sunspots! let us introduce ourselves…
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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/index.html?collection_id=13587&media_id=162085261 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=rWYpy1y-leM)• How can we evidence the rotation of Sun?(Reference:http://www.nasa.gov/multimedia/videogallery/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%CE%B5%CE%B9%CE%BF+%CE%9A%CE%B1%CF%81%CE%B4%CE%AF%CF%84%CF%83%CE%B1%CF%82_PRWS_Odysseus_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 datesMeasuring
dates
t: 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 4
157924 Sept-02 Oct
201227 Sept- 2 Oct
20125• 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 26.011633 4.15 4.00 1.40 94.25 26.731634 4.00 3.80 2.55 111.4 25.851486 4.00 3.15 3.05 101.6 28.341575 4.15 1.45 2.30 54.11 26.611579 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:
1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 166020
21
22
23
24
25
26
27
28
29
30
Number of solar sunspot
Ro
tati
on
al P
erio
d (
Day
s)
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:
0 5 10 15 20 25 30 35 40 4525
26
27
28
29
30
f(x) = 0.064 x + 26.5R² = 0.955223880597015
Heliographic latitude
Sun r
ota
tional peri
od
(days)
0 5 10 15 20 25 3023
24
25
26
27
28
29
f(x) = 0.0841425260718 x + 25.010243337196R² = 0.306355111560624
Heliographic latitude
Sun r
ota
tional peri
od (
days)
• 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 53261486 0,163 0,536 3665 49441635 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]