Date post: | 05-Jul-2015 |
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Sunspots!
Let us introduce ourselves…
Introductory section and preparatory phase
• Short Description: On Sun’s surface we can see sunspots. What actually
are the sunspots? Why are they black? The spots are moving, as the Sun
revolves around himself. Can we calculate the rotation period of the Sun?
Can we study the topography around the spot? Can we calculate the
temperature of the spot peaks? We will try to answer to all these
questions, by studying images freely provided by the Astronomical
Observatory of Coimbra, the National Schools Observatory and the
Faulkes Telescope Project during last month.
• Keywords: Sun, sunspots, rotation period of sun, sunspots
temperature, sunspots topography, umbra, penumbra.
• Target audience: Students studying Natural Sciences (especially
Physics and Astronomy)
• Age range: 14-18 years old
• Context: Natural Sciences School Lab, Computer School Lab, internet
connection.
• Time required: 6 hours
Introductory section and preparatory phase
• Technical Requirements: Internet connection, appropriate software: Salsa
J, Microsoft Office, Microsoft Windows, Computers, video projector could be
useful.
• Author’s background: Knowledge of Physics: equations of movement, simply
harmonic oscillation and thermodynamics (basics), knowledge of Astronomy
sun, sun physics (basics). Salsa J, image processing
software, internet, software related to Astronomical Observatory of Coimbra, the
National Schools Observatory and the Faulkes Telescope Projects.
• Connection with the curriculum: Strongly related with Astronomy (Second
Class of Greek High School), Physics (First, Second and Third Class of Greek
High School). Partly related with Mathematics (Trigonometry, Second Class of
Greek High School).
• Learning Objectives: Hands on learning, Inquiry based learning, connection
between Universities-Institutes and Schools, use of Open Science
Resources, learn students to cooperate and act as researchers.
• Guidance for preparation: Download images from internet (Astronomical
Observatory of Coimbra, the National Schools Observatory and the Faulkes
Telescope Project), videos about sunspots (e.g. NASA), Sun
Physics, applications for smart phones about Solar activity.
Pre-Experiment / Observation– Teaching Phase 1:
Questions Eliciting Activities – PROVOKE CURIOSITY
Teacher presents the following video from
NASA concerning 3 years activity of Sun:
http://www.nasa.gov/multimedia/videogallery/i
ndex.html?collection_id=13587&media_id=16
2085261 asking them about Sun.
Teacher also presents to students the
following video concerning solar sunspots:
https://www.youtube.com/watch?v=rWYpy1y-
leM asking them about sunspots.
Finally teacher asks from students to find and
collect images of Sun (like those beside) from
the Astronomical Observatory of Coimbra, the
National Schools Observatory and the
Faulkes Telescope Project
Pre-Experiment / Observation– Teaching Phase 1:
Questions Eliciting Activities – DEFINE QUESTIONS FROM
CURRENT KNOWLEDGE
• Does Sun rotates?
(Reference:https://www.youtube.com/watch?v=rW
Ypy1y-leM)
• How can we evidence the rotation of Sun?
(Reference:http://www.nasa.gov/multimedia/video
gallery/index.html?collection_id=13587&media_id=
162085261)
• Sun rotates as a solid sphere or
differentially? *
• Is the speed in the Equator of Sun equal
to the speed at the Poles? *
• Why Sunspots appear to be black?**
• Can we calculate the temperature at the
peaks (umbra) of the sunspots? **
**https://docs.google.com/viewer?url=http://www.odysseus-contest.eu/wp-content/uploads/contest/SUNSPOTS+ENGLISH_en.pdf
*https://docs.google.com/viewer?url=http://www.odysseus-contest.eu/wp-
content/uploads/contest/2%CE%BF+%CE%93%CE%B5%CE%BD%CE%B9%CE%BA%CF%8C+%CE%9B%CF%8D%CE%BA%C
E%B5%CE%B9%CE%BF+%CE%9A%CE%B1%CF%81%CE%B4%CE%AF%CF%84%CF%83%CE%B1%CF%82_PRWS_Odysse
us_el.doc
Pre-Experiment / Observation– Teaching Phase 2: Active
Investigation – PROPOSE PRELIMINARY EXPLANATION OR
HYPOTHESES
• Students must gather and print a
sufficient number of Sun photos.
