EVALUATING THE LUMINOSITY, TEMPERATURE AND PERCENTAGE OF THE AREA COVERED OF A SOLAR ECLIPSE

Rosa M. Ros and Ederlinda Viñuales,
"EAAE Summerschools" Working Group
Technical University of Catalonia and Zaragoza University, (Spain)

Abstract

Our interest is in studying the Sun's eclipse from different perspectives. We study the changes in luminosity (with a light meter), temperature (with a thermometer) and the percentage of area covered (by photography). During the eclipse, it is necessary to periodically measure the luminosity, the temperature and to take photographs.

After the eclipse, the results of luminosity and temperature will be printed in a table, which can be used to draw a graph of luminosity/time and another of temperature/time.

With the photos we calculate the percentage of the area covered using 1 mm ruled graph paper. We use a transparency, onto which we have copied the graph paper, and we put it on each photo and we count the number of squares both covered and uncovered, to calculate a good approximation of the percentage of the area covered. With these values we will be able to draw a graph of the percentage of the area covered with respect to time passed.

Luminosity and temperature

A solar eclipse is a very spectacular phenomenon and has always taken people's attention since the Antiquity. The interest increases for observing this kind of phenomena when it's about the a total one, like the next (August 11th, 1999). Scientific, amateurs and all rather curious people prepare expeditions for observing this phenomenon from some place when the eclipse will be total.

   

In paper and book about Astronomy in ancient cultures is easy to find references about the impact, curiosity and fears that solar eclipses caused in members of these communities. Leaders and kings made interpreting to astrologers how this phenomenon might affect in their life, countries and so on; even we can find references about the behaviour's change in animals. It's not difficult to understand this behaviour in ancient people because of, while a solar eclipse occurs, we can verify variations in luminosity, temperature, atmospheric pressure and even, wind's gusts, beside the hiding of the Sun behind the Moon. Whit the end of making well the practice that we propose in this paper, it's necessary to know exactly times of eclipse beginning, maximum and ending for planning previously the sequence of different activities that it's necessary to do during the eclipse. This information can be found in any astronomic yearbook published in our country. We have to prepare the photographic camera and to link up it to the telescope. In the telescope is compulsory to put a solar filter because to observe directly to the Sun through it might be very dangerous. The exposure time given to the photographic camera will be the automatic or using the photometer, as if we would take a photo of a sunset. It's also important to use a lens with not too much enlargement because we are interested in taking all diameter of the solar disc.

Beside of filming the initial contact, the maximum and the moment of the end of the solar eclipse, we will take a photograph each 4 or 5 minutes with the idea of getting a complete sequence of the phenomenon. It's important also to take one photo before beginning the eclipse and another after finishing it. Each time that we take a photo, we'll annotate the luminosity, temperature and atmospheric pressure at that moment, writing the observed values in the table 1.

The two last columns of the table 1 can't be filled up during the eclipse observation, so they will be filled up after developing photographs. It's important also that all those were made with the same enlargement.


table 1

Percentage of the covered area

For calculating the covered area we suggest to use 1 mm ruled graph paper because as it's transparent, it can be placed over the photograph and it allows us to account the small squares of the illuminated zone. As calculating covered area by this method is very difficult, we'll add a complete square when the covered area was more than a half, on the contrary, if more than a half is illuminated we won't count it (Fig.1).


Fig.1

First at all and following the explained way above, we'll account NQ (the total number of small squares corresponding to the total solar surface) if we might take a photo before or after of the eclipse; if we couldn't get it we should use some other one in which we can account all small squares that cover the solar disc. After that, we account nq (the number of squares corresponding to the illuminated zone) for each one of the photographs, and as consequence we'll be able to calculate Si (percentage of the illuminated zone) and St (percentage of the covered zone) in each case.

where
Si signifies percentage of the illuminated zone in each photograph;
St, percentage of the covered zone in each photograph};
nq, number of small squares corresponding to the illuminated zone in each photograph;
and
NQ, number of small squares corresponding to the total solar surface.

We'll calculate the solar radium using a photograph taken near of the eclipse' ma-ximum. For doing that we'll proceed as follows. First at all we should choose a photograph and over a copy of it we take three different points over the border of the lunar surface {xl, y1, z1} and other three of the solar surface {xs, ys, zs}. In each case we'll draw medatrix determinated by{ xl, y1} and by { y1, z1}. The point where both mediatrix cross each other is the centre {Cl} of the lunar circle. So we can measure {rl}, the Moon' radius, over the copy of the photograph (Fig.2). Repeating the same process with points of the Sun we can draw the centre {Cs} of the solar circle and measure { rs}, the Sun' radius over the copy (Fig.2).


