b) How far away is it if its distance is given by the Hubble
relation (The Hubble constant is H = 75 km/s/Mpc)?
Both answers may be done with an accuracy of 30 %.
2.
Young scientists from the Komi-Republic territory
(in the Russian Federation) registered a few days ago a new object
looking like an eclipsing binary star. But the period of this star
was not stable: the stellar magnitude of the object is usually equal
to 24.32m. Once every 7-11 seconds it is rising
to 24.52m for 0.2-0.3 seconds. After investigations
it was clear that the shining object is eyes
of a group of absolutely black cats sitting on a small absolutely
black body in our Solar System and looking towards the Sun! And one of
the cats is blinking! Calculate the number of cats in the group sitting
on the small body and looking to the Sun. Draw a picture explaining your
solution. Consider that all the cats are equal in size.
Groups A and B.
3.
There are two photos of the Moon taken by the same camera mounted on
the same telescope (the telescope is placed on the Earth). The first
photo has been made while the Moon was near its perigee and the
second one Ц near the apogee. Find from these data the value of
the Moon's orbit eccentricity. Estimate the minimal period between
the moments at which these two photos could be taken.
4.
A cosmonaut in a spacecraft is moving over the Moon surface through
the Mare Frigoris at an altitude of 100 km. An astronaut is walking on
the Moon's surface at Mare Frigoris and it is daytime at that place
(the Sun is shining). Can the cosmonaut register the astronaut using
binoculars with a magnification of 20x. Take into
account all the possibilities.
5.
There is a radio source placed on a satellite of some planet named
"Olympia". The radio source is working all the time but an observer does
not register the signal all the time due to eclipses. The figure shows
the level of the receiving signal by the observer vs time. Find from
these data the average density of the planet. Take into account that
the orbit of the satellite is circular, the observer is in the plane of
the satellite's orbit and "Olympia" is far away from the observer.
6.
An 1.2-meter Schmidt camera has a
6ђ ´ 6ђ field of view.
Estimate how many photographs you would have to take to cover
the whole sky. (Please, make an estimation of the maximum and
minimum number of photos.) Explain your calculations. Where do you
have to place your telescope to be able to do this?
Practical round. Problem 1 to solve
Groups A and B.
A SUPERNOVA IN THE GALAXY NGC 3184.
Sorry, figures are not ready.
Introduction:
Special Astrophysical Observatory of Russian Academy of Sciences
participates in an international program on investigation of supernovas
bursting in distant galaxies. Stellar magnitudes of supernovas are measured
with the help of CCD at 1-meter and 60-centimeter telescopes. For the
brightest of galaxies the spectra are also obtained.
Fig.1 presents a recent sample of a CCD image obtained with the
60-centimeter telescope. It was taken on October 7, 2000. It shows
a part of a galaxy cluster, in one of which a supernova burst.
Galaxies are marked with the letter G. Their images differ from sharp
images of stars by fuzzy edges. The visible stellar magnitudes of two
brightest galaxies and the supernova (it is marked with the letters SN)
are indicated.
And now the task itself:
In Fig.2 is shown an image of a spiral galaxy NGC 3184 in which
on December 10, 1999 a supernova was noticed. The image was taken before
the burst! You can see stars up to 23rd magnitude in it.
Fig.3 is a CCD image with a part of the galaxy and the supernova
taken on January 28, 2000 with the 1-meter telescope of SAO.
Galaxy NGC 3184 is in the constellation of Ursa Major. Its
coordinates (1950) are as follows:
α = 10h 15m,
δ = 41ђ 40´. It is similar to the famous
galaxy of M33 in the Triangle (M33 is closer to us, the distance to
it is 700 kpc, its angular size is about 50‡).
By the images of 28.01.2000 in SAO the apparent stellar magnitudes of the supernova in blue, green and red filters were determined. Its apparent stellar magnitude was 14m.67.
Find the supernova in Fig.3.
Estimate its absolute magnitude.
Professional astronomers don't doubt that they deal with a supernova.
In particular, a spectrum was obtained, by which it was assigned to
type II. But nevertheless Ц for non-professionals Ц prove that it is not
a burst of a nearby (foreground)-star on the background of a galaxy.
Practical round. Problem 2 to solve
Group A.
A "DRILLING" OF THE MOON WITH THE HELP OF RATAN
Sorry, figures are not ready.
Introduction:
Dear students, you are to see the first colonies on the Moon.
The areas of the Moon surface consisting of oxygen-bearing rock are
already being searched for them. First of all these are ilmenite basalts.
Beside oxygen (10% from the weight) the ilmenite (FeTiO3) can
give a pure iron.
With the help of the radio telescope RATAN-600 a "radio drilling" of
the Moon was carried out: unlike the visible light, radio waves come from
under its surface. The depth of the "drilling" increases with the increase
of wavelength. At the wavelength of 1 cm the Moon is transparent down to
0.5 m, at 30 cm Ц down to 10 m. The regions with increased content of
ilmenite are also distinguished by an increased radio emission level.
