I
NTERNATIONAL
E
ARTH
S
CIENCE
O
LYMPIAD
7
thIn
ter
na
tio
na
l E
art
h S
cie
nc
e Ol
ym
pia
d
Stu
de
nt C
od
e:
Sta
te
m
en
t
Mass of Planet
Radius of Planet
Inclination of Rotation Axis with
respect to its Orbital Plane
Rotation Period
Length of Semi-major axis of the
orbit
Eccentricity of Orbit
Total Mass of Satellites
Density of Atmosphere
Water Vapour Percentage
Green House Effect
Magnetic Field Strength
Geothermal Activity
T
he
y
ea
rly
m
ea
n
te
m
pe
ratu
res
o
f
pla
ne
ts
d
o
n
ot
m
atc
h
w
ith
th
eir
ex
pe
cte
d b
la
ck
bod
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em
pe
ratu
re
.
A
bs
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te v
ari
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in
th
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em
pe
ratu
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d
uri
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th
e c
ou
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o
f o
ne
da
y d
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rs
sign
ific
an
tly
fr
om
o
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p
la
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t to a
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er.
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bs
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te
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pe
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th
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f th
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la
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t di
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ign
ific
an
tly
fr
om
o
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p
lan
et to a
not
he
r.
O
n
so
m
e
pla
ne
ts,
th
ere
is
a
la
rg
e
lati
tu
di
na
l p
erc
en
tag
e
va
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in
te
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pe
ratu
res.
M
ea
n
te
m
pe
ratu
re
(a
ve
rag
ed
o
ve
r
a
da
y)
o
n
E
arth
is
di
ffe
ren
t
on
di
ffe
ren
t da
ys.
M
yso
re
, I
nd
ia, S
epte
m
be
r 11 – 19, 2013
(T
he
ory
T
est
- A
str
on
om
y)
7
thIn
ter
na
tio
na
l E
art
h S
cie
nc
e Ol
ym
pia
d
Stu
de
nt C
od
e:
Sta
te
m
en
t
Mass
of
Planet
Radius of
Planet
Inclination of
Rotation Axis
with respect to
its Orbital Plane
Rotation Period
Length of Semi-major axis of
the orbit
Eccentricity of Orbit
Total Mass of Satellites
Density of Atmosphere
Water Vapour Percentage
Green House Effect
Magnetic Field Strength
Geothermal Activity
T
he
y
ea
rly
m
ea
n
te
m
pe
ratu
res
o
f
pla
ne
ts
d
o
n
ot
m
atc
h
w
ith
th
eir
ex
pe
cte
d b
la
ck
bod
y t
em
pe
ratu
re
.
X
X
X
X
A
bs
olu
te v
ari
ati
on
in
th
e t
em
pe
ratu
re
d
uri
ng
th
e c
ou
rse
o
f o
ne
da
y d
iffe
rs
sign
ific
an
tly
fr
om
o
ne
p
la
ne
t to a
noth
er.
X
X
X
X
X
A
bs
olu
te
va
ria
tio
n i
n t
he
te
m
pe
ratu
re
d
uri
ng
th
e c
ou
rse
o
f o
ne
ye
ar
at
th
e
eq
ua
to
r o
f th
e p
la
ne
t di
ffe
rs s
ign
ific
an
tly
fr
om
o
ne
p
lan
et to a
not
he
r.
X
X
X
X
X
X
X
O
n
so
m
e
pla
ne
ts,
th
ere
is
a
la
rg
e
lati
tu
di
na
l p
erc
en
tag
e
va
ria
tio
n
in
te
m
pe
ratu
res.
X
X
M
ea
n
te
m
pe
ratu
re
(a
ve
rag
ed
o
ve
r
a
da
y)
o
n
E
arth
is
di
ffe
ren
t
on
di
ffe
ren
t da
ys.
X
X
M
yso
re
, I
nd
ia, S
epte
m
be
r 11 – 19, 2013
(T
he
ory
T
est
- A
str
on
om
y)
7
thInternational Earth Science Olympiad
Student Code:
Theoretical Test
Astronomy
Time: 45 Minutes
Maximum Marks: 28.5
Instructions:
1. Please write your student code on the cover page as well as on the top right of
every page of answer sheet / calculations sheets.
2. Please write your answers legibly. Illegible answers will be counted as incorrect.
3. Please write your final answers in appropriate boxes in the main answer sheet.
For numerical questions, show the calculations on blank calculation sheets
provided.
4. For numerical questions, you may attempt part of the answer even if you don't
know the final result. There will be stepwise marking.
5. You can get as many calculations sheets as you want. Just raise your hand to ask
for extra sheets. The volunteers will bring extra sheets to your table.
6. Write question number clearly at the top of the calculations sheet.
7. Read the entire question group carefully before starting to answer. Each question
has a point value assigned and indicated on the right hand side of the question.
8. Any inappropriate examination behaviour will result in your withdrawal from the
IESO.
7
thInternational Earth Science Olympiad
Student Code:
A1. We list a few facts below about temperatures at the surface of Venus, Earth and Mars.
(a) The yearly mean temperatures of planets do not match with their expected black
body temperature.
(b) Absolute variation in the temperature during the course of one day differs
significantly from one planet to another.
(c) Absolute variation in the temperature during the course of one year at the equator of
the planet differs significantly from one planet to another.
(d) On some planets, there is a large latitudinal percentage variation in temperatures.
(e) Mean temperature (averaged over a day) on Earth is different on different days.
In the table given in your answer sheet, we list a number of physical properties related to a planet
and its various motions, which may or may not be relevant in explaining the facts above. In the
table, tick in appropriate rows those properties which are relevant for each of the facts above.
Number of relevant parameters for each row can be none, one or more than one.
Total 10 points for correct tick-marks.
Warning: Every wrong tick mark has penalty of -0.2 points.
A2. The maximum altitude of the Sun as seen from Mysore on summer solstice day and
winter solstice day are 78
o51' and 54
o17' respectively. Using this information, obtain the
inclination of the Earth's axis (
ε
) and find the latitude of Mysore (
φ
).
(6 points)
A3. The mass ratio of Pluto and Charon is 8:1. The period of revolution of Charon around
Pluto is about 6.387 days. You are given that
M
Pluto= 1.31 x 10
22kg,
R
Pluto= 1195 km,
G = 6.672 x 10
-11N m
2kg
-2the Minimum and maximum distance of Pluto from Earth are 4284.7 x 10
6km and
7528 x 10
6km respectively.
(a) Find the length of the semi-major axis of Charon's orbit of revolution about Pluto.
(3 points)
(b) Find the ratio a:R
Pluto, where 'a' is the distance of the Centre of Mass of the
Pluto-Charon system from the center of Pluto .
(2 points)
(c) Theoretically, what is the minimum diameter of the optical telescope which can
resolve the system from Earth? Ignore effects of Earth's atmosphere.(2 points)
A4. The diagram on the next page shows the Hertzprung-Russell diagram (H-R diagram)
with six positions (A – F) indicated. The y-axis is given in terms of Solar Luminosity
(L
⊙) and x-axis gives effective surface temperature (T) of stars in Kelvin.