Then, they asked to mark the
successive positions of sunspot by help
of transparency, as shown in the
picture.
• They observe that the orbits of the
spots are nearly straight lines. Then
they must transform the linear shifts
into bow shifts.
Pre-Experiment / Observation– Teaching Phase 2:
Active Investigation – PLAN AND CONDUCT SIMPLE
INVESTIGATION
• After recording the successive positions
of spots, students plot the entire arc of
the circle (see solar sphere) and find the
midpoint of the arc. Once they identify
the midline of the arc they measure the
distance from the edges. This distance
essentially corresponds to the radius R
of the orbit of the sunspot to the
concrete heliographic altitude.
• They calculate the distances x1 and x2 of
the initial and final position of the spot
from the middle, respectively. The angle
φ shall be given by the relationship:
φ= arcsin(x1/R) + arcsin(x2/R)
with arcsin the inverse sin.
Pre-Experiment / Observation– Teaching Phase 2:
Active Investigation – PLAN AND CONDUCT SIMPLE
INVESTIGATION
• As soon as students determine
the angle φ, the rotation period of
the Sun will be given by the
relationship:
T= Δt*360/φ
where Δt the time period the
sunspot required to be moved
from the initial to the final position
(in days).
Experiment / Observation– Teaching Phase 3:
Creation – GATHER EVIDENCE FROM OBSERVATION
• Students are collecting observation data, such as those in the Table
below:Number of
solar sunspot
Recording dates Measuring datest: number of measuring
days (d)1635 18-26 Dec 2012 20-26 Dec 2012 61633 15-22 Dec 2012 15-22 Dec 2012 71634 15-23 Dec 2012 15-23 Dec 2012 81486 19-27 May 2012 19-27 May 2012 81575 19-29 Sept 2012 22-26 Sept 2012 41579 24 Sept-02 Oct 2012 27 Sept- 2 Oct 2012 5
• Then, they calculate the rotation period based on equations:
φ= arcsin(x1/R) + arcsin(x2/R) and T= Δt*360/φ as shown in Table:
Number of solar sunspot
R: orbital radius (cm)
x1 (cm) x 2 (cm)φ
(degrees )T:
Period (d)
1635 4.00 3.05 2.20 83.05 26.01
1633 4.15 4.00 1.40 94.25 26.73
1634 4.00 3.80 2.55 111.4 25.85
1486 4.00 3.15 3.05 101.6 28.34
1575 4.15 1.45 2.30 54.11 26.61
1579 4.00 2.20 2.30 68.47 26.29
Experiment / Observation– Teaching Phase 4:
Discussion – EXPLANATION BASED ON EVIDENCE
• Students are asked to confirm or revise their initial ideas about
Sun rotation.
• They asked to calculate the heliographic latitude of each solar
sunspot as in follow Table:
Number of solar sunspot Heliographic latitude Rotational Period (1st method) (days)
1635 17,5 26,01
1633 5 26,73
1634 16 25,85
1486 26 28,34
1575 2 26,61
1579 28,5 26,29
• Then, students must try to explain the association between
heliographic latitude and rotational period.
• We help students to examine if the rotational period differences
are due to the differential movement of the Sun.
Experiment / Observation– Teaching Phase 4:
Discussion – CONSIDER OTHER EXPLANATIONS
• Additionally students can
calculate the rotation period of
Sun assuming the spots
performing simple harmonic
oscillation. To make the method
easier to understand it is
illustrated in the figure beside.
• Essentially, we are projecting
the successive positions of
curve motion of sunspots on a
straight line.
