means the Meridian Passage in the North you can determine the declination of the sun :
hequator, max + d = hsun,max
hequator, min + d = hsun,min
hequator, max = - hequator,min
hsun,max +hsun,min= 2d
d = (hmax + hmin ) / 2 (Eq. 2)
Determine observer's latitude by marking the known values on the blank month's arm of SMD.