(a) Which letters indicate the position of stars that have the largest and the smallest
diameters respectively?
(2 points)
(b) Which letters indicate the stars with the same spectral class but with different
luminosities?
(1 points)
(c) Which letters indicate the stars that are primarily burning Hydrogen? (1.5 points)
(d) Which letter would indicate position of a white dwarf in this diagram? (1 point)
7
thInternational Earth Science Olympiad
Student Code:
7
thInternational Earth Science Olympiad
Student Code:
Theoretical Test
Astronomy Answer Sheet
A1.
Please see next page
A2.
Inclination of the Earth's axis is
Latitude of Mysore is
A3.
Pluto and Charon:
(a) Semi-major axis =
(b) a:R
Pluto=
(c) Diameter =
A4.
H-R diagram
(a) Star of Largest Diameter
Star of Smallest Diameter
(b) Give letters of stars
(c) Give letters of stars
(d) White Dwarf letter
7
thInternational Earth Science Olympiad
Student Code:
Sheet for numerical calculations (write question number clearly)
7
thInternational Earth Science Olympiad
Theoretical Test
Astronomy Model Answers
A1.
Atmosphere of Planets
See table: + 0.5 points for each correct marking, -0.2 for each wrong marking.
A2.
For winter solstice,
a
w= 90 –
φ
–
ε
For summer solstice (in northern tropical region), a
s= 180 – (90 –
φ
+
ε
)
= 90 +
φ
–
ε
Using these, Inclination of the Earth's axis,
ε
= 23
o26'
Latitude of Mysore,
φ
= 12
o17'
(1.5 points for each of the four steps)
A3.
Pluto and charon:
(a) By Kepler's Third Law, a
0 3=
G(M
pl+
M
ch)
T
24 π
2=
9 G M
plT
232 π
2(1.5 points)
Hence a
0=1.96×10
7m
(1.5 points)
(b) The distance of barycentre from Pluto will be a
0/9.
(1 point)
By comparing, a:b =
a
b
=
1.965×10
79×1.195×10
6=1.83
(1 points)
(c) One should try to resolve the Pluto-charon system, when the Pluto is closest to the Earth as
thats when the angular separation will be highest.
(0.5 point)
Let us say we are using optical wavelengths around 550nm (a slightly better approximation
will be to use blue end of visible light around 400 nm)
D=
1.22 λ
θ
=
1.22 λ d
pla
0≈15 cm
(1.5 points)
A4.
H-R diagram
(a) Star of Largest Diameter
B
Star of Smallest Diameter
C
(2 points)
(b)
D
and
F
(1 point)
(c)
A, E
and
F
(1.5 points)
(d)
C
(1 point)
7
thInternational Earth Science Olympiad
Student Code:
Practical Test
Astronomy Questions
Time: 90 Minutes
Maximum Marks: 34
Instructions:
1. Please write your student code on the cover page as well as on the top right of
every page of answer sheet / calculations sheets.
2. Please write your answers legibly. Illegible answers will be counted as incorrect.
3.
Please write your final answers in appropriate boxes in the main answer sheet.
For numerical questions, show the calculations on blank calculation sheets
provided.
4. For numerical questions, you may attempt part of the answer even if you don't
know the final result. There will be stepwise marking.
5. You can get as many calculations sheets as you want. Just raise your hand to ask
for extra sheets. The volunteers will bring extra sheets to your table.
6. Write question number clearly at the top of the calculations sheet.
7. Read the entire question group carefully before starting to answer. Each question
has a point value assigned and indicated on the right hand side of the question.
8. Any inappropriate examination behaviour will result in your withdrawal from the
IESO.
7
thInternational Earth Science Olympiad
Student Code:
1. Construct a Sundial for Mysore (Latitude = +12
o16' N, Longitude = 77
o33'E). You can
ignore corrections due to equation of time.
Materials given: a square plastic board of size of 40 cm x 40 cm, a 1 metre long metal
rod, 2 nut bolts, a 30 cm scale and marker pens to make Sundial markings on the
plasticboard. Use the following procedure.
To make a simple Sundial, you should make the shadow of the rod fall in the equatorial
plane. For this, push the rod through the hole at the centre of the board.
Now put this device on a flat surface such that it rests on a board edge and one end of the
rod. The board should be exactly perpendicular to the rod. For this, fix the nut bolts on
the rod on both the sides of the board. The other end of rod should be pointing towards
the north celestial pole. Write your student code on the plastic board. Show this
arrangement to the examiner.
(1 point)
(a) Measure length of the rod from the end towards the North Celestial Pole to the board
and write on the answer sheet. Mark North facing and South facing sides of the
board with letters N and S respectively.
(3 points)
(b) Mark lines showing the direction of the shadow of the rod on the board for the
winter solstice day. Make markings for every 2 hours.
(4 points)
(c) Mark the similar lines for summer solstice day.
(3 points)
(d) Where do you expect the shadow of the rod will be seen on the equinox days? Write
answer as N (North side) / S (South side) / B (both sides) / X (neither side).(1 point)
2. You are given a sky map which shows sky for 24 hours x 120 degrees. You are also given
a list of all constellations with their IAU designations. Assume that today is the date of
closing ceremony i.e. 19
thSeptember 2013 and you are told that it is a full moon day.
(2 points each)
(a) Mark the Celestial Equator on the map at appropriate place. Denote it with letter 'Q'.
(b) Mark the Ecliptic (apparent path of the Sun over one year) on the map at appropriate
place. Denote it with letter 'E'.
(c) Mark the Sun's position on the map for the noon of given day. Denote it with letter
'S'.
(d) Mark the Moon's position on the map for the noon of given day. Denote it with letter
'M'.
(e) Write the three letter IAU code of the constellation you will observe on the zenith at
the time of Moonrise. Mark the position of the zenith on the map as 'Z'.
(f) Write the three letter IAU code of the constellation you will observe on the nadir at
the time of Moonrise. Mark the position of the nadir on the map as 'N'.
7
thInternational Earth Science Olympiad
Student Code:
3. Picture 1 shows star trails captured by an Astronomy Olympiad student.
(a) Identify constellation(s) in the picture. Write the three letter IAU code of the
constellation(s) in your answer sheet. There are more than one constellations / parts
of constellations visible in the picture. Identify as many as you can. (4 points)
(b) Write the letters from the following table, corresponding to the stars, if they are
present in the picture.
(2 points)
A.
Deneb
B.
Rigel
C.
Spica
D.
Dubhe
E.
Algol
F.
Regulus
G.
Denebola
H.
Mizar
I.
