Half-girths (measurements of girths we divide in half and get half-girths):

Rice. one

Ssh - neck half circumference
SG1 - chest half circumference first
SG2 - half chest circumference of the second
SG3 - chest half circumference third
St - half waist
Sat - semi-circumference of the hips

Lengths:

Rice. 2

Di - product length
Dp - shoulder length
DTS - back length to waist
Dtp - length of the shelf to the waist

Rice. 3

Widths:

Шп - shoulder width
Wh - chest width
Шс - back width

Rice. 4

Heights:

Vpkg - shoulder height oblique chest

Rice. 5

Vpks - shoulder height oblique back

Rice. 6

Vg - chest height

We take measurements from the figure according to figures 1−4. When taking measurements of chest, waist, and hips, you need to pay special attention to the fact that the centimeter tape should be located strictly horizontally in the narrowest / widest place (depending on the measurement). When removing the girths, it is not necessary to stretch the tape, as this may lead to a narrowing of the product. The most difficult task at this stage is to correctly measure the height of the back and front, as well as determine the projected line of the shoulder seam.

Flexibility gains

The increase depends on the type of fabric, its elasticity, as well as the desired freedom of the product, and this must be taken into account when building. For example, we will take the average values. And also you need to take into account that we use the increase to build half of the product.

For an example of building a dress, we will take a size 48 (this is a size of 96.0 cm across the chest) for a height of 164.

Measurements:

W=18.5 cm
Cr1 \u003d 45.9 cm
Cr2 = 50.4 cm
Cr3 = 48.0 cm
St = 38.0 cm
Sat =52.0 cm
Di = 90.0 cm
Dts = 42.9 cm
Dtp = 44.4 cm
W = 13.3 cm
W = 17.3 cm
W = 18.3 cm
Wpx =43.2 cm
Vprz = 21.5 cm
Vg = 27.5 cm

Additions:

Pg = 6.0 cm
Fri = 3.0 cm
Pb = 2.5 cm
Pshs = 0.8 cm
Pshp 0.3 cm
Psh pr \u003d 4.9 cm
Pdts = 0.5 cm
Pdtp = 1.0 cm
Pshgor = 1.0 cm
Psp = 2.0 cm

Calculation for building a grid:

Grid width (A0a1) = Cr3 + Pg \u003d 48.0 + 6.0 \u003d 54.0 cm
Back width (A0a) \u003d Ws + Pshs \u003d 18.3 + 0.8 \u003d 19.1 cm
Shelf width (a1a2) \u003d Wg + (Sg2-Sg1) + Pshp \u003d 17.3 + (50.4−45.9) + 0.3 \u003d 22.1 cm
Armhole width (aa2) \u003d Shpr \u003d Shset-(Wsp + Shpol) \u003d 54.0-(19.1 + 22.1) \u003d 12.8 cm
Armhole depth (A0G) \u003d Vprz + Pspr 0.5 * Pdts \u003d 21.5 + 2.0 + 0.5 * 0.5 \u003d 23.8 cm
The position of the waist line (A0T) \u003d Dts + Pdts \u003d 42.9 + 0.5 cm \u003d 43.4 cm
The position of the hip line (A0B) \u003d Dts / 2-2 \u003d 42.9 / 2-2 \u003d 19.5 cm
The position of the bottom line of the product (A "H1) \u003d Di + Dts \u003d 90.0 + 0.5 cm \u003d 90.5 cm (the length of the back should be postponed after constructing the neck of the back), but at this stage we will postpone the length of the product from point A1.

Mesh building

Step 1

Rice. 7

We take point A0 as the first point of construction and from it we set aside the width of the grid to the right - 54.0 cm, draw a line and put point a1 at the end of the segment.

To the right of the point A0 on the line A0a1 we set aside the width of the backrest, we get point a.

To the left of the point a1 on the line A0a1 we set aside the width of the shelf and get the point a2.
The segment aa2 is the width of the armhole.

Down from point A0, we set aside the height of the grid and set the point H at the end of the segment - the length of the product. Corresponds to the bottom line of the product (at this stage).

From point A0 downwards, we postpone the position of the chest line on the line A0G and get point G.
Also from the point A0 on the segment A0G lays the position of the waist line and we get the point T.
And we postpone the position of the line of the hips from the point T on the segment A0G and get point B.

From point a1 down, we also set aside the height of the grid and get point H3. We close the rectangle.

From points G, T and B we draw horizontal lines and get points G3, T3 and B3 at the intersection with the line a1H3.
In turn, from points, a and a2, we lower the vertical to the chest line GG3 and get points G1 and G4.
The first and important step in building the mesh should look like the one shown in Fig. 7.

Building a drawing of the back

Step 2

Rice. eight

From point A0 we set aside to the left on the line 0.5 cm - this is the withdrawal of the center of the back at the top. We get point A0".

From point A0 "down along the line A0H we set aside the level of the shoulder blades, which is 0.4 * Dts \u003d 0.4 * 42.9 \u003d 17.2 cm and get point U. We connect point U with point A0" with a temporary line.

We build the depth of the neck of the back A0 "A \u003d A2A1 \u003d 7.2 / 3 \u003d 2.4 down from the point A0" on the line A0 "U. We complete the rectangle and draw up the neckline of the back of the curved curve.
This build step should look like the one shown in Fig. eight.

Step 3

Rice. 9

From the point T to the left on the waist line TT3, we postpone the withdrawal along the waist line = 1.5 cm, for semi-adjacent products. We get point T1.

To build the middle seam of the back, we set aside from the point H to the right a tap equal to the tap along the waist line 1.5 cm and get the point H1. We carry out the middle seam of the back through the points A-U-T1-H1.

From the neck of the back along the middle seam, we lay the length of the back down and get the H point (correct length).

This build step should look like the one shown in Fig. 9.

Step 4

Rice. 10

We build the end point of the shoulder, for this we build a radius from point A2 equal to Shp + tuck opening \u003d 13.3 + 2.0 \u003d 15.3 cm, where the tuck opening is 2.0 cm. And also the second radius from point T1 equal to Vpk + Pvpk, where Ppvk \u003d Pdts + Ppn (increase on the shoulder pad, in this case \u003d 0), and we get 43.2 + 0.5 \u003d 43.7 cm.

