HOW TO OBSERVE COMETS
Vitaly Nevsky
Observing comets is a very exciting activity. If you haven't tried your hand at this, I highly recommend giving it a try. The fact is that comets are very unstable objects by nature. Their appearance can change from night to night and quite significantly, especially for bright comets visible to the naked eye. Such comets, as a rule, develop decent tails, which prompted ancestors to various prejudices. Such comets do not need advertising, this is always an event in the astronomical world, but quite rare, but weak telescopic comets are almost always available for observation. I will also note that the results of observations of comets have scientific value, and amateur observations are constantly published in the American journal Internatoinal Comet Quarterly, on the C. Morris website and not only.
First, I’ll tell you what you should pay attention to when observing a comet. One of the most important characteristics is the magnitude of the comet; it must be assessed using one of the methods described below. Then - the diameter of the comet's coma, the degree of condensation, and, if there is a tail, its length and positional angle. This is the data that is valuable to science.
Moreover, comments on observations should note whether a photometric core was observed (not to be confused with the true core, which cannot be seen with a telescope) and what it looked like: star-shaped or disk-shaped, bright or faint. For bright comets, phenomena such as halos, shells, separation of tails and plasma formations, and the presence of several tails at once are possible. In addition, nuclear disintegration has already been observed in more than fifty comets! Let me explain these phenomena a little.
- Halos are concentric arcs around the photometric core. They were clearly visible near the famous comet Hale-Bopp. These are dust clouds that are regularly ejected from the nucleus, gradually moving away from it and disappearing against the background of the comet's atmosphere. They must be sketched indicating the angular dimensions and time of sketching.
- Nuclear decay. The phenomenon is quite rare, but has already been observed in more than 50 comets. The onset of decay can only be seen at maximum magnifications and should be reported immediately. But you need to be careful not to confuse the decay of the nucleus with the separation of the plasma cloud, which happens more often. The decay of the nucleus is usually accompanied by a sharp increase in the brightness of the comet.
- Shells - appear on the periphery of the cometary atmosphere (see figure), then begin to shrink, as if collapsing on the nucleus. When observing this phenomenon, it is necessary to measure the vertex height (V) in arcminutes - the distance from the core to the top of the shell and the diameter P = P1 + P2 (P1 and P2 may not be equal). These assessments need to be done several times throughout the night.
Assessing the brightness of a comet
The accuracy of the estimate should be no lower than +/-0.2 magnitude. In order to achieve such accuracy, the observer must make several brightness estimates during work for 5 minutes, preferably using different comparison stars, finding the average magnitude of the comet. It is in this way that the resulting value can be considered quite accurate, but not the one obtained as a result of just one estimate! In such a case, when the accuracy does not exceed +/-0.3, a colon (:) is placed after the comet's magnitude. If the observer was unable to find the comet, then he estimates the maximum stellar magnitude for his instrument on a given night at which he would still be able to observe the comet. In this case, a left square bracket ([) is placed before the evaluation.
The literature provides several methods for estimating the magnitude of a comet. But the method of Bobrovnikov, Morris and Sidgwick remains the most applicable.
Bobrovnikov's method.
This method is used only for comets whose degree of condensation is in the range of 7-9! Its principle is to move the telescope eyepiece out of focus until the out-of-focal images of the comet and comparison stars are approximately the same diameter. Complete equality cannot be achieved, since the diameter of the comet image is always larger than the diameter of the star image. It should be taken into account that the out-of-focal image of the star has approximately the same brightness, but the comet appears as a spot of uneven brightness. The observer must learn to average the comet's brightness over its entire out-of-focal image and compare this average brightness with comparison stars. Comparison of the brightness of off-focal images of the comet and comparison stars can be made using the Neyland-Blazhko method.
Sidgwick's method.