Fig.2

It's convenient to repeat the described method with other photographs with the end of adopting as radius of the Moon and Sun the average of all obtained results.

Finally we'll check that both radii are practically equals; it signifies that the angular amplitudes of both celestial bodies are the same observed from the Earth. The distances from our planet to each one of them are very different and about this the real diameters have to satisfy the same relation because we see both practically equal (Fig.3).


Fig.3 : Sun and Moon are observed under the same angular amplitude
No real proportions have been kept.

By similarity of triangles in the figure 3, we have:

where
TL is the distance Earth-Moon in km.;

TS, distance Earth-Sun in km.;
Dl, diameter of the Moon in km.
and
Ds diameter of the Sun in km.

Aristarcho already deduced in the III century b.C. that:

TL = 115 Dl

as distance from Earth to Sun is known we can deduce the solar diameter:

All information obtained can be used for drawing a set of graphs in which we'll be able to show the relation among the different parameters studied. We have a discrete information about these parameters, it's say, we have only isolated points because they have been taken in intervals of 5 minutes more or less. If we join these points we'll get a continuous graph which corresponds approximately to phenomena observed. It's very interesting to discuss results after drawing the graphs because some time they don't agree with the expected ones. The theory says that when the eclipse begins the Sun surface is covered and light decreases up to the maximum is got; after, the Moon is leaving the solar disc and the luminosity increases up to the eclipse finishes.

The 1984 solar eclipse had place in the afternoon, close to the sunset; about that when the light had to increase, the sunset began and this fact affected to the collected data, which leaded to obtain unexpected graphs.

Finally we propose to draw the graph of Time/Covered Zone with data of the table 1, taken into account that we can observe peculiarities due to the same eclipse or no. We believe also convenient to draw the graphs Time-Luminosity and Time-Temperature with data taken from the table 1.

Shadow bands.

The phenomenon of shadow bands is an interference model of direct and indirect rays of the Sun which also explains the shimmering of stars. If there are interfering rays the observer can see light bands and shadow bands when the Sun's rays are compressed. The shadow bands resemble the effect observed on the image of the water of a swimming pool on a sunny day.

There are various kinds of shadow bands and it is not generally easy to see them. Normally, at first the bands appear separated by some meters, but afterthat the situation changes and at the end they may only be separated by a few centimeters. For example, the shadow bands can appear as undulated bands oriented in a north-south direction and they move from east to west with a speed of approximately of 3 or 4 m per second, with intervals between them of 7 and 20 cm.


Fig.4 : Shadow bands.
 The shadow bands appear when the Sun's light starts to disappear because the Sun's surface disappears because of the Moon covering it. When the Sun's crescent is almost totally covered (a little before being wholly covered) the bands start to appear and change becoming more regular and differentiated. The cause of the bands is the Sun's brightness decreasing and when light is reduced direct light appears which produces interferences and the phenomenon of shadow bands.

To observe the bands it is a good idea to spread a white sheet on the grass or better still, on a wall and the observer should be situated a little higher.

At first the bands are very weak, but when the Sun is almost totally covered the bands become more intensive and regular. They can be observed when the Sun is almost covered for 4 or 5 minutes (sometimes it is possible to observe them 20 minutes before, but then they are very weak). In general it is not easy to see them. Normally they only appear as a blur and small spots of light which are moving as a flash on the soil or on a wall.

It is difficult to observe this phenomenon because there is only a difference of 1% in brightness between natural light and the shadow band.

Normally the bands appear some minutes before Sun is totally covered and, although it is possible to observe them after the Sun is completely covered this situation is very rare. Sometimes it is possible to see them 10 to 20 minutes before the Sun is totally covered. This is a very variable phenomenon.

It is very difficult to take photographs of shadow bands because of the low level of contrast, their very fast movement and also the lack of general luminosity. It is perhaps advisable to use a video camera to register this phenomena.

To observe them as well as possible a specific instrument can be used, that to say a wooden circle divided in eight zones of 45º. This circle can be oriented according the cardinal points. A white piece of paper covers the circle and on it a mobile arrow is held in the center to mark the direction of the bands. It is possible to measure the time which the bands need to cross the circle and calculate their speed.

Reference

Poitevin, P. : Bandas de sombra, sombras volantes, Universo, 48, 28, 33, Barcelona, 1998.
Ros, R. and Viñuales, E. : Astronomía: Fotografía y Telescopio, Mira Editores, Zaragoza, 1993.