At the intersection of the radii from points A2 and T1, we set the point P1.

This build step should look like the one shown in Fig. 10.

Step 5

Rice. eleven

Let's start building a shoulder tuck by determining the position of the tuck along the shoulder seam. The tuck should be located 1/3 - ¼ of the shoulder width: 1/3 * 13.3 - ¼ + 13.3 \u003d 4.4 - 3.3, take a value of 4.0 cm.

We took the tuck solution when constructing the shoulder seam = 2.0 cm. We set aside point I1 on the shoulder from point A2 and point I2 in increments of 2.0 cm. Further, from points I1 and I2 we draw with a radius equal to 7.0 cm and we get point I. We connect points I and I1 and I2. To align the shoulder seam, it is necessary to raise the sides of the darts from the shoulder seam by 0.2 cm.

We connect the sides of the darts with the points of the neckline A2 and the end of the shoulder seam P2. From point P2 to the vertical a1G1 we draw a perpendicular, we will need it to calculate the auxiliary lines of the armhole.

This build step should look like the one shown in Fig. eleven.

Step 6

Rice. 12

We build auxiliary points of the armhole based on the length of the P1G1 line - the length of this section is 18.9 cm. To build the point P3 = 18.9 / 3 + 2.0 cm = 8.3 cm. segment G1a1.

From the corner G1 of the armhole we draw a bisector with a length = Shpr * 0.2 + 0.5 cm = 12.8 * 0.2 + 0.5 = 3.1 cm.

The auxiliary point G2 is located in the middle of the width of the armhole, i.e. Spr / 2 = 12.8 / 2 = 6.4 cm.

This build step should look like the one shown in Fig. 12.

Step 7

Rice. thirteen

The armhole line of the back is drawn with a smooth line, while the P2 point should have a right angle.

This build step should look like the one shown in Fig. thirteen.

Building a drawing of a shelf

Step 8

Fig.14

To build the point of the center of the chest, the distance G3G4 / 2 - 1.0 = 22.½ - 1.0 = 10.1 cm is set aside from the point G3 to the right and we get the point G6.

For products of the dress group, we draw up the descent of the waist line = 0.5 cm, for this we set aside 0.5 cm from point T3 down and get point T31. From this point we draw a horizontal line to the left with a length equal to the width of Г3Г6.

To build the width of the neck of the shelf Ssh / 3 + Pshgor \u003d 18.5 / 3 + 1.0 \u003d 7.2 cm, set aside from point A3 to the left on the horizontal and get point A4. We calculate the depth of the neck according to the formula A3A4 +1.0 = 8.2 cm and draw a radius from points A4 on the vertical A3T3 and get the neck point A5. In turn, from points A5 and A4 with a radius equal to the depth of the neck, we make serifs and get an auxiliary point A3 "from which we draw the arc of the neck of the shelf.

This build step should look like the one shown in Fig. 14.

Step 9

Fig.15

The position of the highest point of the mammary glands is set aside from point A4 with a radius equal to Bg \u003d 27.5 cm and we get point G7.

At the intersection of two arcs with the radius of the height of the chest from point G7 and the radius of the opening of the tuck from point A4, we find point A9.

We connect points A9 and A4 with point G7 and get the chest tuck of the shelf.

This build step should look like the one shown in Fig. 15.

Step 10

Rice. sixteen

To determine the auxiliary points, it is necessary to calculate the position of the point P4 on the segment a2G4. For this, the distance P1G1 (from the drawing) - 1.0 cm \u003d 18.9 - 1.0 \u003d 17.9 cm, we get the distance P4G4. Further, this distance G4P4 / 3 = 6.0 cm and postpone this distance from the point G4 up and get the point P6.

Point P5 is obtained at the intersection of the arcs from point A9 - shoulder width = 13.3 cm and from point P6 equal to the distance P6P4 = 11.9 cm.

We draw the line of the shoulder through the points A9P5.

This build step should look like the one shown in Fig. sixteen.

Step 11

Fig.17

To build the armhole of the shelf, we draw an auxiliary line, in the middle of which we set a perpendicular 1.0 cm long.

From the angle G4 to build an armhole, we draw the bisector Spr * 0.2 = 12.8 * 0.2 = 2.6 cm.

Through the points P5 - P6 - G2 and the constructed perpendiculars we draw the line of the armhole of the shelf.

This build step should look like the one shown in Fig. 17.

Building sidelines

Step 12

Rice. eighteen

The construction of the side lines along the line of the chest will start from the point G4 - this is the middle of the armhole. From the point G4 we draw a vertical down, this is the center line of the side seam.

At the intersection with the line of the waist, hips and bottom, we get points T2-B2-H2, respectively.

To design the side seam, take 0.4 * R-p vyt tal \u003d 0.4 * 11.5 \u003d 4.6 and divide this amount by two, since this is a complete solution of the tuck in the side seam. To do this, 4.6 / 2 \u003d 2.3 cm and set aside in each direction from the T2 point. And we get points T21 and T22.

Next, we calculate the expansion along the hips, for this (Sb + Pb) - B1B3 \u003d (52 + 2.5) - 52.5 \u003d 2.0 cm. We also divide it in half 2/2 \u003d 1.0 cm, in order to put aside the extension along the hips on both sides of point B2. And we get points B21 and B22.

In this construction example, we will leave the dress of a straight silhouette at the bottom, therefore, along the bottom line along the side seam, we set aside the same values ​​as for the hips. And we get points H21 and H22.

Through the points G4-T21-B22-H22 and G4-T22-B21-H21 we draw the lines of the side seam of the shelf and back.

This build step should look like the one shown in Fig. eighteen.

Step 13

Rice. nineteen

To build a tuck along the waist line of the back, we determine the position of the tuck along the waist line on the back, for this, the distance T1T21 / 2 \u003d 21.8 / 2 \u003d 10.9 cm and we get point T4.

