An astronomical observation made on earth is an example. Astronomical observations
If you want to be alone with yourself, get away from everyday routine, give free rein to your fantasy dormant in you, come on a date with the stars. Postpone dreams until the morning hours. Remember the immortal lines of I. Ilf and E. Petrov: “It is pleasant to sit in the square at night. The air is clean, and smart thoughts come into my head.
And what a pleasure to contemplate the subtle, truly magical heavenly painting! No wonder hunters, fishermen and tourists, having settled down for the night, like to look at the sky for a long time. How often, lying by an extinguished fire and looking into the endless distance, they sincerely regret that their acquaintance with the stars is limited to the bucket of the Big Dipper. At the same time, many do not even think that this acquaintance can be expanded, and they believe that the sky for them is a secret with seven seals. Pretty common misconception. Believe me, taking the first step on the path of an amateur astronomer is not at all difficult. It is available to both junior schoolchildren, and students, and the head of the design bureau, and the shepherd, and the tractor driver, and the pensioner.
The vast majority of people have a preconceived notion that amateur astronomy begins with a telescope (“I’ll make a small telescope and observe the stars.”) However, often a fertile impulse is captured by an absolutely insoluble problem: where to buy the right lenses for a home-made refractor telescope or the necessary glass thickness for making a mirror for a reflecting telescope? Three or four fruitless attempts, and the dialogue with the starry sky is postponed indefinitely, or even forever. It's a pity! After all, if you want to join astronomy or help your children do it, you won’t find a way than observing meteors.
Just remember that it is advisable to start them during the period of maximum action of some intense meteor shower. This is best done on the nights of August 11-12 and August 12-13, when the Perseid stream is activated. For schoolchildren, this is generally an exceptionally convenient time. At this stage, no optical instruments or devices are needed for observations. You just need to choose a place for observations, located away from light sources and giving a fairly large view of the sky. It can be in a field, on a hill, in the mountains, on a large forest edge, on a flat roof of a house, in a fairly wide yard. You only need to have a notebook (observation journal), a pencil and any clock, wrist, desktop or even wall clock with you.
The task is to count the number of meteors you see every hour, and remember or write down the result. It is desirable to conduct observations for as long as possible, say from 22 o'clock until dawn. You can observe lying, sitting or standing: you will choose the most comfortable position for yourself. The largest area of the sky can be: covered with observations while lying on your back. However, such a position is quite risky: many novice amateur astronomers fall asleep in the second half of the night, leaving meteors to “run uncontrollably” across the sky.
After completing the observations, make a table, in the first column of which enter the hourly intervals of observations, for example, from 2 to 3 hours, from 3 to 4 hours, etc., and in the second - the corresponding number of meteors seen: 10, 15, ... For greater clarity, you can plot the dependence of the number of meteors on the time of day - and you will have a picture showing how the number of meteors changed during the night. This will be your little "scientific discovery". It can be done on the very first night of observations. Let yourself be inspired by the thought that all the meteors you see this night are unique. After all, each of them is a fleeting farewell autograph of an interplanetary particle disappearing forever. With luck, observing meteors, you can see one or even more fireballs. The bolide can end with a meteorite falling out, so be prepared for the following actions: set the moment of the bolide’s flight by the clock, try to remember (draw) its trajectory using ground or celestial landmarks, listen for any sounds (shock, explosion, rumble) after the fireball goes out or disappears over the horizon. Record the data in the observation log. The information you received may be useful to specialists in the event of organizing a search for the place where the meteorite fell.
Already on the first night, making observations, you will pay attention to the brightest stars, to their relative position. And if you continue to observe further, then in a few even incomplete nights you will get used to them and will recognize them. Even in ancient times, the stars were grouped into constellations. Constellations need to be gradually studied. This can no longer be done without having a map of the starry sky. It should be purchased at a bookstore. Separately, maps or atlases of the starry sky are rarely sold, more often they are attached to various books, for example, an astronomy textbook for the 10th grade, the School Astronomical Calendar, and popular scientific astronomical literature.
It is not difficult to identify the stars in the sky with their images on the map. You just need to adjust to the scale of the map. When going out with a map, take a flashlight with you. To prevent the map from being lit too brightly, the flashlight's light can be dimmed by wrapping it in a bandage. Getting to know the constellations is an extremely exciting activity. The solution of "Star Crosswords" is never boring. Moreover, experience shows that children, for example, enjoy playing the star game and very quickly memorize both the names of the constellations and their location in the sky.
So, in a week you will be able to swim quite freely in the heavenly sea and speak “you” with many stars. A good knowledge of the sky will expand your scientific meteor observation program. True, this equipment will become somewhat more complicated. In addition to a watch, a magazine and a pencil, you need to take a flashlight, a map, a ruler, an eraser, a card backing (some kind of plywood or a small table). Now, when observing the trajectory of all the meteors you see, you put on the map with a pencil in the form of arrows. If observations were made on the date of maximum flux, then some arrows (and sometimes most) will fan out on the map. Continue the arrows back with dashed lines: these lines will intersect at some area or even a point on the star map. This will mean that the meteors belong to the meteor shower, and the point of intersection of the dashed lines you found is the approximate radiant of this shower. The rest of the arrows you plotted could be sporadic meteor trajectories.
The described observations are carried out, as already noted, without the use of any optical instruments. If you have binoculars at your disposal, then it becomes possible to observe not only meteors and fireballs, but also their traces. It is very convenient to work with binoculars if you mount it on a tripod. After the passage of the fireball, as a rule, a weakly luminous trail is visible in the sky. Point binoculars at him. Before your eyes, the trail under the influence of air currents will change its shape, clots and rarefaction will form in it. It is very useful to sketch several successive views of the trail.
Photographing meteors does not present significant difficulties either. For these purposes, you can use any camera. The easiest way is to mount the camera on a tripod or put it, say, on a stool and point it to the zenith. At the same time, set the shutter to a long exposure and photograph the starry sky for 15-30 minutes. After that, move the film to one frame and continue photographing. In each image, the stars appear as parallel arcs, while the meteors appear as straight lines, usually crossing the arcs. It should be borne in mind that the field of view of one ordinary lens is not very large, and therefore the probability of photographing a meteor is quite small. It takes patience and of course a little luck. When making photographic observations, cooperation is good: several cameras aimed at different areas of the celestial sphere in the same way as professional astronomers do. However, if you manage to create a small group of meteor hunters, it is useful to divide it into two groups. Each group should choose its place of observation at a sufficient distance from each other and conduct joint observations according to a pre-agreed program.