This method is only used for comets whose degree of condensation is in the range of 0-3! Its principle is to compare the focal image of a comet with off-focal images of comparison stars, which, when defocused, have the same diameters as the focal comet. The observer first carefully studies the image of the comet, “recording” its brightness in memory. Then it defocuses the comparison stars and evaluates the brightness of the comet recorded in memory. A certain skill is required here in order to learn to evaluate the brilliance of a comet recorded in memory.
Morris method.
The method combines the features of the Bobrovnikov and Sidgwick methods. it can be used for comets with any degree of condensation! The principle boils down to the following sequence of techniques: an out-of-focal image of the comet is obtained that has approximately uniform surface brightness; remember the size and surface brightness of the out-of-focal image of the comet; they defocus the images of the comparison stars so that their sizes are equal to the sizes of the remembered image of the comet; estimate the brightness of a comet by comparing the surface brightnesses of off-focal images of the comet and comparison stars.
When estimating the brightness of comets, in the case where the comet and comparison stars are at different heights above the horizon, a correction for atmospheric absorption must be introduced! This is especially significant when the comet is below 45 degrees above the horizon. Amendments should be taken from the table and the results must indicate whether an amendment was introduced or not. When using an adjustment, you need to be careful not to make a mistake about whether it should be added or subtracted. Let's say the comet is located below the comparison stars, in this case the correction is subtracted from the comet's brightness; if the comet is higher than the comparison stars, then the correction is added.
Special stellar standards are used to estimate the brightness of comets. Not all atlases and catalogs can be used for this purpose. Of the most accessible and widespread at present, the Ticho2 and Drepper catalogs should be highlighted. For example, directories such as AAVSO or SAO are not recommended. You can see more details about this.
If you do not have recommended catalogs, you can download them from the Internet. An excellent tool for this is the Cartes du Ciel program.
Comet coma diameter
The coma diameter of a comet should be estimated using as low a magnification as possible! It is noticed that the lower the magnification is applied, the larger the diameter of the coma, since the contrast of the comet's atmosphere in relation to the sky background increases. Poor transparency of the atmosphere and a light background of the sky (especially under the Moon and urban illumination) greatly influence the estimate of the diameter of the comet, so in such conditions it is necessary to be very careful when measuring.
There are several methods for determining the coma diameter of a comet:
- Using a micrometer, which is easy to make yourself. Under a microscope, stretch thin threads in the eyepiece diaphragm at certain intervals, or it is better to use an industrial one. This is the most accurate method.
- "Drift" method. It is based on the fact that with a stationary telescope, the comet, due to the daily rotation of the celestial sphere, will slowly cross the field of view of the eyepiece, passing a 15" arc near the equator in 1 second. Using an eyepiece with a cross of threads stretched in it, you should rotate it so that the comet moves along one thread and, therefore, perpendicular to the other thread of the cross.Having determined using a stopwatch the period of time in seconds during which the comet's coma will cross the perpendicular thread, it is easy to find the diameter of the coma in minutes of arc using the formula
d=0.25 * t * cos(b)
where (b) is the declination of the comet, t is the time period. This method cannot be used for comets located in the near-polar region at (b) > +70 degrees!
- Comparison method. Its principle is based on measuring the coma of a comet using the known angular distance between stars located near the comet. The method is applicable if a large-scale atlas is available, for example, Cartes du Ciel.
Its values range from 0 to 9.
0 - completely diffuse object, uniform brightness; 9 is practically a star-shaped object. This can be most clearly represented from the figure
Determination of comet tail parameters
When determining the length of the tail, the accuracy of the estimate is greatly influenced by the same factors as when estimating the coma of a comet. Urban illumination has a particularly strong effect, underestimating the value several times, so in the city you will certainly not get an accurate result.
To estimate the length of a comet's tail, it is best to use the comparison method based on the known angular distance between stars, since with a tail length of several degrees, small-scale atlases available to everyone can be used. For small tails, a large-scale atlas or micrometer is needed, since the "drift" method is only suitable if the tail axis coincides with the declination line, otherwise additional calculations will have to be performed. If the tail length is more than 10 degrees, it must be assessed using a formula, since due to cartographic distortions the error can reach 1-2 degrees.
