DETAILED CONSIDERATIONS

The word SOLSTICE is derived from the Latin word SOLSTITIUM where sol means sun and stitium means stand still. Thus, the solstices occur on the day when the sun stops rising, or lowering, at its mid-day high point and stops changing the azimuth (angular degrees from south) at sunrise and sunset. Further, although we normally think of the solstice as occurring on a single day, it actually occurs at some specific instant during that day.

Accordingly, it is not possible to determine the exact instant of the solstice with a single observation. However, by precise measurement of the movement over a several day period surrounding the solstice the actual time can be determined by plotting the data and observing when the high (or low) point in the resultant curve would have been. Having determined the date and time, and knowing the length of a year, allows a prediction of when it will occur in the next year.

For those who are only interested in the day of the solstice such accuracy is not required - and observations may be made leading to selection of the day without concern about greater precision. However, even simple daily observations require some care and understanding for the daily change in elevation or azimuth is very small on the few days before the solstice. (About 1/2 arc minute.) Select the RATE OF CHANGE from the menu to see a detailed discussion of this subject. Data for San Francisco is given in the DATA TABLE.

The light from a star is said to be a POINT SOURCE, since it comes from such a great distance that the naked eye cannot determine its physical dimension.

The light from the sun is not a point source, but rather has visible width from one edge to the other. The magnitude of the angle formed by lines extending from your eye to each edge is about 0.5 degree (30 minutes). This changes slightly throughout the year due to the varying distance that the sun is from the earth. Select SUN SIZE from the menu to see calculations of the angular diameter of the sun.

Since this is substantially greater than the amount of angular change per day in the few days surrounding the solstices it is important to use the light from only the leading or trailing edge.

DIRECT VIEWING

Direct viewing of the leading or trailing edge may easily be observed providing the source of light is not strong enough to damage the eye - or if filters are used. Since light from the apparent sunrise (and sunset)is really light which has been bent by the earth's atmosphere the brightness is decreased momentarily and allows direct vision. (Select SOLAR REFRACTION from the menu for a discussion of this phenomena.) Further, when only a very small slice of the sun is being viewed the amount of light is proportionately lower. However, the brightness quickly increases at sunrise (decreases at sunset) so that the time available for making a direct viewing observation is rather short. The time it takes for the sun to rise from the top edge being just visible until it is fully visible is approximately two minutes. This time is also limited by the fact that at all latitudes but at the equator, the azimuth of the sun changes as it rises - giving a rise of nearly a 45 degree angle at San Francisco. Accordingly, the azimuth must be measured at a specific point in the sunrise (sunset).

Thus, it is possible to directly view the leading or trailing vertical edge at any time when the image is more than one half visible just above the horizon, and to then record the position relative to a distant horizon at which that edge occurred. The accuracy of this method is on the order of 1/2 minute, about the same as the motion of the sun in one day, so that with very careful observation, the day of the solstice can be observed.

A longer observation period may be used if there is a convenient slanted object on the distant horizon, such as the "heel stone" at Stonehenge, in lieu of simply observing the sun rise on the horizontal plane.

The same method can be used to observe the leading or trailing horizontal edge of the image to determine the elevation of the sun. However, unless a mountain is nearby, the distant marker (such as the roof line of a distant building) will be much closer than a distant horizon and the observers eye is likely to need to be fixed at something other than his normal height. Further, while observations of the azimuth of the sun at sunrise or sunset may be made by direct viewing, observations of the elevation of the sun at mid-day can not be made by direct viewing unless a light filter is used.

Another method to measure the elevation of the sun is to use a sextant, an instrument historically used by navigators to determine their latitude. This instrument has built in light filters allowing direct observation of the sun. The accuracy of such measurements can be as small as about 1 minute (0.2 minutes with a worm gear vernier), which is just about that which is required to observe the change in the sun's elevation one day before the solstice.

While commercial sextants can be expensive, there are a number of ways to inexpensively make your own. Click here to view one of those web sites.

An even simpler method is to use a simple astrolabe. Click here to view a simple model. or Click here to see how one might be constructed and used. However, the accuracy of even a precisely constructed astrolabe is only on the order of 15 minutes.

INDIRECT VIEWING AND SHADOW WIDTH

The simplest method is to allow the bright sunlight to cast a shadow and to make daily marks recording the changing position of that shadow..

However, this method has three inherent potential problems.

1. The first is that unless you have a rather long distance between the object causing the shadow and the marking board the recording of daily observations will result in over lapping marking lines.

2. The second is due to the diffraction of light at a straight edge. When parallel light (such as comes from a distant pin point source) passes a straight opaque edge it does not cast a sharp shadow. Instead, some of the light at the edge bends towards the light obstruction causing some light to be cast into the "shadowed" portion of the observation surface. (Click here for a more detailed description of light diffraction.)

While a relatively small effect, this makes it difficult to obtain a precise viewing of the leading edge of the sun's image since there continues to be some light in the shaded area.

3. The third is that, even ignoring the diffraction phenomena, the sun will cast a shadow which is not sharp but will have 3 parts, the fully illuminated part, a partially illuminated part, and a fully shadowed part, as illustrated here.