Photographic observations themselves are a relatively simple task: click the shutters, rewind the film, record the start and end times of the exposures and the moments of the passage of meteors. The processing of the obtained images is much more difficult. However, you should not be afraid of difficulties. If you have already decided to establish friendly relations with the sky, then be prepared for the need for a certain intellectual tension.
But what about observing comets? If comets appeared as often as meteors, then astronomy lovers would not wish for anything better. But, alas! You can wait a whole "eternity" for a comet and still be left with nothing. Passivity is enemy number one here. Comets are to be found. Search with enthusiasm, with great desire, with faith in success. A lot of bright comets were discovered by amateurs. Their names are forever recorded in the annals of history.
Where do you need to look for comets, in what region of the sky? Is there any clue for a novice observer?
There is. Bright comets should be sought close to the Sun, that is, in the morning before sunrise in the east, in the evening after sunset in the west. The probability of success will greatly increase if you study the constellations, get used to the location of the stars, to their brilliance. Then the appearance of a "foreign" object will not escape your attention. If you have binoculars, a spotting scope, a telescope or other instrument at your disposal that allows you to observe even fainter objects, it will be very useful to make a map of nebulae and globular clusters, otherwise your heart will beat more than once on the occasion of your discovery of a false comet. And this, believe me, is very insulting! The observation process itself is not complicated, you need to regularly examine the near-solar morning and evening part of the sky, spurring yourself on with the desire to find a comet at all costs.
Observations of a comet must be carried out during the smoldering of the entire period of its visibility. If the comet cannot be photographed, then make a series of drawings of its appearance with the obligatory indication of the time and date. Draw especially carefully the various details in the comet's head and tail. Each time put the position of the comet on the star chart, "plotting" its route.
If you have a camera, do not skimp on photography. By combining a camera with a telescope, you will get a fast astrograph, and your photographs will be doubly valuable.
Remember that both during visual observations with binoculars or a telescope, and when photographing, the telescope and camera must be mounted on a tripod, otherwise the image of the object will “tremble with cold”.
It is good if, even during purely visual observations with a telescope or binoculars, it is possible to estimate the brightness of a comet. The fact is that very active comets can “blink” strongly, either increasing or decreasing their brightness. The reasons may be internal processes in the core (sudden ejection of matter) or external influence of solar wind flows.
You probably remember that you can determine the brightness of a star-shaped object by comparing it with the brightness of known stars. This is how, for example, the magnitude of an asteroid is estimated. The comet is more difficult. After all, it is visible not as a star, but as a misty speck. Therefore, the following rather ingenious method is applied. The observer extends the eyepiece of the telescope, bringing the images of the comet and stars out of focus, causing the stars to turn from dots into blurry spots. The observer extends the eyepiece until the size of the star spots is equal or almost equal to the size of the comet. Then two stars are selected for comparison - one is somewhat brighter than the comet, the second is fainter. Their stellar magnitudes are located according to the star catalog.
Undoubtedly, the observation of previously discovered comets is also of interest. Lists of such comets expected to be observed in a given year are published in the Astronomical Calendar (Variable Part). These calendars are published annually. True, very often, after describing the history of the comet and the conditions for its upcoming observation, a very unpleasant phrase is added:
"Unavailable to amateur observations." Thus, all five short-period comets observed in 1988 were inaccessible to amateurs because of their low brightness. Yes, indeed, one must discover one's own comets!
Very faint comets are usually discovered by looking at starry sky negatives. If you have not forgotten, new asteroids are discovered in the same way.
It is almost impossible to observe asteroids with the naked eye. But in small telescopes this can be done. The same "Astronomical Calendar" publishes a list of asteroids available for observations in a given year.
Take note of one piece of advice. Never rely only on your memory, be sure to record the results of your observations in a journal and as detailed as possible. Only in this case can you count on the fact that your wonderful hobby will be useful to science.
Among the methods of astronomy, otherwise the methods of astronomical research, three main groups can be distinguished:
- observation,
- measurement,
- space experiment.
Let's take a look at these methods.
Astronomical observations
Remark 1
Astronomical observations are the main way to study celestial bodies and events. It is with their help that what is happening in near and far space is recorded. Astronomical observations are the main source of knowledge obtained experimentally
Astronomical observations and processing of their data, as a rule, are carried out in specialized research institutions (astronomical observatories).
The first Russian observatory was built at Pulkovo, near St. Petersburg. The compilation of star catalogs of stars with the highest accuracy is the merit of the Pulkovo Observatory. We can say that in the second half of the 19th century, behind the scenes, she was awarded the title of "astronomical capital of the world", and in 1884 Pulkovo claimed the zero meridian (Greenwich won).
Modern observatories are equipped with observation instruments (telescopes), light-receiving and analyzing equipment, various auxiliary devices, high-performance computers, and so on.
Let us dwell on the features of astronomical observations:
- Feature #1. Observations are very inert, therefore, as a rule, they require rather long periods of time. Active influence on space objects, with rare exceptions that are provided by manned and unmanned astronautics, is difficult. Basically, many phenomena, for example, the transformation of the angle of inclination of the Earth's axis to the orbital plane, can only be recorded through observations over several thousand years. Consequently, the astronomical heritage of Babylon and China of a thousand years ago, despite some inconsistencies with modern requirements, is still relevant.
- Feature #2. The process of observation, as a rule, takes place from the earth's surface, at the same time the earth carries out a complex movement, so the earthly observer sees only a certain part of the starry sky.
- Feature number 3. Angular measurements performed on the basis of observations are the basis for calculations that determine the linear dimensions of objects and the distances to them. And since the angular sizes of stars and planets, measured using optics, do not depend on the distance to them, the calculations can be quite inaccurate.
Remark 2
The main instrument of astronomical observations is an optical telescope.
An optical telescope has a principle of operation determined by its type. But regardless of the type, its main goal and task is to collect the maximum amount of light emitted by luminous objects (stars, planets, comets, etc.) to create their images.
Types of optical telescopes:
- refractors (lens),
- reflectors (mirror),
- as well as mirror lenses.
In a refractor (lens) telescope, the image is achieved by the refraction of light in the objective lens. The disadvantage of refractors is an error resulting from blurring the image.
A feature of reflectors is their use in astrophysics. In them, the main thing is not how light is refracted, but how it is reflected. They are more perfect than lenses, and more accurate.
Mirror-lens telescopes combine the functions of refractors and reflectors.