D = arccos * ,
where (a) and (b) are the right ascension and declination of the comet; (a") and (b") - right ascension and declination of the end of the comet's tail (a - expressed in degrees).
Comets have several types of tails. There are 4 main types:
Type I - straight gas tail, almost coinciding with the radius vector of the comet;
Type II - a gas-dust tail slightly deviating from the radius vector of the comet;
Type III - a dust tail spreading along the comet's orbit;
Type IV - anomalous tail directed towards the Sun. Consists of large dust grains that the solar wind is unable to push out of the comet's coma. A very rare phenomenon, I had the opportunity to observe it only on one comet C/1999H1 (Lee) in August 1999.
It should be noted that a comet can have one tail (most often type I) or several.
However, for tails whose length is more than 10 degrees, due to cartographic distortions, the position angle should be calculated using the formula:
Where (a) and (b) are the coordinates of the comet’s nucleus; (a") and (b") are the coordinates of the end of the comet's tail. If the result is a positive value, then it corresponds to the desired value; if it is negative, then 360 must be added to it to obtain the desired value.
In addition to the fact that you eventually obtained the photometric parameters of the comet, in order for them to be published, you need to indicate the date and moment of observation in universal time; characteristics of the tool and its magnification; a method of estimating and source of comparison stars that was used to determine the brightness of a comet. After which you can contact me to send this data.
Astronomy enthusiasts can play a big role in studying Comet Hale-Bopp by observing it with binoculars, spotting scopes, telescopes, and even the naked eye. To do this, they must regularly estimate its integral visual magnitude and separately the magnitude of its photometric core (central condensation). In addition, estimates of the diameter of the coma, the length of the tail and its positional angle are important, as well as detailed descriptions of structural changes in the head and tail of the comet, determination of the speed of movement of cloud condensations and other structures in the tail.
How to evaluate the brightness of a comet? The most common methods for determining brightness among comet observers are:
Bakharev-Bobrovnikov-Vsekhsvyatsky (BBV) method. Images of the comet and comparison star are removed from the focus of the telescope or binocular until their out-of-focal images have approximately the same diameter (complete equality of the diameters of these objects cannot be achieved due to the fact that the diameter of the comet image is always larger than the diameter of the star). It is also necessary to take into account the fact that the out-of-focal image of the star has approximately the same brightness throughout the entire disk, while the comet has the appearance of a spot of uneven brightness. The observer averages the brightness of the comet over its entire out-of-focal image and compares this average brightness with the brightness of the out-of-focal images of comparison stars.
By selecting several pairs of comparison stars, it is possible to determine the average visual magnitude of the comet with an accuracy of 0.1 m.
Sidgwick method. This method is based on comparing the focal image of the comet with out-of-focal images of comparison stars, which, when defocused, have the same diameters as the diameter of the head of the focal image of the comet. The observer carefully studies the image of the comet in focus and remembers its average brightness. Then it moves the eyepiece out of focus until the size of the disks of the out-of-focal star images becomes comparable to the diameter of the head of the focal image of the comet. The brightness of these out-of-focal images of stars is compared with the average brightness of the comet's head "recorded" in the observer's memory. By repeating this procedure several times, a set of stellar magnitudes of the comet is obtained with an accuracy of 0.1 m. This method requires the development of certain skills that allow one to store in memory the brightness of the objects being compared - the focal image of the comet's head and off-focal images of the disks of stars.