Betelgeuse
(c) Let us assume that stars numbered as 1 and 2 have nearly the same Right Ascension
(R.A.) Find exposure time of the photograph. (4 points)
Picture 1: Photo Credit: Mr. Chiraag Juwekar. Taken on 25/03/2012
7
thInternational Earth Science Olympiad
Student Code:
List of Constellations with IAU Codes
Mysore, India, September 11 – 19, 2013
Practical Test - Astronomy
No. Constellation Code No. Constellation Code No. Constellation Code
1 Andromeda And 31 Cygnus Cyg 60 Orion Ori
2 Antlia Ant 32 Delphinus Del 61 Pavo Pav
3 Apus Aps 33 Dorado Dor 62 Pegasus Peg
4 Aquarius Aqr 34 Draco Dra 63 Perseus Per
5 Aquila Aql 35 Equuleus Equ 64 Phoenix Phe
6 Ara Ara 36 Eridanus Eri 65 Pictor Pic
7 Aries Ari 37 Fornax For 66 Pisces Psc
8 Auriga Aur 38 Gemini Gem 67 Pisces Austrinus PsA
9 Bootes Boo 39 Grus Gru 68 Puppis Pup
10 Caelum Cae 40 Hercules Her 69 Pyxis Pyx
11 Camelopardalis Cam 41 Horologium Hor 70 Reticulum Ret
12 Cancer Cnc 42 Hydra Hya 71 Sagitta Sge
13 Canes Venatici CVn 43 Hydrus Hyi 72 Sagittarius Sgr
14 Canis Major CMa 44 Indus Ind 73 Scorpius Sco
15 Canis Minor CMi 45 Lacerta Lac 74 Sculptor Scl
16 Capricornus Cap 46 Leo Leo 75 Scutum Sct
17 Carina Car 47 Leo Minor LMi 76 Serpens Ser
18 Cassiopeia Cas 48 Lepus Lep 77 Sextans Sex
19 Centaurus Cen 49 Libra Lib 78 Taurus Tau
20 Cepheus Cep 50 Lupus Lup 79 Telescopium Tel
21 Cetus Cet 51 Lynx Lyn 80 Triangulum Tri
22 Chamaleon Cha 52 Lyra Lyr 81 Triangulum Australe TrA
23 Circinus Cir 53 Mensa Men 82 Tucana Tuc
24 Columba Col 54 Microscopium Mic 83 Ursa Major UMa
25 Coma Berenices Com 55 Monoceros Mon 84 Ursa Minor UMi
26 Corona Australis CrA 56 Musca Mus 85 Vela Vel
27 Corona Borealis CrB 57 Norma Nor 86 Virgo Vir
28 Corvus Crv 58 Octans Oct 87 Volans Vol
29 Crater Crt 59 Ophiucus Oph 88 Vulpecula Vul
7
thInternational Earth Science Olympiad
Student Code:
This is colour inverted copy of the central part of the picture in the question paper.
Practical Test
Astronomy Answer Sheet
1. Sundial
(a) Length of the rod =
(d)
2. (e) IAU code =
(f) IAU code =
3. Star Trails
(a) Constellation Names
(b) Star Letters
(c) Exposure time =
7
thInternational Earth Science Olympiad
Student Code:
7
thInternational Earth Science Olympiad
Student Code:
Sheet for numerical calculations (write question number clearly)
7
thInternational Earth Science Olympiad
Practical Test
Astronomy Model Answers
1. Sundial
Length of the rod from end to the board = 8.0 cm (7.5 cm)
2. (e) IAU code – Oph (We will also accept Her - 0.75)
(f) IAU code – Lup (We will also accept Ori - 0.75)
3. Star Trails
(a) UMa (1.5 points), CVn (1 point), Leo, LMi, Dra (0.5 point each)
(b) Star Letters D, H
(c) Exposure time = 30 minutes
Numerical Calculations
Question 1:
(a) As the rod should point to NCP, length of the rod on the ground side should be
x = 20 / tan (
φ
) = 92 cm,
where
φ
is the latitude.
Thus, the length on the other side is 8.0 cm. (may be 7.5 cm, given plastic board is 0.5 cm thick)
(2 points)
Marking N and S
(1 point)
(b) winter solstice markings should be on side marked by S
(1 point)
Marking local noon shadow line
(0.6 points)
Symmetric markings for other lines at 30 degrees
(0.4 points each)
(c) Realising that Summer Solstice markings will be on the other side of the board (1.5 points)
Actual markings for Summer Solstice
(1.5 points)
(d) B
(1 point)
Question 3 (c)
Connecting start and end points for trails of a few stars (at least 3) and drawing their perpendicular
bisectors to find NCP
(1.5 points)
Measuring the angle subtended by these trails at the NCP as 7.5 degrees (6-9 degrees accepted)
(1 point)
Estimating exposure time as 30 minutes
(1.5 point)
7
thInternational Earth Science Olympiad
I
NTERNATIONAL
E
ARTH
S
CIENCE
O
LYMPIAD
IESO 2012 Written TEST ASTRONOMY
Name_____________________________ Nationality __________________________ 1. The duration of spring and summer in the southern hemisphere is 178.7 days, whilst the
duration of autumn and winter is 186.5 days (the opposite is valid for the northern hemisphere). This apparently strange fact is related to: (1.pt)
(A) The magnetic field of the Sun affects the velocity of the Earth when it approaches the perihelion
(B) The fact that the Earth changes its velocity in accordance to Kepler’s Second Law (C) The precession of the Earth
(D) The Earth is in its perihelion in July
2. If you were at the North Pole, Polaris would be ... (1.pt) (A) at your zenith
(B) at your northern horizon (C) below the horizon
(D) It depends on the time of day
3. The magnifying power of a (refracting) telescope can be calculated ...(1.pt) (A) using sophisticated computer simulations
(B) from the focal lengths of the two lenses (C) from the diameters of the two lens (D) from the price of the telescope
4. For similar tidal amplitudes in different geographic locations, the surface of beach covered by the water during each tidal cycle is related to: (1.pt)
(A) The absolute value of low tide above mean sea level (B) The slope of the beach
(C) The influence of local winds on the tide (D) The influence of the local temperature
5. Right ascension is the sky's equivalent to the Earth's ... (1.pt) (A) Latitude
(B) Longitude (C) Altitude (D) Meridian
6. Azimuth is the ___?(1.pt)
(A) angle, measured in degrees, above the nearest horizon (B) horizontal direction (angle) or bearing of an object in the sky (C) point in the sky (on the "celestial sphere") directly overhead
(D) great circle on the celestial sphere that passes through your zenith and also through both celestial poles
7. If your latitude is 30 , what is the most southerly declination of a star to be circumpolar? (2.pt) (A) +90 (B) +60 (C) +30 (D) -30
8. The amount of light that a telescope can collect is limited by the telescope's ...(1.pt) (A) chromatic aberration
(B) focal point (C) aperture (D) eyepiece
9. What is the correct term for the time taken for any object in the Solar System (such as the Moon) to return to the same position relative to the Sun as seen from Earth? (1.pt) (A) year
(B) solar time (C) sidereal period (D) synodic period
10. The color of a star is mainly due to its ...(1.pt) (A) surface temperature
(B) composition (C) distance (D) twinkling
11. A superior planet can be seen to retrograde when it is near ...(1.pt) (A) conjunction
(B) quadrature (C) opposition (D) the Moon
12. When a planet is less than one astronomical unit (AU) from Earth AND shares the same AR as the Sun, that planet must be ...(1.pt)
(A) Venus (B) Mercury
(C) at superior conjunction (D) at inferior conjunction
13. An inferior planet at its greatest eastern elongation is best seen ...(2.pt) (A) around midnight
(B) around noon (C) just after sunset (D) just before sunrise
14. Two optical telescopes A & B are used toobserve the same celestial object. (Assume both have the same transmission rate.)
