At true noon, use a goniometer to measure the height of the Sun hc. When using a gnomon, the height of the Sun is determined by the formula
tgh c \u003d AB - penumbra length; BC - gnomon height
Explanations: redraw the drawing, indicate the angle corresponding to the specified height, use a tree (building) of known height as the segment BC, measure the segment AC by the shadow in steps. The solution is presented in the form of a table, where to enter the values \u200b\u200bof the quantities and make calculations.
Calculate the latitude of the area using the formula
φ = 90 0 – h s – δ s
where δ s is the declination of the Sun on the date of observation (determined by the astronomical calendar or by the position of the Sun on the ecliptic of the star chart), h s is taken from the previous task.
Explanations: arrange in the form of a task through given.
Draw conclusions (compare the obtained φ data with the data of a geographical map and justify the possibility of determining the geographic latitude of the area in this way; explain the reason for the change in the height of the Sun)
Observation of sunspots
Make a drawing of the surface of the solar photosphere with groups of spots.
Determine the activity of the Sun by the formula
where W is the relative Wolf number; g is the number of spot groups; f is the number of individual spots
Explanations: the decision should be presented in the form of a table with the values \u200b\u200band entered and calculations.
Draw conclusions about the activity of the Sun at the present time. Analyze the activity of the Sun in previous years, now and give a forecast of activity for the next 1 - 2 years, plot the dependence of the Wolf number on time, from 2000 to 2020
Explanations: redraw the chart, mark the specified period.
Determination of the midday line by the movement of the sunspot
The method is as follows. In one of the south-facing windows, a screen with a small opening (about 1 cm in diameter) is installed at a suitable height. Starting observation 1.5 - 2 hours before noon, the position of the sun spot from this hole on the floor is noted for 3-4 hours. The result is a line AB (Fig. 53). Holding the thread at hole 0, its other end describes an arc (dashed line) that will intersect the line AB at points C and D. Two notches are made from these points with the same radius and points E and F are obtained. Line EF will be the midday line. Make a drawing, fixing the position of the sun spot on the floor every 15 minutes.
It should be noted that the curve that a sunspot describes during the day changes depending on the declination of the Sun. On the days of the equinoxes, this is a straight line, with positive declinations of the Sun (from March 21 to September 23), the curves are hyperbolas, convex from the base, with negative declinations (from September 23 to March 21) - convex to the base.
Explanations: Redraw the drawing, supplement with the necessary constructions described in the method and sign the resulting midday line
Draw conclusions by substantiating the considered method for finding the noon line. What other methods can be used to determine the noon line, what is the practical significance of finding the noon line.
The great circle of the ecliptic intersects the great circle of the celestial
equator at an angle of 23 ° 27 "On the day of the summer solstice, July 22-
nya, the sun rises at noon above the horizon above the point at
which the celestial equator crosses the meridian by this amount
(Fig. 17). How much is the sun below the equator per day?
winter solstice, 22 December. Thus, the height of the Sun
The temperature at the upper climax changes during the year by 46°54".
It is clear that at midnight there is a zodiac in the upper climax.
constellation opposite to the one in which the Sun is located
tse. For example, in March, the Sun passes through the constellation Pisces, and in
Midnight culminates in the constellation Virgo. Figure 18 shows
daily paths of the Sun above the horizon on the days of the equinoxes and solar
cestoes for mid-latitudes (top) and the Earth's equator (bottom)
Rice. 18. Daily paths of the Sun over
horizon at different times
change of year when observing
niyakh: a - in medium geo-
graphic latitudes;
b - at the equator of the Earth.
Rice. 19. Equatorial coordinates
no misters.
2 1. Find the 12 zodiac constellations
on the star map and if possible
look for some of them in the sky.
2. Using an eclimeter or gnomon
(known to you from the physical geographical
fii), measure at least once a month
the height of the sun above the horizon
noon for several months.