Next, we calculate the tuck solution along the waist line (R-r vyt tal - R-r vyt tal side) * 0.55 \u003d (11.5 - 4.6) * 0.55 \u003d 3.8 cm. We also divide this solution in half 3.8 / 2 \u003d 1.9 and set aside from point T4 and get points T41 and T42.

The height of the tuck from the waist line up and down is 15.0 cm each - we get points K1 and K2, respectively.

This build step should look like the one shown in Fig. nineteen.

Step 14

Rice. twenty

To build a tuck along the waist line of the shelf, we use the position of the center of the chest on the shelf, for this we lower the vertical down from the waist line from point T6 to the line of the hips - we get point T5.

Next, we calculate the solution of the tuck along the waist line R-r vyt tal - R-r vyt tal side-R-r pulled out sp \u003d 11.5 - 4.6 - 3.8 \u003d 3.1 cm. We also divide this solution in half 3, ½ \u003d 1.55 and set aside from point T5 and get points T51 and T52.

The height of the tuck from the waistline up and down is the same as on the back, 15.0 cm each - we get points K3 and K4.

This build step should look like the one shown in Fig. twenty.

Step 15

Rice. 21

To build relief lines, it is necessary to translate part of the chest tuck of the shelf. To do this, with a notch equal to the distance from the neck to the tuck of the back = 4.0 cm, set aside 4.0 cm on the shoulder line of the shelf and get point A81.

We connect point A81 and point G7 - this is the length of the radius of the transfer of the chest tuck = 26.3 cm.

Now, from point A4, we set aside the radius A4A8, equal to the section A9A81 \u003d 4.0 cm, put the first notch, and from point G7 with a radius equal to the segment A81G7, we make the second notch. At the intersection of the radii, we get point A8. Then we connect points A8 and G7, as well as points A8 and A4 - we get the line of the shoulder to the line of the relief of the shelf and the section of the relief of the shelf.

This build step should look like the one shown in Fig. 21.

Step 16

Rice. 22

To design the bottom line of the product, you need to lower the line of the center of the shelf - the descent of the bottom line H3H31 is 1.0 cm.

We lower the relief lines of the shelf and back to the bottom line and get the points H4 and H5, respectively.

This build step should look like the one shown in Fig. 22.

Rice. 23

The construction of the dress has come to an end and our drawing should look like the one shown in fig. 23.

Step 17

Rice. 24

Next, you need to transfer the main details of the shelf, the barrel of the shelf, the back and the barrel of the back to tracing paper and add allowances for the seams.

This build step should look like the one shown in Fig. 24.

If these are your first steps in designing, then the design must be checked, that is, the dress should be sewn from mock fabric and tried on to be sure that there were no errors in the calculations and construction.

Also, after construction, it is necessary to add the details of the facings of the neck and armholes of the back and shelves. And also, if desired, decorative elements - coquettes, flounces, edgings, etc.

Photo: site
Text and illustrations: Olga Kuznetsova
The material was prepared by Anna Soboleva

Proper motion and radial velocities of stars. Peculiar velocities of stars and the Sun in the Galaxy. Rotation of the Galaxy.

A comparison of the equatorial coordinates of the same stars, determined at significant intervals of time, showed that a and d change over time. A significant part of these changes is caused by precession, nutation, aberration and annual parallax. If we exclude the influence of these causes, then the changes are reduced, but do not disappear completely. The remaining displacement of the star on the celestial sphere per year is called the proper motion of the star m. It is expressed in seconds. arcs per year.

Proper motions are different for different stars in magnitude and direction. Only a few dozen stars have proper motions greater than 1” per year. Barnard's “flying” star has the largest known proper motion m = 10”,27. Most of the stars have their own motion equal to hundredths and thousandths of an arc second per year.

Over long periods of time, equal to tens of thousands of years, the patterns of the constellations change greatly.

The proper motion of the star occurs along a great circle arc at a constant speed. The right ascension changes by the value m a , called the right ascension proper motion, and the declination by the value m d , called the proper declination motion.

The proper motion of the star is calculated by the formula:

m = r(m a 2 + m d 2).

If the proper motion of the star for a year and the distance to it r in parsecs are known, then it is not difficult to calculate the projection of the spatial velocity of the star onto the picture plane. This projection is called the tangential velocity V t and is calculated by the formula:

V t \u003d m "r / 206265" ps / year \u003d 4.74 m r km / s.

to find the spatial velocity V of a star, it is necessary to know its radial velocity V r , which is determined from the Doppler shift of the lines in the spectrum of the star. Since V t and V r are mutually perpendicular, the space velocity of the star is:

V = r(V t 2 + V r 2).

The fastest stars are RR Lyrae variables. Their average speed relative to the Sun is 130 km/s. However, these stars move against the rotation of the Galaxy, so their speed is low (250 -130 = 120 km/s). Very fast stars, with velocities of about 350 km/s relative to the center of the Galaxy, are not observed, because the speed of 320 km/s is enough to leave the gravitational field of the Galaxy or rotate in a highly elongated orbit.

Knowing the proper motions and radial velocities of stars allows us to judge the motions of stars relative to the Sun, which also moves in space. Therefore, the observed movements of stars are composed of two parts, of which one is a consequence of the movement of the Sun, and the other is the individual movement of the star.

In order to judge the motions of the stars, one should find the speed of the Sun and exclude it from the observed speeds of the stars.

The point on the celestial sphere to which the Sun's velocity vector is directed is called the solar apex, and the opposite point is called the anti-apex.

Apex of the solar system is located in the constellation Hercules, has the coordinates: a = 270 0 , d = +30 0 . In this direction, the Sun moves at a speed of about 20 km / s, relative to the stars located no further than 100 ps from it. During the year, the Sun travels 630,000,000 km, or 4.2 AU.