telescope A B
diameter 25 cm 100 cm
To obtain the same number of photons, what would be the exposure of telescope A to have the same amount of photons obtained by telescope B? (2.pt)
(A) 4 times (B) 8 times (C) 16 times (D) 32 times
15. The star Alpha Centauri is approximately 4.0x1013 km away from Earth. If Alpha Centauri moves closer like the Moon (about 4.0 x105 km away), about how much brighter is Alpha Centauri than before? (2.pt)
(A) 108 times (B) 1012 times (C) 1016 times (D) 1024 times
16. If the Sun set below your western horizon about 6 hours ago, and the Moon is barely visible on the eastern horizon. Which phase of the Moon would this be? (2.pt)
(A) Full Moon (B) First Quarter (C) New Moon (D) Third Quarter
17.If we have our own aircraft and want to fly directly from Albany, Australia (35º1’ South, 117º53’ East) to Olavarria (36º52’South, 60º5’ West), with shortest distance, we will pass through the following region: (2.pt)
(A) Antarctic (B) South Africa (C) Hawaii (D) New Zealand
18.Dating impact craters
From time to time, the planets are struck by bodies coming from the space. The impact of these bodies on Mercury’s surface results in circular structures known as an impact craters. The superimposing relationships between craters provide a useful tool for relative dating of these structures. Please carefully analyze the photo below. Which of the options below is the correct sequence from oldest to youngest? : (2.pt)
(A) A - B - C (B) A - C - B (C) B - A - C (D) B - C - A
A
B
C
IESO 2012 Written TEST ASTRONOMY
Name_____________________________ Nationality __________________________
(1) The full moon was photographed using a telescope equipped with a camera whose field of view was too small, so that only part of the moon is visible. Recalling that the angular diameter of the moon is about 30’, using rulers and/or compass, estimate the field of view of this camera. You must write down the whole process on this paper. (10 pts)
(2) In the image of Jupiter with its moons (taken from Hubble Space Telescope on March 28, 2004), three shadows from the Io, Ganymede, and Callisto are visible, respectively, and two moons are visible in this image, Io in the center and Ganymede at the upper right. However, Callisto is out of the image.
(2-1) Callisto is out of the image. On the image above, draw an arrow pointing to where Callisto would be located. (1 pt)
(2-2) The diameter of Io is 3646 km, and the diameter of Ganymede is 5262 km. What is the scale (km/mm) of this image. (2 pts)
Ganymede
Io Shadow of Ganymede
(2-3). Find the direction of light from Sun to Jupiter
Refer to the image and drawing on the page below. The image, taken from the Hubble Space Telescope is shown on the upper-left side, and the circle on upper-right side is a view from the northern sky of Jupiter, with the circle line representing the equator of Jupiter. The diameter of Jupiter is 143000 km.
(i) Plot a circle, C, inside the equator circle of Jupiter, showing the latitude of the shadow of Io. (2 pts)
(ii) Plot the position of the shadow of Io on circle C. (2 pts) (iii) Draw the line through Io to the Earth. (1 pt)
(iv) The rays of light from the Sun to Jupiter and its moons are almost parallel. The radius of the orbit of Io is about 422000 km. Draw a circle outside the equator circle representing the orbit of Io. (1 pt)
(v) Mark a point representing the location of Io. (1 pt)
(vi) Draw a line from the shadow of Ioto the direction of Sun. (1 pt) (vii) Calculate the distance between Io and its shadow in km? (2 pts)
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ASTRONOMY written test IESO 2011
Name__________________ Country ___________________________
1. Imagine that a new planet, named Pippo, is discovered beyond Pluto. Its revolution period is 320
years. What would be its average distance from the Sun in Astronomical Units (AU), assuming
circular orbit?
_/1 pt.
a. 23.4 AU
b. 30.7 AU
c. 46.8 AU
d. 93.6 AU
2. A person weights 70 kg on Earth, if he goes to the surface of the Moon and Jupiter, he weights:
_/1 pt.
a. more on the Moon and Jupiter than on Earth
b. more on Jupiter and less on the Moon than on Earth
c. more on the Moon and less on Jupiter than on Earth
d. less on the Moon and Jupiter than on Earth
3. Given your passion for Astronomy, your friends have given you a sidereal watch as a present for
your birthday. At 10 a.m. you adjust it with the time of your clock. Following the time given by the
sidereal watch, when arriving at the railway station next day to catch the 8.00 a.m. train, you find
that the train is not there. What do you do?
_/1.5 pt.
a. I wait for the train because it will be there in few minutes
b. I go home because the train has already left few minutes before my arrival
c. I wait for the train because it will be there in some hours
d. I guess the train has been cancelled today.
4. In a science fiction movie, the main character decides to look for his friends’ spaceship, lost on
Mars surface, using an optical telescope placed on the Earth. The resolution of the telescope is 1
arcsec and Mars is at a distance of 60 million km. What is the minimum size of the spacecraft to
allow him to see it?
_/1,5 pt.
a. 2.90 m
b. 290.9 km
c. 290.9 m
d. 2.90 km
5. Looking at the given stellar map, can you estimate the position of the Sun as seen from Sirius,
using the same map?
_/ 2 pt.
a. yes, the Sun is diametrically opposed to Sirius in the constellation of Hercules
b. no, the Sun is not visible from Sirius
c. yes, the Sun is diametrically opposed to Sirius in the constellation of Ursa Minor
d. yes, the Sun is diametrically opposed to Sirius in the constellation of the Octans
6. Assume the diameter of the Moon to be 20% smaller than the reality, what should the average
distance between the Earth and the Moon be, in order to still have total solar eclipses on the Earth?
_/1.5 pt.
a. 20% bigger than the reality
b. 80% smaller than the reality
c. 20% smaller than the reality
d. 80% bigger than the reality
7. The following illustration shows the Hertzsprung–Russell (H-R) diagram for an evolutionary
track of our Sun. The Sun currently locates at position A, but it will to move to position B after 5
billion years. (Assume the Sun is a blackbody and its current radius is 7x10
5km. 1AU=1.5x10
8km.)
(i) When the Sun evolves to B, what is its radius? Calculate it by using the information of the
diagram.
_/1.5 pt.
a) 100 times larger
b) 57.8 times larger
c) 126.4 times larger
d) 157.3 times larger
(ii) Write your process of calculation.