By plotting the change in height
Sun in time, you'll get cry-
Vuyu, by which you can, for example,
plot part of the ecliptic on the star
map, given that the Sun for the month
shifts in the starry sky to the east
ku about 30°.
f .STAR CHARTS,
SKY COORDINATES
AND TIME
1. Maps and coordinates. To make-
make a star map, depict
constellation on the plane, it is necessary
know the coordinates of the stars. Coor-
dinats of stars relative to the horizon
umbrella, such as height, although
visual, but unsuitable for
putting cards, since all the time
me are changing. Must use
a coordinate system that
would revolve with the stars
sky. It's called equa-
torial system. AT
its one coordinate is
the angular distance of the luminary from
celestial equator, called
declination b (Fig. 19). It me-
nyatsya within ± 90 ° and considers -
Xia positive north of eq-
vator and negative - to the south.
Declination similar to geo-
graphic latitude
The second coordinate is similar
geographic longitude and name
right ascension
a.
Accurate spring
equinoxes
Right ascension of star M
measured angle between the plane
mi of a large circle held by
cutting the poles of the world and this light
lo M, and a large circle, passing-
through the poles of the world and the point
spring equinox(Fig. 19).
This angle is measured from the point ve-
vernal equinox T against stroke
clockwise when viewed from the
right pole. It changes from O
up to 360 ° and is called direct reproduction
walking because the stars, dis-
placed on the celestial equator,
ascend in ascending order
direct ascension. In the same
in a row they culminate one after the other
hom. Therefore, a is usually expressed
not in angular measure, but in time,
and proceed from the fact that the sky rotates by 15 ° in 1 hour, and in 4 minutes -
on G. Therefore, right ascension 90 ° will otherwise be 6 hours, and
7 h 18 min = 109°30/. In units of time along the edges of the sidereal
maps label right ascensions.
There are also star globes, where the stars are depicted
on the spherical surface of the globe.
On one map, only a part of the map can be depicted without distortion.
of the starry sky It is difficult for beginners to use such a map,
because they don't know which constellations are currently visible
and how they are positioned relative to the horizon. More convenient to move
naya map of the starry sky. The idea behind her device is simple. On the map
superimposed circle with a cutout depicting the horizon line. cutout
the horizon is eccentric, and when the overlay circle is rotated in you-
section, constellations will be visible that are above the horizon at different
time. How to use such a card is described in Appendix VII.
3 1. Express 9 hours 15 minutes 11 seconds in degrees.
According to the table of coordinates of bright stars given in appendix IV, find
on the star map are some of the indicated stars.
On the map, count the coordinates of several bright stars and check yourself,
using the table in annex IV.
According to the "School astronomical calendar" find the coordinates of the planets
at a given time and determine on the map in which constellation they are located.
Find them in the evening in the sky.
Using a mobile map of the starry sky, determine which zodiac
constellations will be visible above the horizon on the evening of observation.
2. The height of the luminaries at the climax. Let's find the relationship between you-
hundredth h of the luminary M in the upper culmination, its declination is 6
and the latitude of the area f.
Rice. 20. The height of the luminary at the top
climax.
Figure 20 shows a plumb line ZZ", the axis of the world
PP" and projections of the celestial equator EQ and horizon line NS
(noon line) to the plane of the celestial meridian (PZSP "N)
The angle between the noon line NS and the axis of the world PP" is equal to
we know the latitude of the area
celestial equator to the horizon, measured by the angle
equal (Fig. 20). Star M with declination 6, culminatingsouth of the zenith, has an altitude of +
From this formula it can be seen that the geographical latitude can be determined
pour by measuring the height of any star with a known declination of 6
top climax. In this case, it should be borne in mind that if the star
at the moment of climax is south of the equator, then its declination
negative.
4 1. Sirius(a B. Psa, see Appendix IV) was in the upper climax on
height 10°. What is the latitude of the observation point?
For the following exercises, the geographic coordinates of cities can be
count on a geographic map.