Morris method is a combination of the BBB and Sidgwick methods, partially eliminating their disadvantages: the difference in the diameters of the out-of-focal images of the comet and comparison stars in the BBB method and the variations in the surface brightness of the cometary coma when the focal image of the comet is compared with the out-of-focal images of stars using the Sidgwick method. The brightness of a comet's head is estimated by the Morris method as follows: first, the observer receives an out-of-focal image of the comet's head that has approximately uniform surface brightness, and remembers the size and surface brightness of this image. It then defocuses the images of the comparison stars so that their sizes are equal to the size of the remembered image of the comet, and estimates the brightness of the comet by comparing the surface brightnesses of the off-focal images of the comparison stars and the head of the comet. By repeating this technique several times, the average value of the comet's brightness is found. The method gives an accuracy of up to 0.1 m, comparable to the accuracy of the above methods.
Beginners can be recommended to use the BBW method, as it is the simplest. More trained observers are more likely to use the Sidgwick and Morris methods. As a tool for brightness assessments, you should choose a telescope with the smallest possible lens diameter, and best of all, binoculars. If the comet is so bright that it is visible to the naked eye (as it should be with Comet Hale-Bopp), then people with farsightedness or nearsightedness can try a very creative method of "defocusing" the images - simply by removing their glasses.
All the methods we have considered require knowledge of the exact magnitudes of the comparison stars. They can be taken from various star atlases and catalogues, for example, from the star catalog included in the “Atlas of the Starry Sky” set (D. N. Ponomarev, K. I. Churyumov, VAGO). It is necessary to take into account that if the magnitudes in the catalog are given in the UBV system, then the visual magnitude of the comparison star is determined by the following formula:
m = V+ 0.16(B-V)
Particular attention should be paid to the selection of comparison stars: it is desirable that they be close to the comet and at approximately the same altitude above the horizon at which the observed comet is located. In this case, you should avoid red and orange comparison stars, giving preference to white and blue stars. Estimates of the brightness of a comet based on a comparison of its brightness with the brightness of extended objects (nebulae, clusters or galaxies) have no scientific value: the brightness of a comet can only be compared with stars.
A comparison of the brightnesses of a comet and comparison stars can be made using Neyland-Blazhko method, which uses two comparison stars: one brighter, the other fainter than the comet. The essence of the method is as follows: let the star A has a magnitude m a, star b- magnitude m b, comet To- magnitude m k, and m a
b
3 degrees or brighter than a star a by 2 degrees. This fact is written as a3k2b, and therefore the comet's brilliance is:m k =m a +3p=m a +0.6Δm
or
m k =m b -2p=m b -0.4Δm
Visual assessments of the comet's brightness during periods of night visibility must be made periodically every 30 minutes, or even more often, given the fact that its brightness can change quite quickly due to the rotation of the comet's nucleus of an irregular shape or a sudden flash of brightness. When a large burst of brightness is detected from a comet, it is important to follow the various phases of its development, while recording changes in the structure of the head and tail.
In addition to estimates of the visual magnitudes of the comet's head, estimates of the diameter of the coma and the degree of its diffuseness are also important.
Coma diameter (D) can be assessed using the following methods:
Drift method is based on the fact that with a stationary telescope, the comet, due to the daily rotation of the celestial sphere, will noticeably move in the field of view of the eyepiece, passing 15 seconds of arc in 1 second of time (near the equator). Taking an eyepiece with a cross of threads, you should turn it around so that the comet is mixed along one thread and perpendicular to the other. Having determined using a stopwatch the time interval At in seconds during which the comet's head will cross the perpendicular filament, it is easy to find the diameter of the coma (or head) in minutes of arc using the following formula:
D=0.25Δtcosδ
where δ is the declination of the comet. This method cannot be used for comets located in the circumpolar region at δ<-70° и δ>+70°, as well as for comets with D>5".
Interstellar angular distance method. Using large-scale atlases and star maps, the observer determines the angular distances between nearby stars visible in the vicinity of the comet and compares them with the apparent diameter of the coma. This method is used for large comets whose coma diameter exceeds 5".
Note that the apparent size of the coma or head is highly susceptible to the aperture effect, that is, it strongly depends on the diameter of the telescope lens. Estimates of the diameter of the coma obtained using different telescopes may differ from each other several times. Therefore, small instruments and low magnifications are recommended for such measurements.