_/1.5 pt.
8. The synodic period of a certain asteroid is 8/7 years. Assume the Earth revolution speed is 30
km/s. Answer with the rounded-off figure below decimal point. In the assumption of circular orbit,
find:
(i) the period of the revolution of the asteroid (year)
_/1 pt.
(ii) the radius of the revolution orbit (AU)
_/1 pt.
(iii) the speed of the asteroid (km/s)
_/1 pt.
TOTAL SCORE: 14.5
IESO 2011 ASTRONOMY PRACTICAL TEST –
STOP 11
NAME:-_______________________________________________________________
COUNTRY:_________________________________________________________
___
On Friday, September 9, 2011, you will perform 3 trials. Each trial is individual, but in some cases you will have to work together with some of the other participants. This is what happens every day in science: you compete and cooperate at the same time with other scientists, to get an higher level of shared knowledge.
ACT I: THE POLE STAR FOR MARS (60 minutes for each group of individual participants)
Materials: Pocket torch light (red), paper, pencil, rubber
Remember that the celestial poles are the projection of the geographic poles onto the sky. At the present time there is a star, visible from Earth with the naked eye, close to the celestial North Pole: for this reason it is called Polaris. But what if you were at the geographic North Pole of Mars?
The celestial North Pole of the red planet is not the same of the Earth. To do the comparison, recall that the stars are so far that the imaginary designs of the constellations remain the same as seen both from the Earth and Mars. So the orientation of Mars' axis is such that its celestial North Pole has Right Ascension 21h 10m 42s and Declination +52.9°. This means that is in the constellation of Cygnus. (i) The most brilliant star of the constellation of Cygnus could be a good choice for the martian North Pole star. Which way the modern terrestrial astronomers indicate it? For the Martian sky watcher, who knows… _/1 pt.
a. 1 Cyg b. A Cyg c. α Cyg d. β Cyg
(ii) Look at the sky projected by the Planetarium on the inner surface of the dome. At the zenith you have the North Pole of the ecliptic. Find Polaris and thus you know the position of the Earth’s celestial North Pole. Please notice the scale on the celestial meridian joining the Earth’s North Pole with the zenith: every step is 10°. There is the same scale also on the quarter of celestial meridian joining Mars’ North Pole with the zenith. What can you say about the axial tilt of the Earth and Mars with respect to the North Pole of the ecliptic? _/3 pt.
a. The axial tilt of Mars is twice the axial tilt of the Earth
b. The two planets have more or less the same axial tilt, but in different directions c. The axial tilt of Mars is one half of the axial tilt of the Earth
d. The two planets have more or less the same axial tilt, but in opposite directions
(iii) Considering all the information you have collected, can you say something about the inclination of the orbital plane of Mars with respect to that of the Earth, called the ecliptic plane? _/3 pt.
a. The orbital plane of Mars has a slight inclination with respect to the Earth’s ecliptic b. The orbital plane of Mars is exactly the same of the Earth and all the other planets in the Solar System
c. The orbital plane of Mars is perpendicular to the Earth’s ecliptic
d. The orbital plane of Mars has an inclination of 45° with respect to to the Earth’s ecliptic
ACT II: I’LL FOLLOW THE SUN (45 minutes for each group of individual participants)
Materials: Pencil, rubber, paper, chronometer, piece of chalk
In the Solar Laboratory in Modena you can look at the image of the Sun projected on a blackboard without risks for your sight (remember: never look directly at the Sun!). When the tracking of the telescope pointed toward the Sun is on, the image is still and you can appreciate, for instance, if there are sunspots. When the tracking is off, the Sun moves until it disappears from the blackboard. Even when not working, the instrument is useful: the magnification of the Sun’s image allow you to measure the time the Sun needs to cover a certain angular distance and thus the angular speed of its apparent daily motion in the sky.
(i) The apparent angular diameter, in degrees, of the Sun as seen from the Earth is about… _/2 pt.
(ii) After taking the measurements in the Solar Laboratory, which is the angular speed for the daily motion of the Sun, in degrees per hour, that you have found? Write your calculation process. _/4 pt.
ACT III: NEVER LOOK DIRECTLY AT THE SUN (45 minutes for each group of individual participants)
Materials: Pencil, rubber, paper, aligned telescope with solar filter
… Unless you use the filters as you have on your telescope for the practical test -- but also in this case it is better not to look through it more than few seconds. This is enough time as to point the telescope, already aligned with the celestial poles, toward to the Sun. So you can find some quite interesting information about the position of our star and the position of the celestial North Pole, even if it’s daytime!
(i) First complete the following scheme, inserting in the squares the cardinal points (N, E already inserted, S, W) and in the rectangles the name of the local coordinates (Altitude, Azimuth): _/2 pt
(ii) Now you can move the telescope, center the Sun and complete the following table:
DATE OF THE OBSERVATION: _____________________ _/0.5 pt.
SUN’S RIGHT ASCENSION: ________________________ _/1.5 pt.
SUN’S DECLINATION: ____________________________ _/1 pt.
CELESTIAL NORTH POLE ALTITUDE: _________________ _/1 pt.
LATITUDE OF MODENA: __________________________ _/1 pt.
ACT II PLAN B: THE STARS LOOK DOWN (45 minutes for each group of individual participants)
Materials: Pencil, rubber
… And you look up all the same! Unluckily, the weather is not fine, but you can see the stars: ok, it is only a drawing on your worksheet, but these are the same constellations and stars that will be above your head tonight in Modena -- and that those nasty clouds probably will not allow you to see
Can you identify the constellation indicated by the numbers?
1 is:_/1 pt. a. Libra b. Virgo c. Scorpius 2 is:_/1 pt. a. Cassiopeia b. Perseus c. Pegasus 3 is:_/1 pt. a. Delphinus b. Aquila c. Lyra 4 is:_/1 pt. a. Ursa Major b. Ursa Minor c. Draco 5 is:_/1 pt. a. Ursa Major b. Ursa Minor c. Draco 5
d. Sagittarius d. Andromeda d. Cygnus d. Boötes d. Boötes
ACT III PLAN B: DISCOVER THE TELESCOPE (45 minutes for each group of individual participants)
Materials: Pencil, rubber, paper, clock, aligned telescope with solar filter, ruler
Unluckily, the weather is not fine and it seems you can not use the telescope… But it has been already aligned by the responsible of the Planetarium in Modena. You can find very quickly and easily some quite interesting information about the telescope itself and the position of the celestial North Pole, even if it’s daytime and clouds do not allow to look at the sky.
(i) First complete the following scheme, in the squares insert the cardinal points (N, E already inserted, S, W) and in the rectangles the name of the local coordinates (Altitude, Azimuth): _/2 pt
(ii) Now complete the following table:
DATE OF THE OBSERVATION: ___________________________________ _/0.5 pt.
CELESTIAL NORTH POLE ALTITUDE: ______________________________ _/1 pt.
LATITUDE OF MODENA: ________________________________________ _/1 pt.