If some group of stars moves at the same speed, then being on one of these stars, it is impossible to detect a common movement. The situation is different if the velocity changes as if a group of stars were moving around a common center. Then the speed of stars closer to the center will be less than those farther from the center. The observed radial velocities of distant stars demonstrate such motion. All stars, together with the Sun, move perpendicular to the direction towards the center of the Galaxy. This movement is a consequence of the general rotation of the Galaxy, the speed of which varies with distance from its center (differential rotation).

The rotation of the Galaxy has the following features:

1. It occurs clockwise if you look at the Galaxy from its north pole, located in the constellation Coma Veronica.

2. The angular velocity of rotation decreases with distance from the center.

3. The linear speed of rotation first increases with distance from the center. Then, approximately at the distance of the Sun, it reaches its maximum value of about 250 km/s, after which it slowly decreases.

4. The sun and stars in its vicinity make a complete revolution around the center of the Galaxy in about 230 million years. This period of time is called a galactic year.

24.2 Stellar populations and galactic subsystems.

Stars located near the Sun are very bright and belong to the I type of population. they are usually found in the outer regions of the galaxy. Stars located far from the Sun, located near the center of the Galaxy and in the corona belong to the II type of population. The division of stars into populations was carried out by Baade when studying the Andromeda Nebula. The brightest population I stars are blue and have absolute magnitudes up to -9 m , while the brightest population II stars are red with abs. -3 m . In addition, population I is characterized by an abundance of interstellar gas and dust, which are absent in population II.

A detailed division of stars in the Galaxy into populations includes 6 types:

1. Extreme population I - includes objects contained in spiral branches. This includes interstellar gas and dust concentrated in the spiral arms from which stars form. The stars of this population are very young. Their age is 20 - 50 million years. The region of existence of these stars is limited by a thin galactic layer: a ring with an inner radius of 5000 ps, ​​an outer radius of 15,000 ps, ​​and a thickness of about 500 ps.

These stars include stars of spectral types from O to B2, supergiants of late spectral types, Wolf-Rayet type stars, class B emission stars, stellar associations, T Tauri type variables.

2. The stars of the ordinary population I are slightly older, their age is 2-3 space years. They have moved away from the spiral arms and are often located near the central plane of the Galaxy.

These include stars of subclasses from B3 to B8 and normal stars of class A, res. clusters with stars of the same classes, class A to F stars with strong metal lines, less bright red supergiants.

3. Stars of the disk population. Their age is from 1 to 5 billion years; 5-25 space years. These stars include the Sun. This population includes many low-observable stars located within 1000 ps from the central plane in the galactic belt with an inner radius of 5000 ps and an outer radius of 15,000 ps. These stars include ordinary giants of classes from G to K, main sequence stars of classes from G to K, long-period variables with periods of more than 250 days, semi-regular variables, planetary nebulae, new stars, old open clusters.

4. Intermediate population II stars include objects located at distances greater than 1000 pc on either side of the central plane of the Galaxy. These stars rotate in elongated orbits. These include the majority of old stars, with an age of 50 to 80 cosmic years, stars with high velocities, with weak lines, long-period variables with periods from 50 to 250 days, Virgo W-type Cepheids, RR Lyrae variables, white dwarfs, globular clusters .

5. Population of the galactic crown. include objects that arose in the early stages of the evolution of the Galaxy, which at that time was less flat than it is now. These objects include subdwarfs, coronal globular clusters, RR Lyrae stars, stars with extremely faint lines, and stars with the highest velocities.

6. Core population stars include the least known objects. In the spectra of these stars observed in other galaxies, the sodium lines are strong, and the cyanide (CN) bands are intense. These can be class M dwarfs. Such objects include RR Lyrae stars, globular stars. metal-rich clusters, planetary nebulae, M-class dwarfs, G- and M-class giant stars with strong cyanide bands, infrared objects.

The most important elements of the structure of the Galaxy are the central cluster, spiral arms, and disk. The central cluster of the Galaxy is hidden from us by dark opaque matter. Its southern half is best seen as a bright star cloud in the constellation Sagittarius. In infrared rays, it is possible to observe the second half. These halves are separated by a powerful band of dusty matter, which is opaque even to infrared rays. The linear dimensions of the central cluster are 3 by 5 kiloparsecs.

The region of the Galaxy at a distance of 4-8 kpc from the center is distinguished by a number of features. It contains the largest number of pulsars and gas remnants from supernova explosions, intense nonthermal radio emission, and young and hot O and B stars are more common. Hydrogen molecular clouds exist in this area. In the diffuse matter of this region, the concentration of cosmic rays is increased.

At a distance of 3-4 kpc from the center of the Galaxy, radio astronomy methods discovered a neutral hydrogen sleeve with a mass of about 100,000,000 solar masses, expanding at a speed of about 50 km/s. on the other side of the center, at a distance of about 2 kpc, there is a sleeve with a mass 10 times smaller, moving away from the center at a speed of 135 km/s.

In the region of the center there are several gas clouds with masses of 10,000 - 100,000 solar masses, moving away at a speed of 100 - 170 km/s.

The central region with a radius less than 1 kpc is occupied by a ring of neutral gas, which rotates at a speed of 200 km/s around the center. Inside it, there is a vast disk-shaped H II region with a diameter of about 300 ps. In the region of the center, non-thermal radiation is observed, which indicates an increase in the concentration of cosmic rays and the strength of magnetic fields.

The totality of phenomena observed in the central regions of the Galaxy indicates the possibility that more than 10,000,000 years ago, gas clouds with a total mass of about 10,000,000 solar masses and a speed of about 600 km/s were ejected from the center of the Galaxy.

In the constellation Sagittarius, near the center of the Galaxy, there are several powerful sources of radio and infrared radiation. One of them - Sagittarius-A is located in the very center of the Galaxy. It is surrounded by an annular molecular cloud with a radius of 200 ps, ​​expanding at a speed of 140 km/s. In the central regions, there is an active process of star formation.

At the center of our Galaxy, there is most likely a nucleus, similar to a globular star cluster. infrared receivers detected an elliptical object with dimensions of 10 ps there. It may contain a dense star cluster with a diameter of 1 ps. It may also be an object of unknown relativistic nature.

