___Lab 001 1 Template-Solar Rotation (1)
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Tyler Junior College *
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1403
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Astronomy
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Dec 6, 2023
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Stellar & Galactic Astronomy Lab 01
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Solar Rotation Copyright 2021, James T. Hooten, All Rights Reserved 01-1 01 The S
un’s
Period of Rotation Purpose The purpose of this laboratory activity is to empirically determine the rotational period of the Sun using solar images from the SOHO spacecraft. This lab is written for both face-to-face and online labs. In some cases, special instructions are included for online students only. For this lab you will utilize the following item(s): Name of Item Item Description Lab 01 Template-Solar Rotation.pdf The file you are currently reading Lab 01 Data File-Solar Rotation.xls Excel file for online submissions Lab 01 Questions-Solar Rotation Online quiz for Follow-Up questions Excel Spreadsheet software Background Information The Sun is the star nearest to Earth. Because of this we know more about the Sun than any other star. Like all rotating bodies, the Sun has a north pole and a south pole, and the Sun rotates about its polar axis. The time required for the Sun to rotate once on its axis is considerably longer than that for Earth. Unlike the Earth, the Sun is not solid and rotates differently at different latitudes. This means the Sun rotates at a different rate near the equator compared to near the poles. This is known as differential rotation (see Figure 01.01).
Stellar & Galactic Astronomy Lab 01
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Solar Rotation 01-2 Copyright 2021, James T. Hooten, All Rights Reserved
Figure 01.01: Differential Rotation on the Sun The Sun displays differential rotation because it is not solid. It is a gigantic ball of mostly hydrogen plasma. Rotation is faster near the equator and slower near the poles. Occasionally, dark spotted regions appear on the “surface” of the Sun. These sunspots are cooler areas of strong magnetic activity in the photospheric layer of the Sun. Sunspots are usually short-lived and are seen to move across the visible face of the Su
n due to the Sun’s rotation. Visually, over the course of several days, an observer can determine the rotational period of the Sun by measuring the changing positions of sunspots. The rotational period is the amount of time required for the Sun to rotate once on its axis. This time will vary by latitude due to differential rotation.
Stellar & Galactic Astronomy Lab 01
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Solar Rotation Copyright 2021, James T. Hooten, All Rights Reserved 01-3 Figure 01.02: Sunspots Visible on the Sun’s Photosphere
Sunspots appear as dark areas on the Sun’s visible surface (photosphere). The dark center of the sunspot is called the umbra. The average temperature of the photosphere is about 10,000°F, while that of the umbra is about 6500°F. The lighter area surrounding the sunspot’s umbra is the penumbra. The Solar and Heliospheric Observatory, known as SOHO, is a satellite that continuously observes the Sun. It was launched on December 2, 1995 and is still an ongoing mission that is a joint project of both the European Space Agency (ESA) and the National Aeronautics and Space Administration (NASA). What’s to Come?
For this lab, you will use SOHO satellite observational images of sunspots to determine the rotational period of the Sun at different latitudes. The images are at the end of this lab.
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Stellar & Galactic Astronomy Lab 01
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Solar Rotation 01-4 Copyright 2021, James T. Hooten, All Rights Reserved
Procedure Part 1: Inspecting the Raw Data Images 1.
Look at the end of this lab and you will find 12 SOHO images of the Sun which you will use for this lab. Inspect each image. Notice that each SOHO image has sunspot groups that are visible. Some of the sunspot groups are marked as A, B, and C. Each image also has a date printed on the upper left. Also, you may notice that not all sunspot groups are visible in all images; for example, group B is missing from the first image. Longitude is marked off on the images as vertical lines. To the left of center the lines of longitude are negative, and to the right they are positive. Part 2: Data Collection 2.
For each SOHO image, record in Data Table 01.01 the longitude position of the three sunspot groups A, B, and C. For example, group A appears at -59° longitude on June 22 and at -45° longitude on June 23. These values are recorded in Data Table 01.01. NOTE: Do not enter the degree sign in the data table. It is understood that the numbers will be in units of degrees. 3.
Repeat the step above for all SOHO images to fill in Data Table 01.01. If necessary, estimate between the longitude lines to the nearest degree. If a sunspot is not visible on a date, then leave that entry blank. Do not write 0 because that is a legitimate value for longitude. Do not write anything in the data table if a sunspot is not visible. NOTE: All data tables are located in the Data Presentation section of this lab and reproduced as tabs in the Excel data file for online students. 4.
After collecting all available longitude data from the SOHO images and recording your findings in Data Table 01.01, continue to the Analysis section.