Since the angular movement of the shadow will be the same as the angular movement of the sun, the movement of the shadow per day is substantially less than the width of the shadow. Thus, analogous to the need to use the leading or trailing edge for direct viewing, it is useful to find a method to determine the leading or trailing edge of the sun rather than its full shadow.

Three methods and their resultant shadows are shown below.

The first uses a simple straight edge, and does not easily allow a determination of the position of the leading or trailing edge.

The pin hole method suffers from the same problem, merely posing it on in a circular fashion along with the overlapping diffraction light.

The tunnel method, if the tunnel is long enough, minimizes the width, but still provides light as long as the sun is passing across the opening. However, it works well for determining the solstice if it is aligned so that only the leading edge of the sun appears until the sun reverses its course.

The use of an astrolabe which uses a drinking straw for its alignment with the sun uses the same principle.

PRECISION METHODS

Precision of the observation of a shadow can be improved by two approaches.

The first is to have the shadowing object be far removed so that the daily movement of the shadow it causes is large. The use of a mountain to partially shadow the rising sun at Machu Pichu, Peru, is an example of such a case.

The second is to be able to observe and record very small changes in the position of the shadow.

This latter aspect has two consideration, your ability to determine the exact edge of the shadow due to the shadow width phenomena and your ability to record these small changes.

One method to precisely determine the edge is to use a very thin mirror to cause reflection of the shadow such that only a very narrow slice of the leading or trailing edge of the sun is reflected back to the eye. With extreme care this can be done by the naked eye, but a suitable filter should be used to avoid problems when the mirror is inevitably accidentally adjusted so as to give a reflection of the full sun.

Click here to view an important discussion of the hazards of direct viewing of the sun.

A safer, and more accurate method is to use a poorly reflecting mirror so that the sun cannot damage the eyes.

If the recording method is to simply place a mark on a marking board, then the limit will be when the daily shadow movement is less than the width of the pencil mark, and the marks will overlap. (Providing a date record on each mark will be an even further limit.)

An alternative is to observe the edge of the shadow on a marking board which has very narrowly spaced grooves, such that the number of grooves from the edge of the shadow to a fixed elevation position can be counted and recorded separately.

A method of combining these two techniques is discussed in the section on Do Your Own Tests.

ALIGNMENT

In order to make observations there must be an alignment along a straight line of several things.

DIRECT VIEWING OF THE DECLINATION OF THE SUN

Direct viewing requires the establishment of a straight line between your eye and the sun which crosses some intermediate marker, such as the horizon or some other distant mark. In order to be accurate two conditions must be met. First, you must pick out the point on the horizon where you see the sun. Second, unless you are a very long distance away from the horizon, you must not move your eye for subsequent observations. One way to do this is to align your eye so that it just passes a nearby fixed object in looking at the sun. There will then be four items in line, your eye, the place which fixes your eye position, the point you select on the horizon, and the sun.

Another way to accomplish the same thing is to have two objects with vertical sides, so spaced that when you move your eye their edges seem to nearly touch, leaving a narrow slit in which you can see just the leading or trailing edge of the sun when your eye is in the correct position.

If this mechanism is movable then you can track the movement of the declination of the sun. If you have already determined the position of the sun at the solstice you can set your objects so that the leading edge of the sun is just visible and then wait for it to occur again on the next day of the solstice.

INDIRECT VIEWING OF THE ELEVATION OF THE SUN

Indirect viewing also requires an alignment of objects. If using a shadow you need a south facing straight line overhead light obstruction (such as the edge of a roof) and a surface on which the shadow will fall. This surface should be such that you can mark the position of the more distinct dark edge of the shadow on successive days. After you have observed a solstice you will have a mark for it, and can watch as the shadow approaches this mark in subsequent years.

While it is obvious that azimuth observations must be made at sunrise or sunset, it is not required that shadow observations be made at exactly mid-day. However, they must be made at exactly the same time each day. This can be done by using a clock. It may also be done by using the equivalent of a sun-dial by creating a vertical marker on the roof line so that this marker casts a small vertical shadow and drawing a vertical line on your marking surface from the point where that marker appears. On subsequent days take your readings only when that marker is even with that vertical line, which will be close enough to the same time for this purpose.

Although the roof line does not have to be facing exactly south, and the time of day does not have to be exactly mid-day, making accurate observations will be easier if your shadow is cast from direct south and your marking time is 12:00 noon (not daylight saving time).

OBSERVATIONS AT THE EQUINOXES VERSUS THE SOLSTICES

Since the suns movement per day is nearly zero for the day covering the instant of the solstice, determining the exact day on which the direction of movement stops, and then changes, is difficult. In contrast to this fact, the suns movement per day is the greatest at the equinoxes. Additionally, for some, the Spring equinox may have been more important than the solstice due to its closer proximity to the best day for planting crops.

Observations of the equinoxes require the same considerations as those for the solstices, except that there is greater movement each day - perhaps allowing more accuracy in the observations.