Figure 1. Small optical telescope. Author24 - online exchange of student papers
Astronomical measurements
Since measurements in astronomical research are carried out using various instruments and instruments, we will briefly review them.
Remark 3
The main astronomical measuring instruments are coordinate measuring machines.
These machines measure one or two rectangular coordinates from a photographic image or spectrum diagram. Coordinate measuring machines are equipped with a table on which photographs are placed and a microscope with measuring functions used to aim at a luminous body or its spectrum. Modern devices can have a readout accuracy of up to 1 micron.
Errors may occur during the measurement process:
- the instrument itself
- operator (human factor),
- arbitrary.
Instrument errors arise from its imperfection, therefore, its accuracy must be checked beforehand. In particular, the following are subject to verification: scales, micrometric screws, guides on the object table and the measuring microscope, reference micrometers.
Errors associated with the human factor and randomness are stopped by the multiplicity of measurements.
In astronomical measurements, there is a widespread introduction of automatic and semi-automatic measuring instruments.
Automatic devices work an order of magnitude faster than conventional ones, and have half the mean square error.
space experiment
Definition 1
A space experiment is a set of interconnected interactions and observations that make it possible to obtain the necessary information about the studied celestial body or phenomenon, carried out in a space flight (manned or unmanned) in order to confirm theories, hypotheses, as well as improve various technologies that can contribute to development of scientific knowledge.
The main trends of experiments in space:
- The study of the course of physical and chemical processes and the behavior of materials in outer space.
- The study of the properties and behavior of celestial bodies.
- The influence of space on man.
- Confirmation of theories of space biology and biotechnology.
- Ways of space exploration.
Here it is appropriate to give examples of experiments carried out on the ISS by Russian cosmonauts.
Plant Growth Experiment (Veg-01).
The objective of the experiment is to study the behavior of plants in orbital conditions.
Experiment "Plasma Crystal"- study of plasma-dust crystals and liquid substances under microgravity parameters.
Four stages were carried out:
- The plasma-dust structure in a gas-discharge plasma at a high-frequency capacitive discharge was studied.
- The plasma-dust structure in a plasma was studied in a glow discharge with direct current.
- It was investigated how the ultraviolet spectrum of cosmic radiation affects macroparticles, which can be charged with photoemission.
- Plasma-dust structures were studied in open space under the action of solar ultraviolet and ionizing radiation.
Figure 2. Experiment "Plasma Crystal". Author24 - online exchange of student papers
In total, more than 100 space experiments were carried out by Russian cosmonauts on the ISS.
The main way to study celestial objects and phenomena. Observations can be made with the naked eye or with the help of optical instruments: telescopes equipped with various radiation receivers (spectrographs, photometers, etc.), astrographs, special instruments (in particular, binoculars). The purposes of observations are very diverse. Precise measurements of the positions of stars, planets, and other celestial bodies provide material for determining their distances (see Parallax), the proper motions of stars, and studying the laws of motion of planets and comets. The results of measurements of the visible brightness of the luminaries (visually or with the help of astrophotometers) make it possible to estimate the distances to stars, star clusters, galaxies, to study the processes occurring in variable stars, etc. Studies of the spectra of celestial bodies with the help of spectral instruments make it possible to measure the temperature of the luminaries, radial velocities, and provide invaluable material for a deep study of the physics of stars and other objects.
But the results of astronomical observations are of scientific significance only when the provisions of the instructions that determine the procedure for the observer, the requirements for instruments, the place of observation, and the form of registration of observation data are unconditionally fulfilled.
Observation methods available to young astronomers include visual without instruments, visual telescopic, photographic and photoelectric observation of celestial objects and phenomena. Depending on the instrumental base, the location of 1 observation points (city, town, village), 1 climatic conditions and the interests of an amateur, any (or several) of the proposed topics can be chosen for observations.
Observations of solar activity. When observing solar activity, sunspots are drawn daily and their coordinates are determined using a pre-prepared goniometric grid. It is best to make observations using a large school refractor telescope or a home-made telescope on a parallactic tripod (see Home-made telescope). You must always remember that you should never look at the Sun without a dark (protective) filter. It is convenient to observe the Sun by projecting its image onto a screen specially adapted to the telescope. On a paper template, outline the contours of groups of spots and individual spots, mark the pores. Then their coordinates are calculated, the number of sunspots in groups is counted, and at the time of observations, the index of solar activity, the Wolf number, is displayed. The observer also studies all the changes that occur within a group of spots, trying to convey their shape, size, and relative position of details as accurately as possible. The Sun can also be observed photographically with the use of additional optics in the telescope, which increases the equivalent focal length of the instrument and therefore makes it possible to photograph larger individual formations on its surface. Plates and films for photographing the Sun should have the lowest possible sensitivity.
Observations of Jupiter and its satellites. When observing planets, in particular Jupiter, a telescope with a lens or mirror diameter of at least 150 mm is used. The observer carefully sketches the details in Jupiter's bands and the bands themselves and determines their coordinates. By making observations over a number of nights, one can study the pattern of changes in the cloud cover of the planet. Interesting to observe on the disk of Jupiter is the Red Spot, the physical nature of which has not yet been fully studied. The observer draws the position of the Red Spot on the planet's disk, determines its coordinates, gives descriptions of the color, brightness of the spot, and registers the observed features in the cloud layer surrounding it.
To observe the moons of Jupiter, a school refractor telescope is used. The observer determines the exact position of the satellites relative to the edge of the planet's disk using an ocular micrometer. In addition, it is of interest to observe phenomena in a system of satellites and to record the moments of these phenomena. These include the eclipse of the satellites, the entry and exit from the disk of the planet, the passage of the satellite between the Sun and the planet, between the Earth and the planet.
Search for comets and their observations. Searches for comets are carried out using high-aperture optical instruments with a large field of view (3-5 °). Field binoculars, AT-1 astronomical tube, TZK, BMT-110 binoculars, as well as comet detectors can be used for this purpose.
The observer systematically examines the western part of the sky after sunset, the northern and zenith regions of the sky at night, and the eastern part before sunrise. The observer must know very well the location in the sky of stationary nebulous objects - gaseous nebulae, galaxies, star clusters, which in appearance resemble a comet with a faint brightness. In this case, he will be assisted by atlases of the starry sky, in particular, A. D. Marlensky’s “Educational Star Atlas” and A. A. Mikhailov’s “Star Atlas”. About the appearance of a new comet, a telegram is immediately sent to the Astronomical Institute named after PK Sternberg in Moscow. It is necessary to report the time of detection of the comet, its approximate coordinates, the name and surname of the observer, his postal address.