24.3 Spiral structure of the Galaxy.

The nature of the spiral structure of the Galaxy is associated with spiral density waves propagating in the stellar disk. These waves are similar to sound waves, but due to rotation, they take on the appearance of spirals. The medium in which these waves propagate consists not only of gas-dust interstellar matter, but also of the stars themselves. Stars also form a kind of gas, which differs from the usual one in that there are no collisions between its particles.

A spiral density wave, like an ordinary longitudinal wave, is an alternation of successive densification and rarefaction of the Medium. Unlike gas and stars, the spiral pattern of waves rotates in the same direction as the entire Galaxy, but noticeably slower and with a constant angular velocity, like a solid body.

Therefore, the substance constantly catches up with the spiral branches from the inside and passes through them. However, for stars and gas, this passage through the spiral arms occurs in different ways. Stars, like gas, condense in a spiral wave, their concentration increases by 10 - 20%. Accordingly, the gravitational potential also increases. But since there are no collisions between the stars, they conserve momentum, slightly change their path within the spiral arm and exit it in almost the same direction in which they entered.

Gas behaves differently. Due to collisions, entering the arm, it loses momentum, slows down, and begins to accumulate at the inner boundary of the arm. The oncoming new gas portions lead to the formation of a shock wave with a large density difference near this boundary. As a result, gas sealing edges are formed near the spiral arms and thermal instability occurs. The gas quickly becomes opaque, cools down and passes into a dense phase, forming gas-dust complexes favorable for star formation. Young and hot stars excite the glow of the gas, which gives rise to bright nebulae, which, together with hot stars, outline a spiral structure that repeats the spiral density wave in the stellar disk.

The spiral structure of our galaxy has been studied by examining other spiral galaxies. Studies have shown that the spiral arms of neighboring galaxies are composed of hot giants, supergiants, dust and gas. If you remove these objects, the spiral branches will disappear. Red and yellow stars fill evenly the areas in and between the branches.

To clarify the spiral structure of our galaxy, we need to observe hot giants, dust and gas. It is quite difficult to do this, because the Sun is in the plane of the Galaxy and various spiral branches are projected onto each other. Modern methods do not allow accurately determining the distances to distant giants, which makes it difficult to create a spatial picture. In addition, large masses of dust of inhomogeneous structure and different densities lie in the plane of the Galaxy, which makes it even more difficult to study distant objects.

Great hopes are given by the study of hydrogen at a wavelength of 21 cm. With their help, it is possible to measure the density of neutral hydrogen in various places in the Galaxy. This work was done by the Dutch astronomers Holst, Muller, Oort and others. As a result, a picture of the distribution of hydrogen was obtained, which outlined the contours of the spiral structure of the Galaxy. Hydrogen is found in large quantities near young hot stars, which determine the structure of the spiral arms. The radiation of neutral hydrogen is long-wavelength, is in the radio range, and for it the interstellar dusty matter is transparent. The 21-centimeter radiation comes from the most distant regions of the Galaxy without distortion.

The galaxy is constantly changing. These changes are slow and gradual. They are difficult for researchers to detect because human life is very short compared to the life of stars and galaxies. Turning to cosmic evolution, one must choose a very long unit of time. Such a unit is the cosmic year, i.e. the time it takes the sun to complete one revolution around the center of the galaxy. It is equal to 250 million earth years. The stars of the Galaxy are constantly intermixed and in one cosmic year, moving even at a low speed of 1 km/s relative to each other, two stars will move away by 250 ps. During this time, some stellar groups may break up, while others may form again. The appearance of the Galaxy will change dramatically. In addition to mechanical changes, the physical state of the Galaxy changes during the cosmic year. Stars of classes O and B can only shine brightly for a time equal to some part of the cosmic year. The age of the brightest observable giants is about 10 million years. However, despite this, the configuration of the helical arms can remain quite stable. Some stars will leave these regions, others will arrive in their place, some stars will die, others will be born from a huge mass of gas-dust complexes of spiral branches. If the distribution of the positions and movements of objects in a galaxy does not undergo large changes, then this stellar system is in a state of dynamic equilibrium. For a certain group of stars, the state of dynamic equilibrium can be maintained for 100 cosmic years. However, over a longer period equal to thousands of cosm. years, the state of dynamic equilibrium will be disturbed due to random close passages of stars. It will be replaced by a dynamically quasi-permanent state of statistical equilibrium, more stable, in which the stars are more thoroughly mixed.

25. Extragalactic astronomy.

25.1 Classification of galaxies and their spatial distribution.

The French comet seekers Messier and Masham compiled in 1784 a catalog of nebulous objects observed in the sky with the naked eye or through a telescope in order not to confuse them with incoming comets in future work. The objects of the Messier catalog turned out to be of the most diverse nature. Some of them - star clusters and nebulae - belong to our Galaxy, the other part - objects more distant and are the same star systems as our Galaxy. Understanding the true nature of galaxies did not come immediately. It wasn't until 1917 that Ritchie and Curtis, observing a supernova in the galaxy NGC 224, calculated that it was at a distance of 460,000 ps, ​​i.e. 15 times the diameter of our Galaxy, which means far beyond its borders. The issue was finally clarified in 1924-1926, when E. Hubble, using a 2.5-meter telescope, obtained photographs of the Andromeda Nebula, where the spiral branches decomposed into individual stars.

Today, a lot of galaxies are known, located at a distance from us from hundreds of thousands to billions of light years. years.

Many galaxies are described and catalogued. The most commonly used is Dreyer's New General Catalog (NGC). Each galaxy has its own number. For example, the Andromeda Nebula is designated NGC 224.

Observation of galaxies has shown that they are very diverse in shape and structure. In appearance, galaxies are divided into elliptical, spiral, lenticular and irregular.

elliptical galaxies(E) have the shape of ellipses in photographs without sharp borders. The brightness gradually increases from the periphery to the center. The internal structure is usually absent. These galaxies are built from red and yellow giants, red and yellow dwarfs, a certain number of white stars of low luminosity, i.e. mostly from population type II stars. There are no blue-white supergiants, which usually create the structure of spiral arms. Outwardly, elliptical galaxies differ in greater or lesser compression.