In parallel with determining the diameter of the coma, the observer can evaluate it degree of diffuseness (DC), which gives an idea of the comet's appearance. The degree of diffuseness ranges from 0 to 9. If DC = 0, then the comet appears as a luminous disk with little or no change in surface brightness from the center of the head to the periphery. This is a completely diffuse comet, in which there is no hint of the presence of a more densely luminous condensation at its center. If DC=9, then the comet is no different in appearance from a star, that is, it looks like a star-shaped object. Intermediate DC values between 0 and 9 indicate varying degrees of diffuseness.
When observing a comet's tail, its angular length and position angle should be periodically measured, its type determined, and various changes in its shape and structure recorded.
To find tail length (C) You can use the same methods as for determining the diameter of the coma. However, when the tail length exceeds 10°, the following formula should be used:
cosC=sinδsinδ 1 +cosδcosδ 1 cos(α-α 1)
where C is the length of the tail in degrees, α and δ are the right ascension and declination of the comet, α 1 and δ 1 are the right ascension and declination of the end of the tail, which can be determined from the equatorial coordinates of the stars located near it.
Tail position angle (PA) counted from the direction to the north celestial pole counterclockwise: 0° - the tail is exactly directed to the north, 90° - the tail is directed to the east, 180° - to the south, 270° - to the west. It can be measured by selecting the star onto which the tail axis is projected, using the formula:
Where α 1 and δ 1 are the equatorial coordinates of the star, and α and δ are the coordinates of the comet's nucleus. The RA quadrant is determined by the sign sin(α 1 - α).
Definition comet tail type- a rather complex task that requires accurate calculation of the value of the repulsive force acting on the tail substance. This is especially true for dust tails. Therefore, for astronomy enthusiasts, a technique is usually proposed that can be used to preliminary determine the type of tail of the observed bright comet:
Type I- straight tails directed along the extended radius vector or close to it. These are gaseous or purely plasma tails of blue color, often a screw or spiral structure is observed in such tails, and they consist of individual streams or rays. In type I tails, cloud formations are often observed moving at high speeds along the tails from the Sun.
Type II- a wide, curved tail, strongly deviating from the extended radius vector. These are yellow gas and dust tails.
III type- a narrow, short curved tail, directed almost perpendicular to the extended radius vector (“creeping” along the orbit). These are yellow dust tails.
IV type- anomalous tails directed towards the Sun. Not wide, consisting of large dust particles that are almost not repelled by light pressure. Their color is also yellowish.
V type- detached tails directed along the radius vector or close to it. Their color is blue, since they are purely plasma formations.
Astronomy is a whole world full of beautiful images. This amazing science helps to find answers to the most important questions of our existence: learn about the structure of the Universe and its past, about the Solar system, about how the Earth rotates, and much more. There is a special connection between astronomy and mathematics, because astronomical predictions are the result of rigorous calculations. In fact, many problems in astronomy became possible to solve thanks to the development of new branches of mathematics.
From this book, the reader will learn about how the position of celestial bodies and the distance between them is measured, as well as about astronomical phenomena during which space objects occupy a special position in space.
If the well, like all normal wells, was directed towards the center of the Earth, its latitude and longitude did not change. The angles that determine Alice's position in space remained unchanged, only her distance to the center of the Earth changed. So Alice didn't have to worry.
Option one: altitude and azimuth
The most understandable way to determine coordinates on the celestial sphere is to indicate the angle that determines the height of the star above the horizon, and the angle between the north-south straight line and the projection of the star onto the horizon line - azimuth (see the following figure).
HOW TO MEASURE ANGLES MANUALLY
A device called a theodolite is used to measure the altitude and azimuth of a star.
However, there is a very simple, although not very accurate, way to measure angles manually. If we extend our hand in front of us, the palm will indicate an interval of 20°, the fist - 10°, the thumb - 2°, the little finger -1°. This method can be used by both adults and children, since the size of a person’s palm increases in proportion to the length of his arm.