REFLECTOR OR REFRACTOR TELESCOPE? __________________________ _/1 pt.
DIAMETER AND FOCAL LENGTH (mm): ____________________________ _/1.5 pt.
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ASTRONOMY
Students can use the table provided in the last page for solving the problems if necessary. A. Multiple Choice
1. Suppose you see a new planet in the night sky. Based on observations, you find that the planet is close to the Sun, with maximum elongation of 30 degrees. Given that the maximum elongations of Venus and Mercury are 46 and 23 degrees respectively, you can conclude that : a. the orbit of the planet is closer to the Sun than that of Mercury
b. the orbit of the planet is located between those of Mercury and Venus c. the orbit of the planet is located between those of Venus and Earth d. the position of the planet can not be determined from the given data e. all the answers above are incorrect
[1 point]
2. For an astronaut who is standing on the surface of the Moon facing the Earth, which one of the following statements is correct?
a. The Earth will always appear as a full disk
b. The length of one day and one night is equal to the synodic period of the Moon seen by an observer on the Earth
c. The length of the day is half of the sidereal period of the Moon orbiting the Earth
d. The duration between Earth rise and Earth set is the same as the duration between New Moon and Full Moon on the Earth
e. The surface of the Earth facing the Moon is always the same so that only one side of the Earth is visible from the Moon
[1.5 points]
3. How would the length of the solar day change if the direction of the Earth’s rotation is suddenly reversed while maintaining the direction of revolution?
a. It would be 4 minutes longer than before b. It would be 4 minutes shorter than before c. It would be 8 minutes longer than before d. It would be 8 minutes shorter than before
e. It would not change, but remains the same as before [1.5 points]
4. According to stellar evolution theory, the Sun will evolve into the red giant stage in a few billion years. How would the average temperature on the surface of the Earth change compared to the present temperature, in the time when the Sun becomes a red giant with a radius of 1.12×107 km and its temperature drops to 2900 K ? Assume that the current radius of the Sun is 7×105 km, its surface temperature is 5800 K and neglect the possible change of the albedo of the Earth.
a. Becomes four times the present temperature b. Becomes twice the present temperature c. Becomes half the present temperature
d. Becomes a quarter of the present temperature e. No change
[2 points]
5. The parallax of a star measured on the Earth is 0.05 arc-seconds. Determine its parallax if we measure it from Jupiter (heliocentric distance of Jupiter is 5.2 AU).
a. 1.00 arc- seconds b. 0.52 arc- seconds c. 0.33 arc- seconds d. 0.26 arc- seconds e. 0.15 arc- seconds [1.5 points]
6. If the mass of the Sun increases by two times its present value, and the planets remain in their present orbits, then the Earth’s period of revolution will be about:
a. 423 days b. 365 days c. 321 days d. 258 days e. 147 days [1.5 points]
7. If the perihelion of comet Halley is 8.9× 1010 meters and its period is 76 years, then the eccentricity of Halley is:
a. 0.567 b. 0.667 c. 0.767 d. 0.867 e. 0.967 [1.5 points]
8. A particular spectral line of a star is observed at 4999 Å. According to laboratory experiments, this spectral line should appear at 5000 Å. What is the velocity of this star relative to the observer?
a. 60 km/s approaching the observer b. 60 km/s receding the observer c. 75 km/s approaching the observer d. 75 km/s receding the observer
e. The star does not move relative to the observer [1.5 points]
1. Some time ago, there was a rumour that the planet Mars as seen from the Earth would appear as big as the Moon (about 0.5°). The following data are given. The semi-major axis and eccentricity of the Earth are aE = 1 AU and eE = 0.017 respectively and those of Mars are aM =
1.5 AU, eM = 0.093, and the radius of Mars is R = 3393.4 km. Determine the maximum
angular diamater of Mars and justify the rumour (answer with a RIGHT or WRONG). To answer these you have to
a. Draw a sketch of the situation.
b. Show the formula(s) that will be used. c. Show the calculations and the final results. [5 points]
2. On January 15, 2010, there was an annular eclipse, where at maximum 97% of Solar disk was covered by the Moon. At that time the Earth was very close to its perihelion. The following data are given. The semi major axis of the Earth’s orbit is 1.5×108 km, the solar radius is 7×105 km, eccentricity 0.017 and the radius of the Moon is 1.738×103 km. What is the distance of the Moon from the Earth ?
(Show the formula(e), calculations and the final results) [3 points]
Table of constants and units
Constants Symbols Values
Solar luminosity L 3.86 x 10 26 Js-1 = 3.86 x 1026 watt Solar constant F 1.368 x 10 3 Jm-2 Universal gravitational constant G 6.67 x 10-11 Nm2kg-2 Earth’s gravitational acceleration g 9.8 ms-2
Earth mass M⊕ 5.98 x 1024kg Lunar mass M 7.34 x 1022kg Solar mass M 1.99 x 10 30 kg Stefan-Boltzmann constant σ 5.68 x 10-8 Js-1m-2K-4 Astronomical Unit AU 1.496 x 1011 m Moon-Earth average distance D 3.84 x 108 m
Earth radius R⊕ 6.37 x 106 m
Solar radius R
6.96 x 10
8 m
Sidereal year τ 365.256 days = 3.16 x 107 s Solar effective temperature T
5880° K
Light year Ly 9.5 x 1015 m
Parsec pc 3.26 Ly
IESO 2010
Astronomy Practical Test
Yogyakarta, 19-28 September 2010
Plan A; Good weather
Time: 15 minutes
Problem:
Night observation using telescope with eye piece (coordinates
of the
location: South 07
55’.0144, East 110
34’.344). Find and look carefully
Jupiter (RA: 23h 56m 32s; Dec: -02
006’59”) and Galilean satellites
a. Please select a suitable (provided) eye-piece for viewing all
Galilean satellites in one field of view
(20 points)
b. Draw the positions of Jupiter satellites with the proper orientation
on the provided answer sheet. How many satellites of Jupiter are
seen?
(60 points)
c.
Give marking the N-S and E-W directions on your answer sheet
(20 points)
Plan B: Bad weather
Time: 10 menit
Problem:
1. Mark by names or numbers (1, 2 and 3) on the printed sky map, the
positions of the bright stars as listed below (15 minutes)
1. Antares (Alpha Scorpii)
(RA: 16h 29m 24.461s; Dec: -26
025’ 55.209”)
2. Vega (Alpha Lyra)
(RA: 18h 36m 56.336s; Dec: +38
047’ 01.290”)
3. Arcturus (Alpha Bootis)
(RA: 14h 15m 39.672s; Dec: +19
010’ 56.67”)
2. Draw the ecliptic line in the map and identify the position of Mars
(10 for ecliptic and 10 for Mars)
3. Calculate the hour angle of Jupiter (RA: 23h 56m 32s; Dec: -02
006’59”) in
the sky at 8.00 PM local time. (coordinates
of the location : South 07
55’.0144, East 110
34’.344 )
(20)(5 minutes)
4. Point the telescope to the direction of Jupiter (RA: 23h 56m 32s; Dec:
-02
006’59”) and show to the jury (coordinates
of the location : South 07
55’.0144, East 110
34’.344 )
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Astronomy (total of 20 pts)
15. The diameter of the Moon is about a quarter of that of the Earth, and the diameter of the Sun is about 100 times of that of the Earth. The distance from the Earth to the Sun is about 400 times of the distance from the Earth to the Moon. At each astronomical event, which of the following bright shapes will be observed? Choose one suitable item from A to D.