At what height in Leningrad is the upper climax of Antares
(a Scorpio, see Appendix IV)?
What is the declination of the stars that culminate at the zenith in your city?
at a point south?
Determine the noon height of the Sun in Arkhangelsk and Ashgabat in
summer and winter solstices.
3. Exact time. For measuring short periods of time
in astronomy, the basic unit is the average duration
solar day, i.e., the average time interval
between two upper (or lower) center climaxes
Sun. The average value has to be used because
The duration of the solar day varies slightly throughout the year.
This is because the earth revolves around the sun
circle, but in an ellipse and the speed of its movement is slightly
is changing. This causes slight unevenness in the visible
the movement of the sun along the ecliptic during the year.
The moment of the upper culmination of the center of the Sun, as we have already said
Riley, is called true noon. But to check the clock,
to determine the exact time, there is no need to mark them
the moment of the climax of the sun. It is more convenient and more accurate to mark
climax points of the stars, since the difference between the climax points
any star and the sun is exactly known for any time.
Therefore, to determine the exact time using special
optical instruments mark the moments of the climaxes of the stars and check
ryayut on them the correctness of the clock, "keeping" the time. Definition-
the time thus obtained would be absolutely accurate if
the observed rotation of the sky occurred with a strictly constant
angular speed. However, it turned out that the rotation speed
Earth around its axis, and hence the apparent rotation of the celestial
spheres undergoes very little change over time. Poet
Therefore, for the "storage" of the exact time, special
real atomic clock, the course of which is controlled by oscillatory
processes in atoms occurring at a constant frequency.
The clocks of individual observatories are checked against the signals of the atomic
time. Comparison of time determined by atomic clocks and
according to the apparent motion of stars, allows you to explore the uneven
of the Earth's rotation.
Determination of the exact time, its storage and transmission according to the
dio to the entire population constitute the task of the service of accurate
time that exists in many countries.
Radio time signals are received by navigators of the sea
th and air fleet, many scientific and industrial organizations
nizations that need to know the exact time. Know the exact
time is needed, in particular, to determine the geographic
goth different points of the earth's surface.
10-11 grade
Task number 1
1. Rise and set of stars
2. Changing the phases of the moon
4. Sunrise and sunset
5. Solar eclipses
6. Tides
Task number 2
( Comment
Task number 3
Task number 4
h
Task number 5
Evaluation criteria
All-Russian Olympiad for schoolchildren
School stage of the Olympiad in Astronomy 2017-2018 academic year
10-11 grade
Time to complete the job 60 minutes
Task number 1
From the above list of phenomena, select those that are caused, among other things, by the rotation of the Moon around the Earth. Write your answer as a sequence of numbers.
1. Rise and set of stars
2. Changing the phases of the moon
3. Change of seasons (winter, spring, summer, autumn)
4. Sunrise and sunset
5. Solar eclipses
6. Tides
Answer: 2,5,6.
For each correct of the three answers 5 points. Maximum 15 points.
Task number 2
The winter solstice will take place on December 22, 2015, and the spring equinox will occur on March 20, 2016. How many days will pass between these events?
( Comment . Assume that 1 day passes between December 1 and December 2.)
Answer: 89 - for the correct answer 10 points.
Task number 3
Task. Sirius (α Canis Majoris = - 17) was in the upper culmination at an altitude of 10. What is the latitude of the observation site?
Answer:
Given: Solution:
δ= declination of Sirius is given in the conditions of the problem. From the formula
hwe find that the latitude.
φ =?
Answer:
10 points for correct calculations, 5 points for correctly chosen formula. Maximum - 10 points.
Task number 4
Determine the noon height of the sunhin Arkhangelsk () and in Ashgabat () on the days of the summer and winter solstices.
Answer:
Given:
To find:
Decision: approximate values of the latitude of Arkhangelsk () and Ashgabat () are given in the conditions of the problem. The declinations of the Sun at the summer and winter solstices are known.