The compression indicator is the value

easily found if the large a and small b semiaxes are measured in the photograph. The compression index is added after the letter indicating the shape of the galaxy, for example, E3. It turned out that there are no highly compressed galaxies, so the largest indicator is 7. A spherical galaxy has an indicator of 0.

Obviously, elliptical galaxies have the geometric shape of an ellipsoid of revolution. E. Hubble posed the problem of whether the variety of observed forms is a consequence of the different orientation of equally oblate galaxies in space. This problem was solved mathematically and the answer was obtained that in the composition of galaxy clusters, galaxies with a compression index of 4, 5, 6, 7 are most often found and there are almost no spherical galaxies. And outside the clusters, almost only galaxies with exponents 1 and 0 are found. Elliptical galaxies in clusters are giant galaxies, and outside clusters they are dwarf galaxies.

spiral galaxies(S). They have a structure in the form of spiral branches that emerge from the central core. The branches stand out against a less bright background due to the fact that they contain the hottest stars, young clusters, luminous gaseous nebulae.

Edwin Hubble broke down spiral galaxies into subclasses. The measure is the degree of development of the branches and the size of the core of the galaxy.

In Sa galaxies, the branches are tightly twisted and relatively smooth, and poorly developed. The nuclei are always large, usually about half the observed size of the entire galaxy. Galaxies of this subclass are most similar to elliptical ones. There are usually two branches emerging from opposite parts of the nucleus, but there are rarely more.

In Sb galaxies, the spiral arms are noticeably developed, but do not have branchings. The core is smaller than the previous class. Galaxies of this type often have many spiral arms.

Galaxies with highly developed branches dividing into several arms and a nucleus small in comparison with them belong to the Sc type.

Despite the variety of appearance, spiral galaxies have a similar structure. Three components can be distinguished in them: a stellar disk, the thickness of which is 5-10 times less than the diameter of the galaxy, a spheroidal component, and a flat component, which is several times smaller in thickness than the disk. The flat component includes interstellar gas, dust, young stars, and spiral branches.

The compression ratio of spiral galaxies is always greater than 7. At the same time, elliptical galaxies are always less than 7. This indicates that a spiral structure cannot develop in weakly compressed galaxies. For it to appear, the system must be strongly compressed.

It is proved that a strongly compressed galaxy cannot become weakly compressed during evolution, as well as vice versa. This means that elliptical galaxies cannot turn into spiral ones, and spiral ones into elliptical ones. Different compression is due to different amounts of rotation of the systems. Those galaxies that received a sufficient amount of rotation during formation took a highly compressed shape, spiral branches developed in them.

There are spiral galaxies in which the core is located in the middle of a straight bar and spiral branches begin only at the ends of this bar. Such galaxies are designated SBa, SBb, SBc. The addition of the letter B indicates the presence of a jumper.

lenticular galaxies(S0). Outwardly similar to elliptical, but have a stellar disk. They are similar in structure to spiral galaxies, but differ from them in the absence of a flat component and spiral arms. Lenticular galaxies differ from edge-on spiral galaxies by the absence of a dark matter band. Schwarzschild proposed a theory according to which lenticular galaxies can form from spiral galaxies in the process of sweeping out gas and dust matter.

Irregular galaxies(ir). They have an asymmetrical appearance. They do not have spiral branches, and hot stars and gas-dust matter are concentrated in separate groups or scattered throughout the disk. There is a spheroidal component with low brightness. These galaxies are characterized by a high content of interstellar gas and young stars.

The irregular shape of the galaxy may be due to the fact that it did not have time to take the correct shape due to the low density of matter in it or because of its young age. A galaxy can also become irregular due to shape distortion as a result of interaction with another galaxy.

Irregular galaxies are divided into two subtypes.

The Ir I subtype is characterized by high surface brightness and irregular structure complexity. In some galaxies of this subtype, a destroyed spiral structure is found. Such galaxies often occur in pairs.

Subtype Ir II is characterized by low surface brightness. This property interferes with the detection of such galaxies, and only a few are known. The low surface brightness indicates a low stellar density. This means that these galaxies must very slowly move from an irregular shape to a regular one.

In July 1995, a study was conducted on the space telescope. Hubble to search for irregular faint blue galaxies. It turned out that these objects, located at distances from us at distances from 3 to 8 billion light years, are the most common. Most of them have an extremely saturated blue color, which indicates that they are actively undergoing the process of star formation. At close distances corresponding to the modern Universe, these galaxies do not occur.

Galaxies are much more diverse than the considered species, and this diversity concerns shapes, structures, luminosity, composition, density, mass, spectrum, radiation features.

We can distinguish the following morphological types of galaxies, approaching them from different points of view.

Amorphous, structureless systems- including E galaxies and most of S0. They have no or almost no diffuse matter and hot giants.

Haro galaxies- bluer than the others. Many of them have narrow but bright lines in the spectrum. Maybe they are very rich in gas.

Seyfert galaxies- different types, but characteristic of a very large width of strong emission lines in their spectra.

Quasars- quasi-stellar radio sources, QSS, indistinguishable in appearance from stars, but emitting radio waves, like the most powerful radio galaxies. They are characterized by a bluish color and bright lines in the spectrum that have a huge redshift. Supergiant galaxies are superior in luminosity.

Quazagi- QSG quasi-stellar galaxies - differ from quasars in the absence of strong radio emission.

The stars are clear, the stars are high!
What do you keep, what do you hide
Stars, concealing deep thoughts,
By what power do you captivate the soul?
Frequent stars, tight stars!
What is beautiful in you, what is powerful in you?
What do you carry, heavenly stars,
The power of the great burning knowledge?
S. A Yesenin

Lesson 6/23

Topic: Spatial speed of stars

Target: To acquaint with the movement of stars - spatial velocity and its components: tangential and ray, Doppler effect (law).