(i) solar eclipse (0.5 pt) Answer: (ii) lunar eclipse (0.5 pt)
Answer:
(iii) In the future, people will be able to watch a solar eclipse on the surface of the moon. Which of A to D patterns would the shape of the Sun be observed on the moon? (0.5 pt)
Answer:
(iv) Under the condition of (iii), what phenomenon is seen then from the Earth? (0.5 pt) (A) Solar eclipse (B) Lunar eclipse (C) Earth eclipse
Answer:
16. At the present time, the energy of the Sun is generated by thermonuclear fusion reactions in the central core. The thermonuclear processes convert four nuclei “X” into a heavier nucleus and also produce energy. What is the nucleus “X”? (1 pt)
(A) Hydrogen (B) Helium (C) Oxygen (D) Carbon (E) Uranium Answer:
17. If the temperature inside the umbra of a sunspot is 1500 K cooler than the solar
photosphere (its temperature ~ 5800 K) outside the sunspot, let B1 be the energy flux out of the umbra and B2 be the energy flux from the area surrounding the sunspot. What will be the ratio, B2/B1? (1 pt)
(A) 0.004 (B) 1.35 (C) 0.74 (D) 3.31 (E) 223 Answer:
18. Circle the leap year(s) in the following list. (0.5 pt) (A) (B) (C) (D)
1890 1972 1998 2000 2002 2100
3rd IESO Written Test
19. There are four celestial objects shown in the following pictures. Arrange the size of objects from the smallest to the largest. Fill your answer in A, B, C and D. (1 pt) ( ) < ( ) < ( ) < ( )
(A) Pleiades Star Cluster (B) Andromeda Galaxy
(C) Sun (D) Saturn
20. Continued from the preceding question, arrange the objects according to their distances from the Earth in the ascending order. Fill your answer in A, B, C and D. (1 pt) ( ) < ( ) < ( ) < ( )
21. If we observe the planets through a telescope on the Earth, which planets’ images will appear to be similar to the lunar phase, . Circle the planets. (1 pt)
Mercury Venus Mars Jupiter Saturn Uranus Neptune
22. The celestial coordinates of Vega are R.A. 18h 36m 56.2s and Dec +38º 47′ 1″. Assume the Sun passes the meridian at noon (12:00:00), on which date will Vega transit the meridian at midnight (00:00:00)? Note that the vernal and autumnal equinoxes in 2009 are March 20 and September 23, respectively. (2 pts) (Show calculation with your answer) Answer:
3rd IESO Written Test
23. The following photo shows the lunar surface of the side facing the Earth. Four surface features are marked and they are Mare Imbrium, Crater Tycho, Crater Copernicus and Montes Apenninus. Apply the cross-cutting principle to estimate the ages of these surface features. Determine the relative age of these features from old to young. (1.5 pts)
(A) Crater Copernicus > Mare Imbrium > Montes Apenninus > Crater Tycho (B) Crater Tycho > Crater Copernicus > Mare Imbrium > Montes Apenninus (C) Mare Imbrium > Montes Apenninus > Crater Copernicus > Crater Tycho (D) Montes Apenninus > Crater Copernicus > Mare Imbrium > Crater Tycho (E) Montes Apenninus > Mare Imbrium > Crater Copernicus > Crater Tycho Answer:
24. Any object as large as a star will collapse under its own weight unless some other force stops it. The Sun has maintained its appearance for a long time. Under what condition is the interior of the Sun in balance? (1 pt)
(A) The interaction of the atoms prevents the gravitational collapse. (B) The repulsive forces between ions prevent the gravitational collapse. (C) The strong forces in nuclei prevent the gravitational collapse. (D) The thermal pressure prevents the gravitational collapse. (E) The magnetic field prevents the gravitational collapse. Answer:
The moon
3rd IESO Written Test
25. The synodic period for outer planets can be determined by the time interval between two successive oppositions. Based on observations, the synodic period of the Mars is about 779.9 days. The Earth’s revolution period is 365.2564 days. What is the revolution period of the Mars in days ? (2 pts) (Show calculation with your answer)
26. Nowadays, astronomers believe that the solar system formed from a cloud of interstellar gas and dust about 4.6 billion years ago. The pictures below show the representative stages in the phases of the formation. Arrange the order of the pictures to demonstrate the formation process. (2 pts)
Figure (a). The Sun became hotter and drifted the gas from the inner region, leaving heavier debris revolving in orbits.
Figure (d). The protosun has begun to shine, with a flattened disk of gas and dust surrounding it.
Figure (b). The planets have been accreting in their orbits.
Figure (e). The protosun formed at the center and the cloud rotated faster.
Figure (c). A cold, slowly rotating cloud
began to contract under its own gravity. Figure (f). The planets were formed and orbit the Sun.
Answer: ( c ) → ( ) → ( ) → ( ) → ( ) → ( f )
3rd IESO Written Test
27. The following diagram gives the predicted positions of the four moons relative to Jupiter. The number 1, 2, 3 and 4 indicate the tracks of Io, Europa, Ganymede and Callisto respectively. The width defined by the two lines marks the visual disk of Jupiter. The E and W give the east and the west as view from the Earth. The ordinate marks the date. Now, we have a photo of Jupiter and its moons taken in 2008 October but the date is unknown. Use the predicted diagram to allocate the four moons and to estimate the date for photography.
Answer: The photo was taken at the night of 2008 Oct. ( ) (1 pt)
The satellites are a: ( ) ; b: ( ) ; c: ( ) ; d: ( ) (1 pt)
3rd IESO Written Test
28. The apparent magnitude of a star is a measure of how bright the star appears to be. This depends on its luminosity and distance. On the other hand, the absolute magnitude of a star is the brightness defined that if the star were 10 parsecs (pc) from the Earth, which is independent of the star’s actual distance. The table presents apparent magnitude and distance of four stars. Calculate their absolute visual magnitude (give the answers in two decimal places, e.g. the format XX.XX) and answer the following questions.