According to the formula we find: , .
5 points for each correctly calculated height. Maximum 20 points.
Task number 5
How long does it take for an observer on the moon to go from one star climax to the next?
Answer: 27.3 days. This period of time is the period of revolution of the Moon around the Earth in a reference frame associated with the stars (sidereal month). The culmination of the star is the moment of crossing the celestial meridian.
10 points for a correct answer.
Maximum points for all tasks: 65 points
a) For an observer at the north pole of the Earth ( j = + 90°) non-setting luminaries are those in which d-- i?? 0, and non-ascending are those for which d--< 0.
Table 1. Height of the midday sun at different latitudes
The positive declination of the Sun occurs from March 21 to September 23, and negative - from September 23 to March 21. Consequently, at the north pole of the Earth, the Sun is a non-setting star for about half a year, and a non-rising luminary for half a year. Around March 21, the Sun appears above the horizon here (rises) and, due to the daily rotation of the celestial sphere, describes curves close to a circle and almost parallel to the horizon, rising higher and higher every day. On the day of the summer solstice (around June 22), the sun reaches its maximum height. h max = + 23° 27 " . After that, the Sun begins to approach the horizon, its height gradually decreases, and after the day of the autumnal equinox (after September 23) it disappears under the horizon (sets). The day, which lasted six months, ends and the night begins, which also lasts six months. The sun, continuing to describe curves, almost parallel to the horizon, but below it, sinks lower and lower, On the day of the winter solstice (about December 22), it will sink below the horizon to a height h min = - 23° 27 " , and then again begins to approach the horizon, its height will increase, and before the day of the vernal equinox, the Sun will again appear above the horizon. For an observer at the south pole of the Earth ( j\u003d - 90 °) the daily movement of the Sun occurs in a similar way. Only here the Sun rises on September 23, and sets after March 21, and therefore, when it is night at the north pole of the Earth, it is day at the south, and vice versa.
b) For an observer on the Arctic Circle ( j= + 66° 33 " ) non-setting are luminaries with d--i + 23° 27 " , and non-ascending - with d < - 23° 27". Consequently, on the Arctic Circle, the Sun does not set on the day of the summer solstice (at midnight, the center of the Sun only touches the horizon at the point of north N) and does not rise on the day of the winter solstice (at noon, the center of the solar disk will only touch the horizon at the point of south S, and then descend below the horizon again). On other days of the year, the Sun rises and sets at this latitude. At the same time, it reaches its maximum height at noon on the day of the summer solstice ( h max = + 46° 54"), and on the day of the winter solstice its midday height is minimal ( h min = 0°). At the southern polar circle ( j= - 66° 33") The sun does not set on the winter solstice and does not rise on the summer solstice.
The northern and southern polar circles are the theoretical boundaries of those geographical latitudes where polar days and nights(days and nights lasting more than 24 hours).
In places lying beyond the polar circles, the Sun is a non-setting or non-rising luminary the longer, the closer the place is to the geographical poles. As we get closer to the poles, the duration of the polar day and night increases.
c) For an observer on the northern tropic ( j--= + 23° 27") The sun is always a rising and setting luminary. On the day of the summer solstice, it reaches its maximum height at noon. h max = + 90°, i.e. passes through the zenith. On the rest of the year, the Sun culminates south of the zenith at noon. On the day of the winter solstice, its minimum noon height h min = + 43° 06".
On the southern tropic j = - 23° 27") The sun also always rises and sets. But at the maximum midday height above the horizon (+ 90°) it happens on the day of the winter solstice, and at the minimum (+ 43° 06 " ) on the day of the summer solstice. On the rest of the year, the Sun culminates north of the zenith here at noon.
In places lying between the tropics and the polar circles, the sun rises and sets every day of the year. For six months here the duration of the day is longer than the duration of the night, and for six months the night is longer than the day. The midday height of the Sun here is always less than 90° (except for the tropics) and greater than 0° (except for the polar circles).