The observer must draw the position of the comet among the stars, study the visible structure of the comet's head and tail (if any), and determine its brilliance. Photographing the region of the sky where the comet is located makes it possible to determine its coordinates more accurately than when sketching, and, consequently, to calculate the comet's orbit more accurately. When photographing a comet, the telescope must be equipped with a clock mechanism that leads it behind the stars moving due to the apparent rotation of the sky.
Observations of noctilucent clouds. Noctilucent clouds are the most interesting, but still little-studied phenomenon of nature. In the USSR they are observed in summer north of 50° latitude. They can be seen against the background of the twilight segment, when the angle of the Sun's immersion under the horizon is from 6 to 12°. At this time, the sun's rays illuminate only the upper layers of the atmosphere, where noctilucent clouds form at an altitude of 70-90 km. Unlike ordinary clouds, which appear dark at dusk, noctilucent clouds glow. They are observed in the northern side of the sky, not high above the horizon.
The observer examines the twilight segment every night at 15-minute intervals and, in the event of the appearance of noctilucent clouds, evaluates their brightness, registers changes in shape, and using a theodolite or other goniometric instrument, measures the length of the cloud field in height and azimuth. In addition, it is advisable to photograph noctilucent clouds. If the lens aperture is 1:2 and the film sensitivity is 130-180 units according to GOST, then good pictures can be obtained with an exposure of 1-2 s. The image should show the main part of the cloud field and silhouettes of buildings or trees.
The purpose of patrolling the twilight segment and observing noctilucent clouds is to determine the frequency of occurrence of clouds, the prevailing forms, the dynamics of the field of noctilucent clouds, as well as individual formations within the cloud field.
Meteor observations. The tasks of visual observations are to count meteors and determine meteor radiants. In the first case, the observers are positioned under a circular frame that limits the field of view to 60° and register only those meteors that appear inside the frame. The observation log records the serial number of the meteor, the moment of passage with an accuracy of one second, the magnitude, angular velocity, direction of the meteor and its position relative to the frame. These observations make it possible to study the density of meteor showers and the brightness distribution of meteors.
When determining meteor radiants, the observer carefully marks each observed meteor on a copy of the starry sky map and notes the meteor's serial number, moment of passage, magnitude, meteor length in degrees, angular velocity and color. Weak meteors are observed with the help of field glasses, AT-1 tubes, TZK binoculars. Observations under this program make it possible to study the distribution of small radiants on the celestial sphere, determine the position and displacement of the studied small radiants, and lead to the discovery of new radiants.
Observations of variable stars. The main instruments for observing variable stars: field binoculars, AT-1 astronomical tubes, TZK binoculars, BMT-110, comet detectors providing a large field of view. Observations of variable stars make it possible to study the laws of change in their brightness, to specify the periods and amplitudes of change in brightness, to determine their type, and so on.
Initially, variable stars are observed - Cepheids, which have regular brightness fluctuations with a sufficiently large amplitude, and only after that one should proceed to observations of semi-regular and irregular variable stars, stars with a small brightness amplitude, as well as investigate stars suspected of variability, and patrol flaring stars.
With the help of cameras, you can photograph the starry sky in order to observe long-term variable stars and search for new variable stars.
Observations of solar eclipses
The program of amateur observations of a total solar eclipse may include: visual registration of the moments of contact between the edge of the Moon's disk and the edge of the Sun's disk (four contacts); sketches of the appearance of the solar corona - its shape, structure, size, color; telescopic observations of phenomena when the edge of the lunar disk covers sunspots and flares; meteorological observations - registration of the course of temperature, pressure, air humidity, changes in direction and strength of the wind; observing the behavior of animals and birds; photographing partial phases of the eclipse through a telescope with a focal length of 60 cm or more; photographing the solar corona using a camera with a lens having a focal length of 20-30 cm; photographing the so-called Bailey's rosary, which appears before the outbreak of the solar corona; registration of changes in the brightness of the sky as the phase of the eclipse increases with a homemade photometer.
Observations of lunar eclipses
Like solar eclipses, lunar eclipses occur relatively rarely, and at the same time, each eclipse is characterized by its own characteristics. Observations of lunar eclipses make it possible to refine the orbit of the moon and provide information about the upper layers of the earth's atmosphere. A lunar eclipse observation program may consist of the following elements: determination of the brightness of the shadowed parts of the lunar disk from the visibility of the details of the lunar surface when observed through 6x recognized binoculars or a telescope with low magnification; visual estimates of the brightness of the Moon and its color both with the naked eye and with binoculars (telescope); observations through a telescope with a lens diameter of at least 10 cm at 90x magnification throughout the eclipse of the craters Herodotus, Aristarchus, Grimaldi, Atlas and Riccioli, in the area of which color and light phenomena may occur; registration with a telescope of the moments of covering by the earth's shadow of some formations on the lunar surface (the list of these objects is given in the book "Astronomical calendar. Permanent part"); determination using a photometer of the brightness of the surface of the moon at various phases of the eclipse.
Observations of artificial earth satellites
When observing artificial satellites of the Earth, the path of the satellite on the star map and the time of its passage around noticeable bright stars are noted. Time must be recorded to the nearest 0.2 s using a stopwatch. Bright satellites can be photographed.
Astronomical observations always arouse the interest of others, especially if they manage to look through the telescope themselves.
I would like to tell beginners a little about what can be seen in the sky - in order to avoid disappointment from what is actually seen in the eyepiece. In really high-quality instruments, you will see much more than what is written here, but their price is high, and their weight and dimensions are quite large ... The first telescope for astronomical observations is usually not the largest and most expensive.
Astronomical observations of Mars are not for everyone, at most - the polar caps can be seen. Changes of seasons and patches of dust storms are visible only in expensive telescopes and in a good atmosphere.
Observation of the rest of the planets is disappointing: at most, what is seen in ordinary inexpensive telescopes is unclear small disks (more often just faint stars). But you can always say: "Yes, I saw it with my own eyes - there is such a planet, astronomers don't lie."
Neither the legendary "face of the Sphinx" on Mars, nor the truly bewitching sunrise of planetary satellites, you will not see even in the best telescope. However, during the Great Confrontations, it is simply a crime not to point a pipe at them ... Yes, and just look from time to time ... Of course, if you buy an expensive apochromatic refractor with a large aperture or a good light filter, then the quality will increase noticeably, but this not really for beginners.
in the constellation Hercules - one of the favorite objects of observation and an unofficial measure of the quality of the telescope on the subject of "does it resolve the stars to the center or not."