Option two, more convenient: declination and hour angle
Determining the position of a star using azimuth and altitude is not difficult, but this method has a serious drawback: the coordinates are tied to the point at which the observer is located, so the same star, when observed from Paris and Lisbon, will have different coordinates, since the horizon lines in these cities will be located differently. Consequently, astronomers will not be able to use this data to exchange information about their observations. Therefore, there is another way to determine the position of the stars. It uses coordinates reminiscent of the latitude and longitude of the earth's surface, which can be used by astronomers anywhere on the globe. This intuitive method takes into account the position of the Earth's rotation axis and assumes that the celestial sphere rotates around us (for this reason, the Earth's rotation axis was called the axis mundi in Antiquity). In reality, of course, the opposite is true: although it seems to us that the sky is rotating, in fact it is the Earth that is rotating from west to east.
Let us consider a plane cutting the celestial sphere perpendicular to the axis of rotation passing through the center of the Earth and the celestial sphere. This plane will intersect the earth's surface along a great circle - the earth's equator, and also the celestial sphere - along its great circle, which is called the celestial equator. The second analogy with earthly parallels and meridians would be the celestial meridian, passing through two poles and located in a plane perpendicular to the equator. Since all celestial meridians, like terrestrial ones, are equal, the prime meridian can be chosen arbitrarily. Let us choose as the zero meridian the celestial meridian passing through the point at which the Sun is located on the day of the vernal equinox. The position of any star and celestial body is determined by two angles: declination and right ascension, as shown in the following figure. Declination is the angle between the equator and the star, measured along the meridian of a place (from 0 to 90° or from 0 to -90°). Right ascension is the angle between the vernal equinox and the meridian of the star, measured along the celestial equator. Sometimes, instead of right ascension, the hour angle, or the angle that determines the position of the celestial body relative to the celestial meridian of the point at which the observer is located, is used.
The advantage of the second equatorial coordinate system (declination and right ascension) is obvious: these coordinates will be unchanged regardless of the position of the observer. In addition, they take into account the rotation of the Earth, which makes it possible to correct the distortions it introduces. As we have already said, the apparent rotation of the celestial sphere is caused by the rotation of the Earth. A similar effect occurs when we are sitting on a train and see another train moving next to us: if you do not look at the platform, you cannot determine which train has actually started moving. We need a starting point. But if instead of two trains we consider the Earth and the celestial sphere, finding an additional reference point will not be so easy.
In 1851 a Frenchman Jean Bernard Leon Foucault (1819–1868) conducted an experiment demonstrating the motion of our planet relative to the celestial sphere.
He suspended a load weighing 28 kilograms on a 67-meter-long wire under the dome of the Parisian Pantheon. The oscillations of the Foucault pendulum lasted 6 hours, the oscillation period was 16.5 seconds, the pendulum deflection was 11° per hour. In other words, over time, the plane of oscillation of the pendulum shifted relative to the building. It is known that pendulums always move in the same plane (to verify this, just hang a bunch of keys on a rope and watch its vibrations). Thus, the observed deviation could be caused by only one reason: the building itself, and therefore the entire Earth, rotated around the plane of oscillation of the pendulum. This experiment became the first objective evidence of the rotation of the Earth, and Foucault pendulums were installed in many cities.
The Earth, which appears to be motionless, rotates not only on its own axis, making a complete revolution in 24 hours (equivalent to a speed of about 1600 km/h, that is, 0.5 km/s if we are at the equator), but also around the Sun , making a full revolution in 365.2522 days (with an average speed of approximately 30 km/s, that is, 108000 km/h). Moreover, the Sun rotates relative to the center of our galaxy, completing a full revolution every 200 million years and moving at a speed of 250 km/s (900,000 km/h). But that’s not all: our galaxy is moving away from the rest. Thus, the movement of the Earth is more like a dizzying carousel in an amusement park: we spin around ourselves, move through space and describe the spiral at breakneck speed. At the same time, it seems to us that we are standing still!