(i) Use the data in the table to find out which star is actually the brightest? (0.5 pt) Answer:
(ii) Among these stars, which star has a luminosity about 100 times brighter than the Sun? (0.5 pt)
Answer: (iii)
Star apparent visual magnitude distance(pc) absolute visual magnitude
A 2.1 29.75
B 0.5 42.94
C 0.8 19.94
D -0.7 95.09
Sun -26.7 ─ 4.83
(Each answer in the table is 0.25 pt)
3rd IESO Written Test
The 3
rdInternational Earth Science Olympiad
Mentor’s Signature:
Practical Test - Astronomy
18 September 2009
Taipei, Taiwan
Student Name: Nationality:
3rd IESO Practical Test
ݦߢ۞ྥΔਚଅլึཛΔᨏॸլึֲΖഩڼृΛ֚چΖ
To seldom speak is the essence of nature. Why the winds and storm do not last whole day? Because the earth that manifests the winds and storm is constantly changing.
π۔ሐᐚᆖρร֥Կີ Laozi Tao Te Chin 4th Century BC
তֱڶଘԳ෫ֳ႓៦Δം֚چࢬאլᏼլະΔଅॸሼᔻհਚΖ༡ਜլۖᚨΔլ ᐞۖኙΔሙᆄढᎅΖ
In the south, there was a man of extraordinary views, named Huang Liao, who asked Shi how it was that the sky did not fall nor the earth sink, and what was the cause of wind, rain, and the thunder's roll and crash. Shi made no attempt to evade the
questions, and answered him without any exercise of thought, talking about all things. π๗ᠧᒧρ֚ՀรԿԼԿ Zhuangzi Tian Xia 4th Century BC.
3rd IESO Practical Test
Instructions for the practical test (Astronomy):
z Please write name and nationality in English on the cover page.
z The time allotted for this examination is 1.5 hours.
z Write your answers legibly. Illegible answers will not be graded.
z Keep your answers short and focus on the key points.
z Write your answers on the white test booklet provided. There is no separate
answer sheet.
z You can use the calculator provided to perform the calculation.
z You may respond to questions either in English, your native language, or a
combination of both.
z Read the entire question group carefully before starting to answer.
Each question has a point value assigned, for example, (1 pt).
z For some questions, you may be asked to provide your answer on the figures.
Please do so carefully.
z Any inappropriate examination behavior will result in your withdrawal from
IESO.
3rd IESO Practical Test
1. The rotation of the Sun
There are sunspots on the solar surface. They can be used to calculate the rate of the solar rotation, based on a sunspot’s motion on the surface. The following figure shows the sunspots during June 30 - July 6, 2006 taken from the SOHO satellite images (listed in the following table). The longitude is marked on the solar disc.
Date Time(h:m) Date Time(h:m)
6/30 17:36 7/04 18:05 7/01 19:02 7/05 17:36 7/02 17:36 7/06 20:12 7/03 17:36
3rd IESO Practical Test
(1) Let’s set June 30, 00:00 to be day 0.000, i.e. Δt = 0.000 for June 30, 00:00. Record Δt in Table 1. (0.6 pts)
(2) Measure the longitude of the sunspot for each date marked, and record in Table 1. (1.2 pts) Table 1
Time Δt(days) Longitude Time Δt(days) Longitude
6/30 17:36 0.733 -42.2° 7/04 18:05
7/01 19:02 7/05 17:36
7/02 17:36 7/06 20:12
7/03 17:36
(3) Using the data in Table 1, plot longitude (in degrees) vs. time (in days) on the graph paper – on the next page. (4.2 pts)
(4) Draw a line of best fit on the graph.
(i) Calculate the slope of the line of best fit (straight line). (2 pts) Answer:
(ii) Calculate the rotation period of the Sun. (2 pts) Answer:
Note: Include the correct unit in both answers.
3rd IESO Practical Test
3rd IESO Practical Test
2. Telescope operations
Go to the telescopes that are already set up and look for the specification of the telescope and two eyepieces.
(1) Complete the following Table. (1.2 pt)
Telescope Eyepieces
Aperture cm Type Focal length Magnification
Focal length mm mm
Focal ratio (f/) mm
** A judge will grade how you operate the telescope. (2) Step-by-step operation (3.8 pts)
(3) Observing the Sun (3 pts)
Warning: You must not look at the Sun through a telescope or a finder
scope without the solar filter! Otherwise it will cause severe
damage to your eyes or permanent blindness.
If it is rainy or cloudy, find any distant building, then adjust the telescope to point to the distant building, and adjust the focus to see it clearly.
(4) Taking a photo of the Sun (2 pts)
When you have finished the above procedure, raise your hand, and the judge will let you return to your seat.
3rd IESO Practical Test
3. Calculating the Earth’s precession
The Earth rotates as a top and Earth’s axis of rotation traces out a cone with an angle shown in Figure 1. That means the Earth’s axis is moving along a circle. This is called precession. The celestial pole rotates about the fixed pole of the ecliptic with a circle of radius about 23.5° and a period of about 25,800 years.
Figure 1
Figure 2 (and a transparent sheet) is the region near Polaris. Figure 3 and Figure 4 are the star tracks around Polaris on the nights of March 10, 1980 and May 20, 2009, respectively.
Figure 2
Star A
Star B
3rd IESO Practical Test
Figure 3 The region of Po laris at March 10, 1980. 3rd IESO Practical Test 9 / 11
Figure 4The region of Polaris at May 20, 2009. (1) Determine the position of the North Celestial Pole and mark it on
(i) March 10, 1980 (Figure 3) (2 pts) (ii) May 20, 2009 (Figure 4) (2pts)
(2) Overlap the transparent sheet (Figure 2) with Figure 3, and mark the position of the
North Celestial Pole determined in Figure 3 on the transparent sheet using a marker pen. (1 pt)
(3) Overlap the transparent sheet (Figure 2) with Figure 4, and mark the position of the
North Celestial Pole determined in Figure 4 on the transparent sheet using a marker
pen. (1 pt)
(4) Measure the interval, Δx, between the positions of the North Celestial Pole in 1980
and 2009 on the transparent sheet.
(i) Δx = ( ) mm (1 pt)
(ii) Use theΔx to calculate the Earth’s precession ( ) mm/year. (1 pt)
[show your calculation]
3rd IESO Practical Test
(5) The angular separation of star A and star B in Figure 2 (or transparent sheet) is 6195″. Use this information to calculate the scale of Figure 2, ( ) arcsec/mm.
(1 pt)
[show your calculation]
(6) Use your results from the previous questions to calculate the Earth’s precession,
( ) arcsec/year. (1 pt) [show your calculation]
3rd IESO Practical Test
I
NTERNATIONAL
E
ARTH
S
CIENCE
O
LYMPIAD
IESO 2008 Written Test 8
15. A recent partial lunar eclipse was observed during the night of August 16th, 2008. The composite images were recorded during the eclipse from Athens, Greece, showing a large part of the umbra (dark part of the earth's shadow). An angular diameter of the lunar image is 31′. You may need a ruler, a compass, and a calculator to answer the questions below. (5 pts in total)
a) Using this picture, calculate an approximate angular diameter of the umbra. Show how you obtained your answer by drawing on the figure above.
(2 pts)
b) Using the sidereal period of the Moon (about 27.5 days) and the distance between the Earth and the Moon (about 380,000 km), calculate the approximate duration time of this lunar eclipse. (3 pts)