It doesn't matter whether you show your loved ones something interesting in the sky, or look at it yourself - it's always useful to know in advance what, in fact, to look for in the sky today. And most importantly - where exactly. In addition, if suddenly you are planning your vacation with an astronomical bias, then you need to consider a lot:
However, it all depends on your climate. In the suburbs, for example, the weather does not indulge - the cloud cover is high, and it's cold. I like it better from the end of August to mid-October - the sky is already quite dark, it’s not so cold yet ... Autumn is considered rainy, but in recent years it has often been lucky with precipitation and cloudiness in its first half - apparently the climate is changing. Closer to winter, cloudiness rises sharply; in November-December, it is rarely possible to see in the Moscow region. More on this topic:
What can be seen in a telescope depending on its size
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FOREWORD
The book is devoted to the organization, content and methodology of advanced level astronomical observations, as well as the simplest mathematical methods for their processing. It begins with a chapter on testing the telescope, the main instrument of observational astronomy. This chapter outlines the main issues related to the simplest theory of the telescope. Teachers will find here a lot of valuable practical advice related to determining the various characteristics of a telescope, checking the quality of its optics, choosing the optimal conditions for observing, as well as the necessary information about the most important telescope accessories and how to handle them when making visual and photographic observations.
The most important part of the book is the second chapter, which considers, on the basis of concrete material, questions of the organization, content, and methods of conducting astronomical observations. A significant part of the proposed observations - visual observations of the Moon, Sun, planets, eclipses - does not require high qualifications and, with skillful guidance from the teacher, can be mastered in a short time. At the same time, a number of other observations - photographic observations, visual observations of variable stars, program observations of meteor showers, and some others - already require considerable skill, certain theoretical training and additional instruments and equipment.
Of course, not all of the observations listed in this chapter can be implemented in any school. The organization of observations of increased difficulty is most likely available to those schools where there are good traditions of organizing extracurricular activities in astronomy, there is experience in the relevant work and, which is very important, a good material base.
Finally, in the third chapter, based on specific material, the main mathematical methods for processing observations are presented in a simple and visual form: interpolation and extrapolation, approximate representation of empirical functions, and error theory. This chapter is an integral part of the book. It directs both school teachers and students, and, finally, astronomy lovers to a thoughtful, serious attitude towards setting up and conducting astronomical observations, the results of which can acquire a certain significance and value only after they have been subjected to appropriate mathematical processing.
The attention of teachers is drawn to the need to use microcalculators, and in the future - personal computers.
The material of the book can be used in conducting practical classes in astronomy, provided for by the curriculum, as well as in conducting optional classes and in the work of an astronomical circle.
Taking this opportunity, the authors express their deep gratitude to the Deputy Chairman of the Council of Astronomical Circles of the Moscow Planetarium, an employee of the SAI MSU M. Yu. Shevchenko and Associate Professor of the Vladimir Pedagogical Institute, Candidate of Physical and Mathematical Sciences E. P. Razbitnaya for valuable suggestions that contributed to improving the content of the book.
The authors will gratefully accept all critical comments from readers.
Chapter I TESTING TELESCOPES
§ 1. Introduction
Telescopes are the main instruments of every astronomical observatory, including the educational one. With the help of telescopes, students observe the Sun and the phenomena occurring on it, the Moon and its topography, the planets and some of their satellites, the diverse world of stars, open and globular clusters, diffuse nebulae, the Milky Way and galaxies.
Based on direct telescopic observations and on photographs taken with large telescopes, the teacher can create in students vivid natural-scientific ideas about the structure of the world around them and, on this basis, form firm materialistic convictions.
Starting observations at the school astronomical observatory, the teacher should be well aware of the possibilities of telescopic optics, various practical methods for testing it and establishing its main characteristics. The fuller and deeper the teacher's knowledge of telescopes, the better he will be able to organize astronomical observations, the more fruitful the work of the students will be and the more convincing the results of the observations will appear before them.
In particular, it is important for an astronomy teacher to know a brief theory of the telescope, to be familiar with the most common optical systems and telescope installations, and also to have fairly complete information about eyepieces and various telescope accessories. At the same time, he must know the main characteristics, as well as the advantages and disadvantages of small telescopes intended for school and institute educational astronomical observatories, have good skills in handling such telescopes and be able to realistically assess their capabilities when organizing observations.
The effectiveness of the work of an astronomical observatory depends not only on its equipment with various equipment and, in particular, on the optical power of the telescopes available on it, but also on the degree of preparedness of observers. Only a qualified observer, who has good skills in handling the telescope at his disposal and who knows its main characteristics and capabilities, is able to obtain the maximum possible information on this telescope.
Therefore, the teacher faces the important task of preparing activists who are able to make good observations that require endurance, careful execution, great attention and time.
Without the creation of a group of qualified observers, it is impossible to count on the widespread continuous functioning of the school observatory and on its great return in the education and upbringing of all other students.
In this regard, it is not enough for the teacher to know the telescopes themselves and their capabilities, he must also possess a thoughtful and expressive explanation method that does not go far beyond school curricula and textbooks and is based on the knowledge of students obtained in the study of physics, astronomy and mathematics.
At the same time, special attention should be paid to the applied nature of the reported information about telescopes, so that the capabilities of the latter are revealed in the process of carrying out the planned observations and manifest themselves in the results obtained.
Taking into account the above requirements, the first chapter of the book includes theoretical information about telescopes in the amount necessary for making well-thought-out observations, as well as descriptions of rational practical methods for testing and establishing their various characteristics, taking into account the knowledge and capabilities of students.
§ 2. Determination of the main characteristics of telescope optics
In order to deeply understand the possibilities of telescope optics, one should first give some optical data on the human eye - the main "tool" of students in most educational astronomical observations. Let us dwell on its characteristics such as extreme sensitivity and visual acuity, illustrating their content on examples of observations of celestial objects.
Under the limiting (threshold) sensitivity of the eye is understood the minimum luminous flux that can still be perceived by an eye fully adapted to the darkness.
Convenient objects for determining the limiting sensitivity of the eye are groups of stars of different magnitudes with carefully measured magnitudes. In a good state of the atmosphere, a cloudless sky on a moonless night far from the city, one can observe stars up to the 6th magnitude. However, this is not the limit. High in the mountains, where the atmosphere is especially clean and transparent, stars up to the 8th magnitude become visible.