Although other coordinates are used in astronomy, the systems we have described are the most popular. It remains to answer the last question: how to convert coordinates from one system to another? The interested reader will find a description of all the necessary transformations in the application.
MODEL OF THE FOUCAULT EXPERIMENT
We invite the reader to conduct a simple experiment. Let's take a round box and glue a sheet of thick cardboard or plywood onto it, onto which we will attach a small frame in the shape of a football goal, as shown in the figure. Let's place a doll in the corner of the sheet, which will play the role of an observer. We tie a thread to the horizontal bar of the frame, on which we attach the sinker.
Let's move the resulting pendulum to the side and release it. The pendulum will oscillate parallel to one of the walls of the room in which we are located. If we begin to smoothly rotate the sheet of plywood together with the round box, we will see that the frame and the doll will begin to move relative to the wall of the room, but the plane of oscillation of the pendulum will still be parallel to the wall.
If we imagine ourselves as a doll, we will see that the pendulum moves relative to the floor, but at the same time we will not be able to feel the movement of the box and the frame on which it is attached. Similarly, when we observe a pendulum in a museum, it seems to us that the plane of its oscillations is shifting, but in fact we ourselves are shifting along with the museum building and the entire Earth.
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Laboratory work No. 15
DETERMINING THE LENGTH OF COMET TAILS
Goal of the work– use the example of calculating the length of comet tails to become familiar with the triangulation method.
Devices and accessories
A moving star map, photographs of a comet and the solar disk, a ruler.
Brief theory
It is known that measurements in general, as a comparison of the measured value with some standard, are divided into direct and indirect. Moreover, if it is possible to measure the quantity of interest using both methods, then direct measurements are, as a rule, preferable. However, it is precisely when measuring large distances that the use of direct methods can be difficult and sometimes impossible. The above consideration becomes obvious if we remember that we can talk not only about measuring large lengths on the earth's surface, but also about estimating distances to space objects.
There are a significant number of indirect methods for assessing large distances (radio and photolocation, triangulation, etc.). This paper discusses an astronomical method that can be used to determine the dimensions of the three tails of Comet Donati from photographs.
To determine the length of cometary tails, the already known triangulation method is used, taking into account knowledge of the horizontal parallax of the observed celestial object.
Horizontal parallax is the angle (Fig. 1) at which the average radius of the Earth is visible from a celestial body.
If this angle and the radius of the Earth are known (R Fig. 1), we can estimate the distance to the celestial body L o . Horizontal parallax is estimated using precision instruments over a quarter of a day of rotation of the Earth around its axis, taking into account that celestial bodies can be projected onto the celestial sphere.
Accordingly, it is possible to determine the angular dimensions of the tails and head of the comet themselves. For this, a star map is used, taking into account the coordinates of the stars of known constellations (declination and right ascension).
If the distances to a celestial body are determined from the known parallax, then the sizes of the tails can be calculated by solving the inverse problem of parallax displacement.
Having determined the angle α, we can determine the dimensions of the object AB:
(angle α expressed in radians)
Taking this into account, we need to introduce the scale that gives us a photograph of a celestial object. To do this, you need to select two stars (at least) from a photograph of a famous constellation. It is desirable that they be located on the first celestial meridian. Then the angular distance between them can be estimated from the difference in their declination.
(αˊ is the angular distance between two stars)
We find the declination of stars using a moving star chart or from an atlas. After this, measuring the dimensions of a section of the starry sky using a ruler or caliper (measuring microscope), we determine the linear coefficient of photographs, which will be equal to:
α 1 is the linear-angular coefficient of a given image, and [mm] is determined from the photograph.
Then we measure the linear dimensions of the celestial body and determine the angular dimensions through γ:
(a" are the linear dimensions of a separate part of the celestial body).
As a result, you can estimate the true dimensions of the object: .
