  |
AN ESTIMATE OF THE NUMBER OF STARS
|
|
|
AN ESTIMATE OF THE NUMBER OF STARS
|
|
We follow several and different objectives with this practice. Our main goal is the sky observation to the naked eye. Trying to acknowledge the most important constellations, so: in what part of sky we can find each one of them, how is the zone where they are, what special celestial objets are in them, and so on; sum up, we want to know the sky.
After becoming familiar with sky to the naked eye we will verify that we can see many more stars in a photograph than if we observe to the naked eye, although atmospheric conditions were very good. For that we will have to take a set of photographs of different sky' zones. So, how have to be photographs taken for being useful for our aims?
With photographs we can be able to check that over the Milk Way' zone density of stars is bigger than over any other; also, that atmosphere effects are more important near of the horizon and about that we see fewer stars in these parts of celestial sphere.
Finally with a set of photographs taken each one in a different zone of the sky and selected taking into account comments done above, we'll try to count visible stars that we can observe using this tool.
As consequence, we'll develop this practice in two different parts. First at all we'll give some general explication about how the necessary material can be obtained, it is said, photographs; after that we'll count visible stars on photographs.
It's not necessary to have great and good material for taking photographs that we will be able to use later in the classroom and to obtain interesting results.
A reflex camera is a big precision tool that if we know how to use correctly it can be very useful in our work.
Our experience says to us that our eyes aren't reliable enough. Instead, a photographic camera is an objective and rigorous observer. For example, the Moon seems bigger on the horizon than it's higher in the sky. This is not an optic phenomenon but a simple illusion of easy explanation.
This illusion that can be observed as for the Moon, the Sun as any constellation, can be refuted taking two photographs the same day of a full Moon, one when it's near horizon and another some hours later when Moon is high in the firmament.
In the following, we are giving a short necessary material list necessary together with some advises which we know from the experience acquired taking a great number of photographs.
In the table 1 we give some indicative pointing data; all depend on the material used. We believe that this table gives an orientation sufficient for beginning, besides one advantage is that all things described are common material.
o Reflex camera
These cameras allow to change lens and they are prepared for the use of a cable release that is necessary if to a taking we want to give an especial exposure time.
o Lens
The majority of reflex cameras are endowed with a lent of 50 mm. or 55 mm. These lens are the most appropriate for obtaining practically all photographs for which a telescope isn't necessary.
Obviously, if we have more and different lens our possibilities increase. With any lent, we'll focus to the infinite with the diaphragm completely opened, if there is not too much surrounding lights.
o Tripod
It's indispensable for giving stability to the camera and long exposure times while photograph is been taken.
o Cable release
It's convenient in all cases and indispensable for taking photographs that need a long time of exposure. The cable release allows us to shoot the camera without touching the button, avoiding in this form vibrations and reducing possibilities that photograph is moving.
o Films
We use different films depending on the end for which we want to take these photographs. So,
- Colour: Results obtained for a long time show us colour slides give better results than paper. If we are interested in constellations or planets' photographs, the exposure time needs to be longer and we should use a more sensible film for avoiding moved photographs or with few contrasts; so, in this case will be convenient to use film of 1000 or 1600 ASA. Instead if we want to photograph risings or settings of the Sun or the Moon then to use 100 ASA films is enough.
- Black and white: This film can be useful when there is contamination or surrounding light because they don't affect for getting a darker sky bottom. This allows to us working easier into a city. Normally it's better to use a more sensible film than we accustomed to utilize for familiar photographs. 400 ASA, 800 ASA and even 3200 ASA films are easy to find in the specialised shop and they are sufficient for our necessities.
o Exposure time.
Bad conditions of the sky, contamination and surrounding lights are the principal obstacles when we want to take photographs. As these conditions are variables, exposure times in table 1 are given only as indicators.
When we take a photograph, we always work in the same way. We will take a set of photographs, all taken in the same conditions and changing only the exposure time. For example, if we give a time of 8 seconds, we'll be a set of photographs with the following exposure times:
Although on a certain day we had obtained a good photograph with a fixed time of exposure, the sky conditions can be changed and the best is to take several photographs to make quite sure that we'll have at least one good.
o Clock with second hand We need a clock with second hand if we want to give different times of exposure to our photographs.
o Red light lantern Red light has the advantage that no to dazzle as white light does. So, if we need light for checking some thing it's preferable to use this kind of lanterns.