An experienced observer must know the limits of his eyes and be able to determine the state of transparency of the atmosphere from observations of the stars. To do this, it is necessary to study well the standard generally accepted in astronomy - the Northern Polar series (Fig. 1, a) and take it as a rule: before carrying out telescopic observations, you first need to determine with the naked eye the stars visible at the limit from this series and establish the state of the atmosphere from them.
Rice. 1. Map of the North Polar Range:
a - for observations with the naked eye; b - with binoculars or a small telescope; c - medium telescope.
The data obtained is recorded in the observation log. All this requires observation, memory, develops the habit of eye assessments and accustoms to accuracy - these qualities are very useful for the observer.
Visual acuity is understood as the ability of the eye to distinguish closely spaced objects or luminous points. Doctors have found that the average sharpness of a normal human eye is 1 minute of arc. These data were obtained by examining bright, well-lit objects and point light sources under laboratory conditions.
When observing stars - much less bright objects - visual acuity is somewhat reduced and is about 3 minutes of arc or more. So, having normal vision, it is easy to notice that near Mizar - the middle star in the handle of the Ursa Major bucket - there is a weak star Alcor. Far from everyone succeeds in establishing the duality of e Lyra with the naked eye. The angular distance between Mizar and Alcor is 1 Г48", and between the components ei and e2 of Lyra - 3"28".
Let us now consider how the telescope expands the possibilities of human vision, and analyze these possibilities.
A telescope is an afocal optical system that converts a beam of parallel beams with a cross section D into a beam of parallel beams with a cross section d. This is clearly seen in the example of the beam path in a refractor (Fig. 2), where the lens intercepts parallel beams coming from a distant star and focuses them to a point in the focal plane. Further, the rays diverge, enter the eyepiece and exit it as a parallel beam of smaller diameter. The beams then enter the eye and are focused to a point at the bottom of the eyeball.
If the diameter of the pupil of the human eye is equal to the diameter of the parallel beam emerging from the eyepiece, then all the rays collected by the objective will enter the eye. Therefore, in this case, the ratio of the areas of the telescope lens and the pupil of the human eye expresses the multiplicity of the increase in the light flux, falling
If we assume that the pupil diameter is 6 mm (in complete darkness it even reaches 7 - 8 mm), then a school refractor with a lens diameter of 60 mm can send 100 times more light energy into the eye than the naked eye perceives. As a result, with such a telescope, stars can become visible, sending us light fluxes 100 times smaller than the light fluxes from stars visible at the limit with the naked eye.
According to Pogson's formula, a hundredfold increase in illumination (luminous flux) corresponds to 5 star magnitudes:
The above formula makes it possible to estimate the penetrating power, which is the most important characteristic of a telescope. The penetrating power is determined by the limiting magnitude (m) of the faintest star that can still be seen with a given telescope under the best atmospheric conditions. Since neither the loss of light during the passage of the optics nor the darkening of the sky background in the field of view of the telescope is taken into account in the above formula, it is approximate.
A more accurate value of the penetrating power of a telescope can be calculated using the following empirical formula, which summarizes the results of observations of stars with instruments of different diameters:
where D is the diameter of the lens, expressed in millimeters.
For orientation purposes, Table 1 shows the approximate values of the penetrating power of telescopes, calculated using the empirical formula (1).
The real penetrating power of the telescope can be determined by observing the stars of the Northern Polar series (Fig. 1.6, c). To do this, guided by table 1 or by the empirical formula (1), set the approximate value of the penetrating power of the telescope. Further, from the given maps (Fig. 1.6, c), stars with somewhat larger and somewhat smaller magnitudes are selected. Carefully copy all the stars of greater brilliance and all selected ones. In this way, a star chart is made, carefully studied, and observations are made. The absence of "extra" stars on the map contributes to the rapid identification of the telescopic picture and the establishment of the stellar magnitudes of the visible stars. Follow-up observations are made on subsequent evenings. If the weather and the transparency of the atmosphere improve, then it becomes possible to see and identify fainter stars.
The magnitude of the faintest star found in this way determines the real penetrating power of the telescope used. The results obtained are recorded in the observation log. From them one can judge the state of the atmosphere and the conditions for observing other luminaries.
The second most important characteristic of a telescope is its resolution b, which is understood as the minimum angle between two stars seen separately. In theoretical optics, it is proved that with an ideal lens in visible light L = 5.5-10
where D is the lens diameter in millimeters. (...)
Rice. 3. Diffraction patterns of close stellar pairs with different angular distances of the components.
It is also instructive to carry out telescopic observations of bright stellar pairs with the lens apertured. As the telescope's inlet is gradually diaphragmed, the diffraction disks of the stars increase, merge and merge into a single diffraction disk of larger diameter, but with much lower brightness.
When conducting such studies, attention should be paid to the quality of telescopic images, which are determined by the state of the atmosphere.
Atmospheric disturbances should be observed with a well-aligned telescope (preferably a reflector), examining diffraction images of bright stars at high magnifications. It is known from optics that with a monochromatic light flux, 83.8% of the energy transmitted through the lens is concentrated in the central diffraction disk, 7.2% in the first ring, 2.8% in the second, 1.5% in the third, and 1.5% in the fourth ring. - 0.9%, etc.
Since the incoming radiation from stars is not monochromatic, but consists of different wavelengths, the diffraction rings are colored and blurred. The clarity of ring images can be improved by using filters, especially narrow-band filters. However, due to the decrease in energy from ring to ring and the increase in their areas, already the third ring becomes inconspicuous.
This should be kept in mind when estimating the state of the atmosphere from visible diffraction patterns of observed stars. When making such observations, you can use the Pickering scale, according to which the best images are rated with a score of 10, and very poor ones with a score of 1.
We give a description of this scale (Fig. 4).
1. Images of stars are undulated and smeared so that their diameters are, on average, twice the size of the third diffraction ring.
2. The image is undulating and slightly out of the third diffraction ring.
3. The image does not go beyond the third diffraction ring. The image brightness increases towards the center.
4. From time to time, the central diffraction disk of the star is visible with short arcs appearing around.
5. The diffraction disk is visible all the time, and short arcs are often visible.
6. The diffraction disk and short arcs are visible all the time.
7. Arcs move around a clearly visible disk.
8. Rings with gaps move around a clearly defined disk,
9. The diffraction ring closest to the disk is motionless.
10. All diffraction rings are stationary.
Points 1 - 3 characterize the poor state of the atmosphere for astronomical observations, 4 - 5 - mediocre, 6 - 7 - good, 8 - 10 - excellent.