Stellar & Galactic Astronomy Lab 01
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Solar Rotation Copyright 2021, James T. Hooten, All Rights Reserved 01-5 Data Presentation ONLINE STUDENTS: To get credit for the lab you must submit all entries online in the data file named in the table at the beginning of this lab. You may find it easier to enter your data directly into the data file. Each table is reproduced on a separate tab in the Excel
spreadsheet. Data Table 01.01: Longitudinal Position of Sunspot Groups Date Sunspot Group A (degrees)
Sunspot Group B (degrees)
Sunspot Group C (degrees)
June 22 -59 June 23 -45 June 24 June 25 June 26 June 27 June 28 June 29 June 30 July 1 July 2 July 3
Stellar & Galactic Astronomy Lab 01
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Solar Rotation 01-6 Copyright 2021, James T. Hooten, All Rights Reserved
Data Table 01.02: Longitudinal Rotation Date Interval Sunspot Group A (degrees)
Sunspot Group B (degrees)
Sunspot Group C (degrees)
1 (Jun 22-23) 14 2 (Jun 23-24) 3 (Jun 24-25) 4 (Jun 25-26) 5 (Jun 26-27) 6 (Jun 27-28) 7 (Jun 28-29) 8 (Jun 29-30) 9 (Jun 30-Jul 1) 10 (Jul 1-2) 11 (Jul 2-3)
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Stellar & Galactic Astronomy Lab 01
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Solar Rotation Copyright 2021, James T. Hooten, All Rights Reserved 01-7 Data Table 01.03: Average Longitudinal Rotation Sunspot Group A Sunspot Group B Sunspot Group C Average Longitudinal Rotation (degrees/day) Data Table 01.04: Corrected Average Longitudinal Rotation Sunspot Group A Sunspot Group B Sunspot Group C Corrected Average Longitudinal Rotation (degrees/day) Data Table 01.05: Rotational Period of the Sun Sunspot Group A Sunspot Group B Sunspot Group C Rotational Period in days Data Table 01.06: Average Rotational Period of the Sun Average of Groups A, B, C Average Period in days
Stellar & Galactic Astronomy Lab 01
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Solar Rotation 01-8 Copyright 2021, James T. Hooten, All Rights Reserved
Analysis Although there may be empty entries, by this step you should have completed Data Table 01.01 for sunspot groups A, B, and C for each date. 5.
As a first step of analysis, determine the number of degrees of longitude that sunspot groups A, B, and C moved each day and record your answers in Data Table 01.02. For example, sunspot A moves in longitude from -59° on June 22 to -45° on June 23, which amounts to 14° (negative 45 minus negative 59 equals positive 14) for Date Interval 1 from June 22 to June 23. This number is already recorded in Data Table 01.02. If you had blank entries in Data Table 01.01, then you will also have blank entries in Data Table 01.02. If you don’t have two numbers to subtract, then leave the entry blank. NOTE: When finished all entries in Data Table 01.02 should be positive. If you have negative values, then you probably incorrectly subtracted your values. Always subtract the latter date from the prior date. 6.
After completing Data Table 01.02, determine the average number of degrees of longitude each sunspot group moves. Do this by summing up the entries in each column and dividing by the number of entries you made. Record your averages in Data Table 01.03. 7.
The next step is to adjust the data recorded in Data Table 01.03 for the revolution of the Earth around the Sun. This is necessary because at the same time the Sun is rotating on its axis the Earth is also orbiting (or revolving) about the Sun. The orbital motion of the Earth skews the observational data and causes the numbers recorded to be off by a little bit, but in this case, we can correct the data. It is easy to correct the data because we understand the reason the data are skewed and the source of the error (i.e., the orbital motion of the Earth). To correct the data, all you must do is add one degree to each of the average values in Data Table 01.03. Record the corrected values in Data Table 01.04. NOTE: To help you understand why one degree must be added, consider it takes about 365 days for the Earth to orbit about the Sun. That means that over the course of one day the Earth moves about 1/365-th, or approximately one degree in its orbit. The Sun rotates in the same direction that the Earth orbits. By adding one degree to the values in Data Table 01.03, you are correcting for this approximately one degree per day of orbital motion of the Earth about the Sun.
Stellar & Galactic Astronomy Lab 01
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Solar Rotation Copyright 2021, James T. Hooten, All Rights Reserved 01-9 8.