Experiment / Observation– Teaching Phase 4:
Discussion – CONSIDER OTHER EXPLANATIONS
• By applying the principles of
simple harmonic oscillation we
have:
x = Asin(ω t + φ)
x/A = sin(ω t + φ)
arcsin(x / A) = ω t + φ
because of ω = 2π / T finally we
have:
arcsin(x / A) = (2π / T)t + φ
Experiment / Observation– Teaching Phase 4:
Discussion – CONSIDER OTHER EXPLANATIONS
arcsin(x / A) = (2π / T)t + φ
• Knowing every time the position x of a sunspot from the middle
of the arc and the radius of the orbit we can design the
following graph arcsin(x)=f(t), as shown in the figure:
Post-Experiment / Observation– Teaching Phase 5:
Reflection – COMMUNICATE EXPLANATION
• Students can now
compare the two
different methods. They
can create Table with
values as beside:
Number of spot
Rotational Period (Days)
1st Method 2nd Method
1635 26.01 25,45
1633 26.73 21,16
1634 25.85 26,08
1486 28.34 29,52
1575 26.61 27,05
1579 26.29 27,02
• Furthermore, students can
plot the rotational periods
in same graph, verifying
similarities and
differences, as shown
beside:20
21
22
23
24
25
26
27
28
29
30
1450 1500 1550 1600 1650
Ro
tati
on
al P
eri
od
(D
ays)
Number of solar sunspot
Post-Experiment / Observation– Teaching Phase 5:
Reflection – COMMUNICATE EXPLANATION
• Students can also
compare the
experimentally
calculated values with
values predicted
theoretically.
• Teachers can provide
students with necessary
information, encouraging
them to create a value
Table as beside:
THEORETICALLY PREDICTED VALUES
Heliographic
latitudeRotational Period (Days)
0 26,710 27,120 27,530 28,340 29,3
EXPERIMENTALLY CALCULATED VALUES
Number of
solar
sunspot
Heliographic
latitude
Average
rotational period
(days)
1635 17,5 25,73
1633 5 23,94
1634 16 25,96
1486 26 28,93
1575 2 26,83
1579 28,5 26,66
Post-Experiment / Observation– Teaching Phase 5:
Reflection – COMMUNICATE EXPLANATION
• Finally, students can plot graphs of the experimentally
calculated and theoretically predicted values, comparing the
equation parameters after linear fit to the plot points, as follow:
y = 0.064x + 26.5R² = 0.955
26
27
28
29
30
0 10 20 30 40 50
Su
n r
ota
tio
na
l p
eri
od
(da
ys)
Heliographic latitude
y = 0.084x + 25.01R² = 0.306
23
24
25
26
27
28
29
0 5 10 15 20 25 30
Su
n r
ota
tio
na
l p
eri
od
(da
ys)
Heliographic latitude
• As follow up activities, students can continue collecting photos
of Sun every day.
• Furthermore, we can additionally suggest the calculation of the
temperature at the peak (umbra) of the sunspots.
• By help of Salsa J, we obtain plot profiles of sunspots, as seen
in the following figures:
Post-Experiment / Observation– Teaching Phase 5:
Reflection – FOLLOW UP ACTIVITIES AND MATERIALS
• According to Stefan-Boltzmann’s law:
(where F the total emitted radiation, σ the Stefan-Boltzmann
constant and the effective temperature) we can calculate the
temperature at the top (umbra) or at penumbra of sunspot, if we
know the photosphere’s temperature.
• Indicative ratio values:
Post-Experiment / Observation– Teaching Phase 5:
Reflection – FOLLOW UP ACTIVITIES AND MATERIALS
Students are asked to determine the temperature of the spots
based on cross-sections profiles, knowing that the photosphere’s
temperature is almost 5800οΚ.
• We encourage students to fill in a Value Table, as follow:
Post-Experiment / Observation– Teaching Phase 5:
Reflection – FOLLOW UP ACTIVITIES AND MATERIALS
Number of
spot
Ratio of radiation
intensity from the
shadow by
photosphere
Ratio of radiation
intensity from the
penumbra by
photosphere
Temperature at
the shadow of the
solar sunspot (oK)
Temperature at
the penumbra of
the solar
sunspot (oK)
1575 0,157 0,686 3635 5258
1635 0,289 0,647 4237 5181
1633 0,192 0,846 3822 5540
1634 0,325 0,722 4361 5326
1486 0,163 0,536 3665 4944
1635 0,183 0,662 3779 5211
1582 0,271 0,681 4168 5247
1484 0,248 0,745 4078 5368
• Calculating thus, the relevant temperatures on umbra and
penumbra of the Solar sunspots.
• After these calculations we ask students why do they think the
spots are black?
Contact Information
• Name Surname: Chiotelis Ioannis
• Affiliation: www.pelopio-lykeio.gr
• Address: Arakinthou 20, 26226, Patras, Greece
• Telephone: +306948372341
• Email: [email protected]