The third important characteristic of a telescope is its lens aperture, which is equal to the square of the ratio of the lens diameter
to its focal length (...)
§ 3. Checking the quality of telescope optics
The practical value of any telescope as an observational instrument is determined not only by its size, but also by the quality of its optics, i.e., the degree of perfection of its optical system and the quality of the lens. An important role is played by the quality of the eyepieces attached to the telescope, as well as the completeness of their set.
The lens is the most critical part of the telescope. Unfortunately, even the most advanced telescopic lenses have a number of drawbacks due to both purely technical reasons and the nature of light. The most important of these are chromatic and spherical aberration, coma and astigmatism. In addition, fast lenses suffer to varying degrees from field curvature and distortion.
The teacher needs to know about the main optical shortcomings of the most commonly used types of telescopes, expressively and clearly demonstrate these shortcomings and be able to reduce them to some extent.
Let us describe successively the most important optical shortcomings of telescopes, consider in what types of small telescopes and to what extent they manifest themselves, and indicate the simplest ways to highlight, display and reduce them.
The main obstacle that prevented the improvement of the refractor telescope for a long time was chromatic (color) aberration, i.e., the inability of a collecting lens to collect all light rays with different wavelengths at one point. Chromatic aberration is caused by the unequal refraction of light rays of different wavelengths (red rays are refracted more weakly than yellow ones, and yellow rays are weaker than blue ones).
Chromatic aberration is especially pronounced in telescopes with single-lens fast lenses. If such a telescope is pointed at a bright star, then at a certain position of the eyepiece
you can see a bright purple speck surrounded by a colored halo with a blurred red outer ring. As the eyepiece extends, the color of the central spot will gradually change to blue, then green, yellow, orange, and finally red. In the latter case, a colored halo with a purple ring border will be visible around the red spot.
If you look at the planet through such a telescope, the picture will be very blurry, with iridescent stains.
Two-lens lenses that are largely free of chromatic aberration are called achromatic. The relative aperture of a refractor with an achromatic lens is usually 715 or more (for school refracting telescopes, it leaves 7o, which somewhat degrades the image quality).
However, an achromatic lens is not completely free from chromatic aberration and converges well only rays of certain wavelengths. In this regard, the objectives are achromatized in accordance with their purpose; visual - in relation to the rays that act most strongly on the eye, photographic - for the rays that act most strongly on the photographic emulsion. In particular, the lenses of school refractors are visual in their purpose.
The presence of residual chromatic aberration in school refractors can be judged on the basis of observations with very high magnifications of diffraction images of bright stars, quickly changing the following filters: yellow-green, red, blue. It is possible to ensure a quick change of light filters by using disk or sliding frames, described in
§ 20 of the book "School Astronomical Observatory"1. The changes in the diffraction patterns observed in this case indicate that not all rays are equally focused.
The elimination of chromatic aberration is more successfully solved in three-lens apochromatic objectives. However, it has not yet been possible to completely destroy it in any lens objectives.
A reflex lens does not refract light rays. Therefore, these lenses are completely free from chromatic aberration. In this way, reflex lenses compare favorably with lenses.
Another major disadvantage of telescopic lenses is spherical aberration. It manifests itself in the fact that monochromatic rays traveling parallel to the optical axis are focused at different distances from the lens, depending on which zone they have passed through. So, in a single lens, the rays that have passed near its center are focused furthest, and the closest - those that have passed through the edge zone.
This can be easily seen if a telescope with a single-lens objective is directed at a bright star and observed with two diaphragms: one of them should highlight the flux passing through the central zone, and the second, made in the form of a ring, should transmit the rays of the edge zone. Observations should be carried out with light filters, if possible, with narrow bandwidths. When using the first aperture, a sharp image of the star is obtained at a slightly larger extension of the eyepiece than when using the second aperture, which confirms the presence of spherical aberration.
In complex lenses, spherical aberration, together with chromatic aberration, is reduced to the required limit by selecting lenses of a certain thickness, curvature, and types of glass used.
[ The remnants of uncorrected spherical aberration in complex lens telescopic objectives can be detected using (the apertures described above, observing diffraction patterns from bright stars at high magnifications. When studying visual lenses, yellow-green filters should be used, and when studying photographic lenses, blue.
! There is no spherical aberration in mirror parabolic (more precisely, paraboloidal) lenses, since the lenses | reduce to one point the entire beam of rays traveling parallel to the optical axis. Spherical mirrors have spherical aberration, and it is the greater, the larger and brighter the mirror itself.
For small mirrors with small luminosity (with a relative aperture of less than 1: 8), the spherical surface differs little from the paraboloidal one - as a result, the spherical aberration is small.
The presence of residual spherical aberration can be detected by the method described above, using different diaphragms. Although mirror lenses are free from chromatic aberration, filters should be used to better diagnose spherical aberration, because the color of the observed diffraction patterns at different apertures is not the same, which can lead to misunderstandings.
Let us now consider the aberrations that arise when rays pass obliquely to the optical axis of the objective. These include: coma, astigmatism, field curvature, distortion.
With visual observations, one should follow the first two aberrations - coma and astigmatism, and study them practically by observing the stars.
The coma manifests itself in the fact that the image of the star away from the optical axis of the objective takes the form of a blurry asymmetric spot with a displaced core and a characteristic tail (Fig. 6). Astigmatism, on the other hand, consists in the fact that the lens collects an inclined beam of light from the star not into one common focus, but into two mutually perpendicular segments AB and CD, located in different planes and at different distances from the lens (Fig. 7).
Rice. 6. Formation of coma in oblique rays. The circle outlines the field near the optical axis, where the coma is insignificant.
With good alignment in the telescope tube of a low-aperture objective and with a small field of view of the eyepiece, it is difficult to notice both aberrations mentioned above. They can be clearly seen if, for the purpose of training, the telescope is somewhat misaligned by turning the lens through a certain angle. Such an operation is useful for all observers, and especially for those who build their telescopes, because sooner or later they will definitely face alignment issues, and it will be much better if they act consciously.
To misalign the reflector, simply loosen and tighten the two opposite screws holding the mirror.
In a refractor, this is more difficult to do. In order not to spoil the thread, you should glue a transition ring truncated at an angle from cardboard and insert it with one side into the telescope tube, and put the lens on the other.