In places lying between the tropics, the Sun is at its zenith twice a year, on those days when its declination is equal to the geographical latitude of the place.
d) For an observer at the Earth's equator ( j--= 0) all luminaries, including the Sun, are rising and setting. At the same time, they are above the horizon for 12 hours, and below the horizon for 12 hours. Therefore, at the equator, the length of the day is always equal to the length of the night. Twice a year the Sun passes at noon at its zenith (March 21 and September 23).
From March 21 to September 23, the Sun at the equator culminates at noon north of the zenith, and from September 23 to March 21 - south of the zenith. The minimum noon height of the Sun here will be equal to h min = 90° - 23° 27 " = 66° 33 " (June 22 and December 22).
Target: to form the ability to navigate by the sun, determine the noon line, the height of the noon sun above the horizon.
Equipment:
gnomon (a flat pole 1-1.5 m long), a vertical goniometer-eclimeter or a protractor with a plumb line, a thin rail or a piece of twine 2 m long.
Guidelines
During the year, the height of the sun above the horizon changes: on June 22 - on the day of the summer solstice - it occupies the highest position, on December 22 - on the day of the winter solstice - the lowest, and on the equinoxes - March 21 and September 23 - intermediate. In the northern and southern hemispheres, the change in the height of the noonday sun has the opposite direction.
Working process
Exercise 1. Definition of the noon line.
Place the gnomon vertically on a flat area closer to noon. Fix with the first peg the end of the shadow falling from it and with a radius (point 1) equal to the length of the shadow and draw a circle with another peg. Pay close attention to how the shadow will be shortened. After a certain time, the shadow will begin to lengthen and touch the circle a second time, but at a different point (point 2) (see Fig. 1) .
Rice. 1. Determination of the noon line
In the second peg, drive into this point. Stretch the twine from the first peg to the second peg. Find the midpoint of this segment. Drive in the third peg. Connect this peg with twine to the base of the gnomon. This will be the noon line, which shows the direction to the north and coincides with the local meridian. Check compass direction.
Task 2. Determining the height of the sun above the horizon.
Install the rail so that it rests with one end on the base of the third peg, and with the other lies on the upper end of the gnomon, forming an angle with a horizontal surface. Determine its value using an eclimeter or a vertical goniometer. This way you will determine the height of the sun above the horizon at noon.
Task 3. Answer the questions.
1. How does the height of the sun above the horizon change during the day
and year?
2. Determine the time of solar noon by the clock. Does the time of noon (12 o'clock) coincide with the solar time? Explain the reason.
Orientation in space
Target: teach the techniques of orientation in space according to local signs and a compass.
Equipment:
compass, measuring tape or 15-meter tape measure, mechanical wristwatch, school rangefinder, tablet.
Guidelines
Orientation in space is the determination on the ground of one's location or standing point relative to the sides of the horizon, surrounding objects of the terrain, as well as directions and distances of movement.
Orientation in space includes:
1) correlation of the real area with the plan and map;
2) determination on the ground of the sides of the horizon and its position in relation to the objects of the terrain: a settlement, a river, a railway, etc.;
3) determination of the distance on the ground and their graphic expression on paper.
4) selection of the required direction of movement.
Working process
Exercise 1. Determination of the direction of the sides of the horizon by compass.
The most accurate way of general orientation in the area is compass orientation. In order to determine the direction of the sides of the horizon using a compass, you must do the following:
1. Remove all metal objects at a distance of 1-2 m from the compass;
2. Install the compass in a horizontal plane on the palm of your hand or tablet;
3. Rotating the compass in a horizontal plane, achieve the alignment of the northern end of the magnetic needle of the compass with the letter C. In this position, the compass is oriented and now it is possible to determine the sides of the horizon from it.
Task 2. Orientation to the sun with a watch.