When we gaze at firmament for some time we are surprised about enormous quantity of celestial bodies that we can observe. Our goal is to realise a simple calculation to estimate the total number of stars on the celestial sphere that we can observer. This number will depend, obviously, on conditions that we make the observation; it said, stars visible to the naked eye are about 6000 assuming ideal conditions, but only about 2000 or 2500 at any one time. We'll count stars using a photographic camera set up on a tripod.
Photography facilitates to us the recount of stars and besides it increases the number of visible celestial bodies; because of films can register much more stars than our eyes can. If we utilise a high sensibility film, for instance colour 1000 ASA or 1600 ASA slides, results will be surprisings and espectaculars.
We suggest to take several photographs to different directions of sky. We advise a minimum of six photographs taking special care of these copies bellow to different zones of celestial sphere. Photos 1 and 2 are only a sample of the ten slides that we usually screen in the classroom for doing this practice with our students.
Some photographs should be of the Milk Way zone, so we can observer the high density of stars that there are in this zone. The rest of photographs is convenient been taken of other areas of sky with the end that recount represents reality as possible as it was.
Due to visibility problems (over all because of refraction atmospherics' phenomena), we can observe fewer stars near of the horizon than really are. About that we only use in our projection one slide taken of these celestial globe' zones.
The slide near of the horizon that we screen is the Gemini constellation. In our slide is impossible to see any stars in the lower part because Gemini is just over the horizon.
It's important also to take all photographs with the same conditions, so we can compare one to other; it's said, same lens, same exposure time (approximately 40 seconds), same atmospheric conditions, and to take into a count in the moment of screening slides or to develop photos all had been made with the same enlargement.
It's interesting for us that some photo or slide had been taken of some known constellation with the end of establishing a relationship between centimetres that this constellation occupies on the photograph and it equivalence on the celestial sphere in degrees.
For example, if we take a photo of the Ursa Major (Fot.1) we can measure the distance d, in centimetres, between Merak and Dubhe; this distance is equivalent to about 5 declination degrees (Fig.1, Table 1), This is p /36 radians.
Knowing this relation we can calculate R, the radius of the celestial sphere that we can take in our slide or photograph (Fig.2).
Establishing a ratio (Fig.3) between d on the photo, the number of equivalent radians nr and the celestial sphere radius R, we have:
For Merak and Dubhe, for instance, nr = p /36 radians.
For each one of the photographs we can choose a circle of radius r (Fig.4) and to count stars that there are inside it ne. This circle corresponds to a zone of the celestial sphere that we are studying (Fig.2).
Establishing a ratio between the area of the sphere, of the circle and the number of stars counted inside this circle, we obtain the total number of stars NE that we can observer under the general conditions with we have carried out this practice, we obtain:
Repeating the process described above for all photographs used in our practice, we will calculate the arithmetic mean of all NE that we have obtained for getting a number of stars closed to the real number because of all zones of firmament have not the same density of stars.
The final NE obtained after doing the media is, of course, an approximation for a number of reasons some of these we have explained above.
As general information we would like to say that we can observe approximately 6000 celestial bodies to the naked eye, with prismatic about 50000 and with a simple telescope more than 100000, depending in this last case on the general characteristics of the instrument.
TABLE 1: Characteristics to consider for taking photographs
TABLE 2: Equatorial coordinates of Merak y Dubhe
Fot.1: The Ursa Major constellation.
Fot.2: Constellation of Orion.
Fig.1: Zone of the Ursa Major on the celestial sphere.
Fig.2: Celestial sphere of radius R, that photographic camera captivates with enlargement that we want. On the sphere there is a circle that it corresponds to zone where we'll count stars.
Fig.3: Celestial sphere of radius R with the circle limiting the zone where we count stars drawing. The distance d between two stars inside circle, correspond to an angle of nr radians.
Fig.4: We will count visible stars within a circle of radius r chosen on the photograph.