Tasks :
1. educational: introduce the concepts: proper motion of stars, radial and tangential velocity. Derive a formula for determining the spatial and tangential speed of stars. Describe the Doppler effect.
2. nurturing: to substantiate the conclusion that the stars move and, as a result, the appearance of the starry sky changes over time, pride in Russian science - the research of the Russian astronomer A.A. Belopolsky, to promote the formation of such worldview ideas as cause-and-effect relationships, the cognizability of the world and its laws.
3. Educational: the ability to determine the direction (sign) of the radial velocity, the formation of the ability to analyze the material contained in the reference tables.

Know:
Level 1 (standard) - the concept of velocities: spatial, tangential and radial. Doppler's law.
2nd level - the concept of velocities: spatial, tangential and radial. Doppler's law.
Be able to:
Level 1 (standard) - determine the speed of movement of stars, the direction of movement by the shift of lines in the spectrum of the star.
2nd level - to determine the speed of movement of stars, the direction of movement by the shift of lines in the spectrum.

Equipment: Tables: stars, star map (wall and movable), star atlas. Transparencies. CD- "Red Shift 5.1", photographs and illustrations of astronomical objects from the Internet, multimedia disk "Multimedia library on astronomy"

Interdisciplinary connections: mathematics (improving computational skills in finding decimal logarithms, decomposition of the velocity vector into components), physics (speed, spectral analysis).

During the classes:

Student survey.

At the blackboard:
1) Parallax method for determining the distance.
2) Determine the distance through the brightness of bright stars ..
3) Solving problems from homework No. 3, No. 4, No. 5 from § 22 (p. 131, No. 5 analogue of additional task 2, lesson 22) - show solutions.
Rest:
1) Find bright stars on the computer and characterize them.
2) Task 1: How many times brighter is Sirius than Aldebaran? (we take the sound value from Table XIII, I 1 / I 2 \u003d 2.512 m 2 -m 1, I 1 / I 2 \u003d 2.512 0.9 + 1.6 \u003d 1 0)
3) Task 2: One star is 16 times brighter than the other. What is the difference between their magnitudes? (I 1 / I 2 \u003d 2.512 m 2 -m 1, 16 \u003d 2.512? m , ?m≈ 1,2/0,4=3}
4) Task 3: Aldebaran parallax 0.05". How long does it take the light from this star to reach us? (r=1/π, r=20pc=65.2 sv

New material.
In 720 I. Xin(683-727, China) in the course of the angular change in the distance between 28 stars, for the first time conjectures about the movement of stars. J. Bruno also claimed that the stars move.
V 1718 E. Halley(England) discovers the proper motion of the stars , exploring and comparing directories Hipparchus(125g to NE) and J. Flamsteed(1720) found that in 1900 years some stars moved: Sirius (α B. Canis) shifted south by almost one and a half diameters of the Moon, Arcturus (α Bootes) two diameters of the Moon south and Aldebaran (α Taurus) shifted by 1 / 4 moon diameters to the east. For the first time he proves that the stars are distant Suns. The first star to have him in 1717 he discovered his own movement was Arcturus (α Bootes), located in 36.7 St.
So, the stars move, that is, they change their coordinates over time. By the end of the 18th century, the proper motion of 13 stars had been measured, and W. Herschel in 1783 discovered that our Sun also moves in space.

	Let m- the angle by which the star has shifted in a year (proper motion - "/ year). From a drawing by the Pythagorean theorem υ= √(υ r 2 +υ τ 2) , where υr - radial velocity (along the line of sight), and υ τ - tangential speed (^ line of sight). Because r= a/π , then, taking into account the bias m ® r .m =a . m/ π ; but r .m / 1 year=u, then substituting numerical data we get the tangential velocity υ τ \u003d 4.74. m/π (form. 43) radial velocity υr determined by the effect H. Doppler(1803-1853, Austria) (radial (radial in astronomy) velocity), who established in 1842 that the wavelength of the source varies depending on the direction of movement. The applicability of the effect to light waves was proven in the 1900s in the laboratory. A. A. Belopolsky. υ r =?λ . s/λ o.
	Approximation source - shifted to Purple (sign " - "). Removal source - shifted to Red (sign " + ") .
He was the first to measure the radial velocities of several bright stars in 1868. William Heggins(1824 - 1910, England). Since 1893 for the first time in Russia Aristarkh Apollonovich Belopolsky(1854 - 1934) began photographing stars and, having carried out numerous accurate measurements of the radial velocities of stars (one of the first in the world to take the Doppler effect into service), studying their spectra, determined the radial velocities of 220 bright (2.5-4 m) stars.

The fastest moving star in the sky ß Ophiuchus (flying Barnard, Barnard's Star, HIP 87937, discovered 1916 E. Barnard(1857-1923, USA)), m\u003d 9.57 m, r\u003d 1.828 pc, m\u003d 10.31 ", a red dwarf. The star has a satellite at M \u003d 1.5 M Jupiter, or a planetary system. ß Ophiuchus has a radial velocity \u003d 106.88 km / s, spatial (at an angle of 38 °) \u003d 142 km / s. After measurements of proper motions of > 50,000 stars, it turned out that the fastest star in the sky in the constellation Dove (m Col) has a spatial velocity = 583 km / s.
At a number of observatories in the world that have large telescopes, including those still in the USSR (at the Crimean Astrophysical Observatory of the Academy of Sciences of the USSR), long-term determinations of the radial velocity of stars are being made. Measurements of the radial velocity of stars in galaxies made it possible to detect their rotation and determine the kinematic characteristics of the rotation of galaxies, as well as our Galaxy. Periodic changes in the radial velocity of some stars make it possible to detect their orbital motion in binary and multiple systems, and when to determine their orbits, linear dimensions and distance to the star.
Addition .
Moving, the star changes its equatorial coordinates over time, so the proper motion of the star can be decomposed into components in equatorial coordinates and we get m =√ (m a 2 + m δ2). The change in the coordinates of a star for a year in astronomy is determined by the formulas: Δα=3.07 s +1.34 s sinα . tanδ and Δδ=20.0" cosα
III. Fixing the material.
1. Example #10(page 135) - view
2.On one's own: From the previous lesson for your star, find the spatial velocity (taking the distance from table XIII) and from this table m and υr. Find by PKZN and determine the coordinates of the star.