If you look at the stars through a misaligned telescope, they will all appear tailed. The reason for this is coma (Fig. 6). If, however, a diaphragm with a small central hole is put on the telescope inlet and the eyepiece is moved back and forth, then one can see how the stars are stretched into bright segments AB, then turn into ellipses of different compression, circles, and again into segments CD and ellipses (Fig. 7).
Coma and astigmatism are eliminated by turning the lens. As it is easy to understand, the axis of rotation during adjustment will be perpendicular to the direction. If the tail lengthens when the mirror adjusting screw is turned, then the screw must be rotated in the opposite direction. The final fine-tuning during adjustment should be carried out with a short-focus eyepiece at high magnifications so that the diffraction rings are clearly visible.
If the telescope lens is of high quality and the optics are aligned correctly, then the out-of-focus images of the star, when viewed through a refractor, will look like a small light disk surrounded by a system of colored concentric diffraction rings (Fig. 8, al). In this case, the patterns of prefocal and extrafocal images will be exactly the same (Fig. 8, a 2, 3).
Out-of-focus images of a star will have the same appearance when viewed through a reflector, only instead of a central bright disk, a dark spot will be seen, which is a shadow from an auxiliary mirror or a diagonal total reflection prism.
The inaccuracy of the telescope alignment will affect the concentricity of the diffraction rings, and they themselves will take an elongated shape (Fig. 8, b 1, 2, 3, 4). When focusing, the star will appear not as a sharply defined bright disk, but as a slightly blurred bright spot with a weak tail thrown to the side (coma effect). If the indicated effect is caused by a really inaccurate adjustment of the telescope, then the matter can be easily corrected, it is enough just to change its position somewhat in the desired direction by acting with the adjusting screws of the lens (mirror) frame. It is much worse if the reason lies in the astigmatism of the lens itself or (in the case of a Newton reflector) in the poor quality of the auxiliary diagonal mirror. In this case, the drawback can be eliminated only by grinding and repolishing the defective optical surfaces.
From out-of-focus images of a star, other shortcomings of the telescopic lens, if any, can be easily detected. For example, the difference in the sizes of the corresponding diffraction rings of the prefocal and extrafocal images of a star indicates the presence of spherical aberration, and the difference in their chromaticity indicates significant chromatism (for linear
call lens); the uneven distribution density of the rings and their different intensities indicate the zoning of the lens, and the irregular shape of the rings indicates local more or less significant deviations of the optical surface from the ideal.
If all the listed disadvantages revealed by the pattern of out-of-focus images of a star are small, then they can be put up with. Specular objectives of amateur telescopes that have successfully passed the preliminary Foucault shadow test, as a rule, have an impeccable optical surface and withstand tests on out-of-focus star images perfectly.
Calculations and practice show that with perfect alignment of the optics, coma and astigmatism have little effect on visual observations when low-aperture objectives (less than 1:10) are used. This applies equally to photographic observations, when luminaries with relatively small angular sizes (planets, the Sun, the Moon) are photographed with the same lenses.
Coma and astigmatism greatly spoil images when photographing large areas of the starry sky with parabolic mirrors or two-lens lenses. Distortion increases sharply with fast lenses.
The table below gives an idea of the growth of coma and astigmatism depending on the angular deviations from the optical axis for parabolic reflectors of different luminosity.
Rice. 9. Curvature of the field of view and images of stars in its focal plane (with correction of all other aberrations).
tism, but there is a curvature of the field. If you take a picture of a large area of the starry sky with such a lens and at the same time focus on the central zone, then as you retreat to the edges of the field, the sharpness of the images of stars will deteriorate. And vice versa, if focusing is performed on the stars located at the edges of the field, then the sharpness of the images of stars will deteriorate in the center.
In order to obtain a photograph sharp across the entire field with such a lens, the film must be bent in accordance with the curvature of the field of sharp images of the lens itself.
The curvature of the field is also eliminated with the help of a plano-convex Piazzi-Smith lens, which turns the curved wave front into a flat one.
The curvature of the field can be most simply reduced by aperture of the lens. It is known from the practice of photographing that with a decrease in the aperture, the depth of field increases - as a result, clear images of stars are obtained over the entire field of a flat plate. However, it should be remembered that aperture reduction greatly reduces the optical power of the telescope, and in order for faint stars to appear on the plate, the exposure time must be significantly increased.
Distortion manifests itself in the fact that the lens builds an image that is not proportional to the original, but with some deviations from it. As a result, when photographing a square, its image may turn out with sides concave inward or convex outward (pincushion and barrel distortion).
Examining any lens for distortion is very simple: to do this, you need to greatly aperture it so that only a very small central part remains uncovered. Coma, astigmatism and curvature of the field with such a diaphragm will be eliminated and distortion can be observed in its purest form
If you take pictures of rectangular grilles, window openings, doors with such a lens, then, by examining the negatives, it is easy to establish the type of distortion inherent in this lens.
The distortion of the finished lens cannot be eliminated or reduced. It is taken into account in the study of photographs, especially when carrying out astrometric work.
§ 4. Eyepieces and limiting magnifications of the telescope
The eyepiece set is a necessary addition to the telescope. Earlier we have already clarified (§ 2) the purpose of the eyepiece in a magnifying telescopic system. Now it is necessary to dwell on the main characteristics and design features of various eyepieces. Leaving aside the Galilean eyepiece from one diverging lens, which has not been used in astronomical practice for a long time, let us immediately turn to special astronomical eyepieces.
Historically, the first astronomical eyepiece, which immediately replaced the Galilean eyepiece, was the Kepler eyepiece from a single short-focus lens. Possessing a much larger field of view in comparison with Galileo's eyepiece, in combination with the long-focus refractors common at that time, it produced fairly clear and slightly colored images. However, later the Kepler eyepiece was superseded by the more advanced Huygens and Ramsden eyepieces, which are still found today. The most commonly used astronomical eyepieces at present are the Kellner achromatic eyepiece and the Abbe orthoscopic eyepiece. Figure 11 shows the arrangement of these eyepieces.
The Huygens and Ramsden eyepieces are most simply arranged. Each of them is composed of two plano-convex converging lenses. The front one (facing the objective) is called the field lens, and the back one (facing the observer's eye) is called the eye lens. In the Huygens eyepiece (Fig. 12), both lenses face the objective with their convex surfaces, and if f \ and / 2 are the focal lengths of the lenses, and d is the distance between them, then the relationship must be satisfied: (...)
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