With the help of a mechanical wrist watch, you can determine the direction of the north-south line at a given time. To do this, do the following:
1. put the clock in a horizontal plane and point the hour hand at the sun;
2. mentally build an angle between the small hour hand
and the number 11 on the clock face. The bisector of this angle will be the local meridian.
Movement in azimuth
Target: teach the techniques of orientation in space and determining the direction of movement in azimuth.
Equipment:
compass, measuring tape or 10-15-meter tape measure, mechanical wristwatch, school rangefinder, tablet.
Guidelines
Using a compass, you can determine the sides of the horizon, the direction of movement in azimuth. Azimuth is the angle between the direction of north and the direction of a given object, which is counted clockwise.
For example, knowing that the azimuth from point A to point B is 45º (A = 45º), you, having oriented the compass, determine the azimuth and go in the right direction.
When moving, it is either set or determined. To determine the azimuth of movement from one point (standing point) to another, a map is needed.
For orientation on the ground, it is important to be able to determine not only the direction, but also the distance. They measure the distance using various methods: counting steps and time of movement, visual, instrumental. Visual (by eye) assessment of distances is the observation of terrain objects and their visibility depending on the distance from the observer (see Table 1). This method allows you to determine the distance approximately, this requires constant training.
Table 1
Eye measurement of distances
| Distance | Observed objects |
| 10 km | Pipes of large factories |
| 5 km | General outlines of houses (without doors and windows) |
| 4 km | The outlines of windows and doors are barely visible |
| 2 km | Tall lonely trees; man is a barely distinguishable point |
| 1 500 m | Large cars on the road, a person is still distinguished in the form of a dot |
| 1 200 m | Individual trees of medium size |
| 1 000 m | telegraph poles; individual logs are visible in the buildings |
| 700 m | The figure of a man without details of clothing is already looming |
| 400 m | The movements of a person's hands are noticeable, the color of clothes differs, the bindings on the window frames |
| 200 m | head outline |
| 150 m | Hands, eye line, clothing details |
| 70 m | Dotted eyes |
Working process
Exercise 1. Determination of azimuth 90º, 145º, 225º using a compass.
Walk in these directions for a short distance. To
do not stray from the chosen direction of movement, write down noticeable objects of the terrain, these will be landmarks of the direction in which you must move.
Task 2. Determining the distance to the selected terrain objects.
To accurately determine distances in professional activities, tape measures, measuring tapes, theodolites, radio direction finders are used.
and other tools. In everyday life, non-instrumental methods are used.
1. Select an object in an open area and visually determine the distance to it, using table 1.
2. To more accurately determine the distance by eye, you can use a technique that is based on a simple mathematical calculation. Let's take the ruler in hand, direct it to a distant object, the height of which is known to you, let's say 10 m. Moving the ruler in the fingers, we will achieve such a position when a segment of the ruler, let's say 10 cm, completely covers this object. Determine the distance from the eye to the ruler. It is approximately 70 cm. Now you know three quantities, but
the distance to the object is not known. Let's make a formula in which the length of the ruler is related to the height of the object X in the same way as the length of the outstretched arm is related to the distance to the object. Let's solve the proportion:
10m: X=10cm:70cm,
10 m: X = 0.1 m: 0.7 m,
X = 70 m.
This method is convenient to use when determining the distance to inaccessible objects located, for example, on the other side of the river.
Task 3. Measuring distance in steps.
You need to know your stride length. Set aside a 50 m long segment on a flat piece of terrain. Walk this distance several times
and determine the arithmetic mean of the steps.
For example, 71 + 74 + 72 = 217 steps. Divide the total number of steps by 3 (217:3 = 72). The average number of steps is 72. Divide 50 meters by 72 steps and you get your average stride length of about 55 cm.
You can measure the distance to any available object in steps. For example, if you took 690 steps, i.e. 55 cm × 690 = 37 m.
Record in a diary and compare the results of determining distances in different ways. Determine the degree of accuracy of each method.