Solution: (sequence) Since υ= √(υ r 2 +υ τ 2), first we find π =1/r, then υ τ =4.74. m/π, but now we find υ= √(υ r 2 +υ τ 2)
3.
Outcome:
1. What is the proper motion of a star?
2. What speed do we call spatial, tangential, radial? How are they located?
3. What is the Doppler effect?
4. Ratings.

Houses:§23, questions p. 135

The lesson was designed by a member of the circle "Internet technologies" Leonenko Katya (11th grade), 2003.

"Planetarium" 410.05 mb		The resource allows you to install the full version of the innovative educational and methodological complex "Planetarium" on the computer of a teacher or student. "Planetarium" - a selection of thematic articles - are intended for use by teachers and students in the lessons of physics, astronomy or natural science in grades 10-11. When installing the complex, it is recommended to use only English letters in folder names.
Demo materials 13.08 mb		The resource is a demonstration materials of the innovative educational and methodological complex "Planetarium".
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Lesson	Lesson topic	Development of lessons in the collection of DER	Statistical graphics from the DER
Lesson 23	Spatial speed of stars		Shift of stars for 100 years 158.9 kb Measurement of angular displacements of stars 128.6 kb Proper motion of a star 128.3 kb Components of the proper motion of a star 127.8 kb Radial and tangential velocities 127.4 kb

If the star's proper motion m in arc seconds per year (see § 91) and the distance r to it in parsecs are known, then it is not difficult to calculate the projection of the star's spatial velocity onto the plane of the sky. This projection is called the tangential velocity Vt and is calculated by the formula (12.3) To find the spatial velocity V of a star, it is necessary to know its radial velocity Vr, which is determined from the Doppler shift of the lines in the spectrum of the star (§ 107). Since Vr and Vt are mutually perpendicular, the spatial velocity of the star is (12.4) Knowledge of the proper motions and radial velocities of stars allows us to judge the motions of stars relative to the Sun, which, together with the planets surrounding it, also moves in space. Therefore, the observed movements of stars are composed of two parts, one of which is a consequence of the movement of the Sun, and the other is the individual movement of the star. To judge the motions of the stars, one should find the speed of the Sun and exclude it from the observed speeds of the stars. Let us determine the magnitude and direction of the Sun's velocity in space. That point on the celestial sphere, to which the velocity vector of the Sun is directed, is called the solar apex, and the point opposite to it is called the anti-apex. To explain the principle on the basis of which the position of the solar apex is found, suppose that all the stars, except for the Sun, are motionless. In this case, the observed proper motions and radial velocities of the stars will be caused only by the movement of the Sun, which occurs at a speed of VS (224). Consider some star S, the direction to which makes an angle q with the vector VS. Since we have assumed that all stars are motionless, then the apparent motion of the star S relative to the Sun must have a speed equal in magnitude and opposite in direction to the speed of the Sun, i.e., VS. This apparent velocity has two components: one - along the line of sight, corresponding to the radial velocity of the star Vr = VScos q, (12.5) and the other, lying in the plane of the sky, corresponding to the proper motion of the star, Vt = VS sin q. (12.6) Taking into account the dependence of the magnitude of these projections on the angle q, we obtain that due to the motion of the Sun in space, the radial velocities of all stars located in the direction of the motion of the Sun must appear to be less than the real ones by VS. For stars in the opposite direction, on the contrary, the speeds should appear to be greater by the same amount. The radial velocities of stars located in a direction perpendicular to the direction of the Sun's motion do not change. On the other hand, they will have their own motions directed towards the antiapex and equal in magnitude to the angle under which the vector VS is visible from the distance of the star. As the apex and antiapex are approached, the magnitude of this proper motion decreases in proportion to sin q, down to zero. In general, it seems that all the stars seem to run away towards the antiapex. Thus, in the case when only the Sun moves, the magnitude and direction of its velocity can be found in two ways: 1) by measuring the radial velocities of stars located in different directions, find the direction where the radial velocity has the greatest negative value; in this direction is the apex; the velocity of the Sun in the direction of the apex is equal to the found maximum radial velocity; 2) having measured the proper motions of the stars, find on the celestial sphere a common point to which they are all directed: the point opposite to it will be the apex; To determine the value of the Sun's velocity, one must first convert the angular displacement into linear velocity, for which it is necessary to select a star with a known distance, and then find VS using formula (12.6). If we now assume that not only the Sun, but also all other stars have individual motions, then the problem becomes more complicated. However, considering a large number of stars in a given region of the sky, we can assume that, on average, their individual movements should compensate each other. Therefore, the average values ​​of proper motions and radial velocities for a large number of stars should show the same regularities as individual stars in the just considered case of the motion of the Sun alone. Using the described method, it has been established that the apex of the solar system is in the constellation Hercules and has right ascension a = 270o and declination d = +30o. In this direction, the Sun moves at a speed of about 20 km/sec.

The star in the constellation Ophiuchus Barnard has the fastest proper motion. In 100 years, it passes 17.26 ", and in 188 years it shifts by the size of the diameter of the lunar disk. The star is at a distance of 1.81 pc. The displacement of stars in 100 years

Stars move at different speeds and are at different distances from the observer. As a result, the relative position of the stars changes over time. It is almost impossible to detect changes in the contour of the constellation during one human life. If you follow these changes over the millennia, they become quite noticeable.

The spatial speed of a star is the speed at which a star moves in space relative to the Sun. The essence of the Doppler effect: The lines in the spectrum of a source approaching the observer are shifted to the violet end of the spectrum, and the lines in the spectrum of a receding source are shifted to the red end of the spectrum (in relation to the position of the lines in the spectrum of a stationary source). Components of proper motion of stars μ - proper motion of a star π - annual parallax of a star λ - wavelength in the spectrum of a star λ 0 - wavelength of a stationary source Δλ - spectral line shift c - speed of light (3 10 5 km/s)