1. From the photograph, determine the linear dimensions of the three tails of Comet Donati. Horizontal parallax p = 23".
3. Estimate the error with which the tail sizes are determined.
Astronomy workbook for grade 11 for lesson No. 16 (workbook) - Small bodies of the Solar system
1. Complete the sentences.
Dwarf planets are a separate class of celestial objects.
Dwarf planets are considered objects that orbit a star that are not satellites.
2. Dwarf planets are (underline as appropriate): Pluto, Ceres, Charon, Vesta, Sedna.
3. Fill out the table: characterize the distinctive features of small bodies of the Solar System.
| Characteristics | Asteroids | Comets | Meteorites |
| Vida in the sky | Star-like object | Diffuse object | "Falling star" |
| Orbits |
|
Short period comets P< 200 лет, долгого периода - P >200 years; orbital shape - elongated ellipses | Varied |
| Medium sizes | From tens of meters to hundreds of kilometers | Core - from 1 km to tens of km; tail ~ 100 million km; head ~ 100 thousand km | From micrometers to meters |
| Compound | Rocky | Ice with rock particles, organic molecules | Iron, stone, iron-stone |
| Origin | Planetesimal collision | Remnants of primordial matter on the outskirts of the Solar System | Collision fragments, remnants of comet evolution |
| Consequences of a collision with Earth | Explosion, crater | Air explosion | Funnel on Earth, sometimes a meteorite |
4. Complete the sentences.
Option 1.
The remnant of a meteorite body that did not burn up in the earth's atmosphere and fell to the surface of the Earth is called a meteorite.
The size of a comet's tail can exceed millions of kilometers.
The comet's nucleus is composed of cosmic dust, ice and frozen volatile compounds.
Meteor bodies burst into the Earth's atmosphere at speeds of 7 km/s (burn up in the atmosphere) and 20-30 km/s (do not burn up).
The radiant is a small area of the sky from which the visible paths of individual meteors in a meteor shower diverge.
Large asteroids have their own names, for example: Pallas, Juno, Vesta, Astraea, Hebe, Iris, Flora, Metis, Hygeia, Parthenope, etc.
Option 2.
A very bright meteor, visible on Earth as a fireball flying across the sky, is a fireball.
The heads of comets reach the size of the Sun.
The tail of a comet consists of discharged gas and tiny particles.
Meteor bodies flying into the Earth's atmosphere glow, evaporate and completely burn up at altitudes of 60-80 km; larger meteorite bodies can collide with the surface.
Solid fragments of the comet are gradually distributed throughout the comet's orbit in the form of a cloud elongated along the orbit.
The orbits of most asteroids in the solar system lie between the orbits of Jupiter and Mars in the asteroid belt.
5. Is there a fundamental difference in the physical nature of small asteroids and large meteorites? Give reasons for your answer.
An asteroid only becomes a meteorite when it enters the Earth's atmosphere.
6. The figure shows a diagram of the meeting of the Earth with a meteor shower. Analyze the picture and answer the questions.
What is the origin of a meteor shower (swarm of meteor particles)?
A meteor shower is formed by the disintegration of cometary nuclei.
What determines the period of revolution of a meteor shower around the Sun?
From the period of revolution of the ancestor comet, from the disturbance of the planets, the speed of the ejection.
In what case will the largest number of meteors be observed on Earth (meteor or star shower)?
When the Earth crosses the main mass of particles of a meteorite swarm.
How are meteor showers named? Name some of them.
According to the constellation where the radiant is located.
7. Draw the structure of a comet. Indicate the following elements: core, head, tail.
8.* What energy will be released when a meteorite with a mass of m = 50 kg hits and has a speed at the Earth’s surface of v = 2 km/s?
9. What is the semimajor axis of the orbit of Halley’s comet if its orbital period is T = 76 years?
10. Calculate the approximate width of the Perseid meteor shower in kilometers, knowing that it occurs from July 16 to August 22.