Fig.1 presents radio cuts of the Moon obtained at its passage through
the "knife" beams of RATAN. From the 6 used wave lengths only 3 are
presented, since the cut at 2.1 cm almost repeats the cut at 1.4 cm,
and the cuts at 3.9 and 31 cm differ little from the cut at 8.2 cm.
The last could be said also about 13-cm cut, but at the moment of
observation the transmitters left at the Moon by American astronauts
were operating, exactly at this wavelength.
The cuts at different wavelengths can be compared both to each other
and to the seas and continents known to you in the image of the Moon
in visible light. A band covered in the observations at 1.4 cm is marked
in it. In other wavelengths the beams cover the entire disk of the Moon
in altitude. The positions of transmitters operating at the wavelength
of 13 cm are also shown.
Task:
What transmitters were operating at the moment of observation?
What is the difference in the image of the Moon in cm wavelength
from its image in visible wavelengths? What is the reason for it?
What region would you recommend for the settlement of first colonies?
Practical round. Problem 2 to solve
Group B.
SPECTRA OF A PLANETARY NEBULA "CAT EYE" AND ITS CENTRAL STAR
Sorry, figures are not ready.
Introduction:
Planetary nebula NGC 6543 ("Cat eye") played its special
part in the history of astrophysics. On August 16, 1865, an English
amateur astronomer William Heggins looked at it with a spectroscope
and, as he writes, "did not see an expected total spectrum, but only
one bright line!" Shortly after it was resolved into two lines with
the wavelengths of 4959 х and 5007 х. Heggins assigned it to
a new element "nebulium".
Later it was found out that these are "forbidden" lines of doubly
ionized oxygen that were never observed before - neither in terrestrial
laboratory nor in stars. Unlike "permitted" lines, only a very thin gas
emits such lines.
Recall that if an atom is neutral, then a Roman numeral I follows
the symbol of its chemical element, if the atom lost one electron then
it is Roman II, etcЕ. for example, the neutral nitrogen is N I,
the ionized nitrogen is N II. In notation of forbidden line the
symbols of atoms and ions are taken in square brackets, for example:
the ionized nitrogen is [N II], doubly ionized oxygen
is [O III].
The spectrum of the central star generating the nebula NGC 6543
and exciting its glow, as well as the spectrum of the nebula itself
were obtained in the course of study of the late stages of stellar
evolution. The high-resolution spectrograph of the 6-meter telescope
of SAO was used. The star and a peripheral part of the nebula were
alternately projected onto its slit. These positions of the slit marked
by a sign ' * ' for the first one and by a sign ' @ '
for the second one in Fig 1a, 1b, 1c.
Task:
The upper parts of Fig. 1a, 1b, 1c show the parts of spectra as
intensity vs wavelength given from the mentioned regions. In each of
them the interesting lines are selected, and their profiles of are
presented in the lower fragments as a relation between intensity and
radial velocity. The figures show also the values of radial velocities
measured by the tops of profiles of separate lines.
Determine which lines belong to the star and which to the nebula;
fill in the appended table:
Lines in the spectra of NGC 6543 and its central star:
|
Figure |
Lines belonging to the nebula |
Lines belonging to the star |
|
2a |
|
|
|
2b |
|
|
|
2c |
|
|
What is the difference between them?
What can be said about the character of motion in the nebula and
in the star's atmosphere from the form of the line profiles?
Estimate the velocity of these motions.
Observational round (the day's part). Problem to solve
Group A.
STARS ON THE DAYTIME SKY
Introduction:
You cannot see stars at daytime with a naked eye.
And can they be seen with a telescope? If yes, explain why? Write here
your explanation:
You have an opportunity to test that with the help of a guide of
1-meter telescope of SAO. Its objective-glass diameter is 20 cm, focus
distance is 3 m, and field of seeing is 21‡.
Preparation to observation.
Using the map of stars, select a star.
Point here your object:
Its coordinates:
Observation.
An operator input the coordinates of your object into a computer
controlling the 1-m telescope. After the telescope is pointed on it,
check if it is seen into the guide.
The winner of the observational round competition is one who sees
the faintest star at a minimum distance from the Sun.
Observational round by photos
Groups A and B.
Sorry, photos are possible only in SAO.
Photo 1.
What nebulae do you recognize?
Why most of them are red, but some are blue?
Photo 2.
What stellar clusters are seen in the photo?
What constellations do the photo borders cross?
What part of the Galaxy is seen in Photo 1 and 2?
Photo 3.
What objects are seen in the photo, their names or at least the types?
In what region of the Galaxy they are?
Photo 4.
Australian aborigines call this system of dark nebulae "Emu"
(Australian ostrich).
In what constellations are its body, neck and head?
What object of the photo is the nearest and the most distant?
|
юҐ¤ѕҐ»
с·«…‚, ?ся ?сю |
20 - 27. 10. 2000. |
SAO RAS, Nizhnij
Arkhyz |
Dr. Michael G. Gavrilov, Chairman of the Coordinating Council
of the International Astronomy Olympiad,
ISSP of Russ. Acad. Sci., Institute avenue 15, 142432 Chernogolovka, Moscow region, Russia.
URL: http://www.issp.ac.ru/iao/2000/
e-mail: gavrilov@issp.ac.ru
fax: +7-(096-52)-49-701