After completing Data Table 01.04, you are now ready to determine the rotational period of the Sun for each sunspot group. Recall that the rotational period is the amount of time required for the Sun to rotate once (360°) on its axis. The entries in Data Table 01.04 show the number of degrees per day. Your task is to use the values you recorded in Data Table 01.04 to determine how many days it takes the Sun to make one full rotation of 360 degrees. As an example, suppose you determine one sunspot group rotates at a rate of 10 degrees per day. If this is true, then how many days will it take the sunspot group to rotate 360 degrees (one complete rotation)? Think it through, and it should start to make sense. Divide 360 degrees by 10 degrees per day. You will see that it takes the sunspot group 36 days to rotate 360 degrees at a rate of 10 degrees per day. So, for this example, the rotation period of the sun is 36 days. 9.
Perform the calculation in the previous step for each sunspot group and record your answers in Data Table 01.05. If you are still uncertain, you may want to confer with your classmates to see how your answers compare. Conclusion 10.
The values recorded in Data Table 01.05 represent the rotational period of the Sun at the latitudes of the three sunspot groups
. Since the Sun is not solid, odds are the Sun’s rotation is different for each group. This is due to differential rotation. For the purpose of comparison, average the three rotational periods, and record your answer in Data Table 01.06. Your answer is the average rotational period of the Sun based upon your data. 11.
Complete this lab by submitting your data file and answering the Follow-Up questions. ONLINE STUDENTS: To receive credit for this lab, you must upload your completed Excel data file and provide answers to the Follow Up questions through the online quiz named in the table at the beginning of this lab.
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Stellar & Galactic Astronomy Lab 01
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Solar Rotation 01-10 Copyright 2021, James T. Hooten, All Rights Reserved
Follow-Up Complete this lab by answering the following questions. ONLINE STUDENTS: To receive full credit for this lab, your answers to the Follow-Up questions should be entered in the online quiz named in the table at the beginning of this lab. Q01.1.
Using your numbers in Data Table 01.05, what did you get for the rotational period of the Sun for sunspot group A? Q01.2.
Using your numbers in Data Table 01.05, what did you get for the rotational period of the Sun for sunspot group B? Q01.3.
Using your numbers in Data Table 01.05, what did you get for the rotational period of the Sun for sunspot group C? Q01.4.
Should the rotational periods in Data Table 01.05 be the same for all three sunspot groups? Why or why not? Q01.5.
Use your number in Data Table 01.06 for this question. The accepted value for the Sun’s rotation
al period is 27.2753 days. A good way to compare your value of the Sun’s rotational period
to the accepted value is through the use of the percent error equation shown below. Use the percent error equation to express how close your measured average is to the accepted value. ??𝑟???? ?𝑟𝑟?𝑟 =
|𝑦??𝑟 ?𝑎𝑙?? − 𝑎??????? ?𝑎𝑙??|
𝑎??????? ?𝑎𝑙??
× 100
By taking the absolute value of the numerator, the value of percent error is always positive. Express your answer as a percentage (e.g., 1.5%, 21.6%).
Stellar & Galactic Astronomy Lab 01
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Solar Rotation Copyright 2021, James T. Hooten, All Rights Reserved 01-11
Stellar & Galactic Astronomy Lab 01
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Solar Rotation 01-12 Copyright 2021, James T. Hooten, All Rights Reserved
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Stellar & Galactic Astronomy Lab 01
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Solar Rotation Copyright 2021, James T. Hooten, All Rights Reserved 01-13
Stellar & Galactic Astronomy Lab 01
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Solar Rotation 01-14 Copyright 2021, James T. Hooten, All Rights Reserved
Stellar & Galactic Astronomy Lab 01
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Solar Rotation Copyright 2021, James T. Hooten, All Rights Reserved 01-15
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Stellar & Galactic Astronomy Lab 01
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Solar Rotation 01-16 Copyright 2021, James T. Hooten, All Rights Reserved
Stellar & Galactic Astronomy Lab 01
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Solar Rotation Copyright 2021, James T. Hooten, All Rights Reserved 01-17
Stellar & Galactic Astronomy Lab 01
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Solar Rotation 01-18 Copyright 2021, James T. Hooten, All Rights Reserved
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Stellar & Galactic Astronomy Lab 01
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Solar Rotation Copyright 2021, James T. Hooten, All Rights Reserved 01-19
Stellar & Galactic Astronomy Lab 01
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Solar Rotation 01-20 Copyright 2021, James T. Hooten, All Rights Reserved
Stellar & Galactic Astronomy Lab 01
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Solar Rotation Copyright 2021, James T. Hooten, All Rights Reserved 01-21
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Stellar & Galactic Astronomy Lab 01
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Solar Rotation 01-22 Copyright 2021, James T. Hooten, All Rights Reserved
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