Astronomy Lab—Rotation Period of the Sun
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Portland Community College *
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PHY 122
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Astronomy
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Dec 6, 2023
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Rod Lee & Bob Ewing | PHY 121: The Solar System Name______________________________ Portland Community College Grade = _______/25 = _______% Lab: Rotation Period of the Sun Purpose
: The purpose of this lab is to determine the rotation period (otherwise known is the “period of rotation”) of the Sun by tracking sunspots and by measuring shifts in spectral lines from the Sun’s surface. Materials
: compass, tracing paper (optional), ruler, protractor (you can download paper versions of rulers and protractors) Background
: In 1611 when Galileo first looked at the Sun with his new telescope, he saw spots on the surface of the Sun. He watched these spots change and made drawings of them over time. He was able to determine that they were indeed on the Sun and not blemishes on the telescope lenses or clouds in between Earth and the Sun. From these observations, he determined the period of rotation of the Sun. Part I: Tracking Sunspots You have been given a set of drawings made from sunspot photos in August and December 1999 (Figure 1 & Figure 2 at the end of this lab). Because the surface of the Sun is spherical, the change in position of sunspots near the edges of the Sun are actually further apart than they appear near the Sun’s equator. It's sort of like looking at the edges of Earth’s globe to measure the size of Antarctica: the continent is bigger than it appears because of that extra dimension popping out of and into the page. Analyzing sunspots near the edges works the same way. In order to reconcile this visual phenomenon, we visualize a line extending from each sunspot parallel to the axis of the star's rotation (demonstrated with a dotted line in Figure 1) to the edge of the circle (edge of the Sun) from our point of view. 1) Using Figure 1, draw parallel lines from the dots to the edge of the circle. Each dot represents one day of data. Sunspots move along this curved surface, not in a straight line! Measure the angle through which the sunspot moved during this time by placing your protractor at the center of the Sun’s circle and measuring the angle difference (in degrees) from the beginning position of the sunspot to the final position of the sunspot along the curved surface of the Sun. Use the formula below the table to determine the rotation period of the Sun (in days). Only fill in column 2 in Table 1. (Drawing = 4 points) 2) For Figure 2, you will need pick a sunspot (there are several on each drawing, but they are the same set) and follow it from drawing to drawing in a similar manner. Suggestion: Draw a vertical line from the sunspot to the edge of the disk in each drawing and follow the directions for Figure 1 above. Fill in column 3 in Table 1. (Drawing = 2 points) Table 1 (4 points)
August 1999 December 1999 Angle Covered by Sunspot (degrees) Days in the Sequence (days) Rotation Period of the Sun (1) % Error ௦௨ௗି௧ௗ
௧ௗ
ݔ
100
(2)
Rod Lee & Bob Ewing | (1)
௧௨
௪
௦௨௦௧
௩ௗ
௨
ௗ௬௦
௧
௦௨
=
ଷ
ௗ௦
௧௧
ௗ
(
ௗ௬௦
)
(2) Find the accepted
value online Now average your answers (rotation periods) from the two values in the table: __________days (1 point) Part II: Measuring the Rotation of the Sun from its Spectra The Doppler Effect is the apparent change in light color due to a light source (such as our sun) moving toward or away from you. This is demonstrated by the horizontal shifting of spectral lines, like in Figure 3. The black lines are iron absorption lines. You will use the shift in the spectral lines between the top and bottom images as well as the Doppler Effect to determine the rotation period of the Sun. 1) Measure the distance (in millimeters) from each of the numbered lines in the upper spectrum to
some arbitrary reference point (e.g. the edge of the picture). Record this value, in millimeters, in the space provided in Table 2. 2) Measured the distance (in millimeters) between each of the numbered lines in the lower spectrum and the same reference point used above and record the values in Table 2. 3) Compute the difference in position -- the total shift -- between the spectra for each numbered line and record the values in Table 2. 4) Take the average of the 4 differences. Divide this result by 2. This is the Doppler shift, in millimeters. Record all values in Table 3. Note: The linear position of each line on the spectrum is linearly proportional to the light’s wavelength, so finding the difference in position of the spectral lines is like finding the shift in wavelength of light (aka color). 5) We will calculate the Doppler shift in angstroms by computing the scale of the spectra. a. In the upper or lower spectrum, measure the distance between the lines marked 6290.971Å and 6302.502Å. b. Divide 11.531Å (the difference in wavelength of those two lines) by the distance you measured. This is the scale of the spectrum. Record this scale in Table 3. 6) Multiply the scaling factor you just calculated by the Doppler shift in millimeters. This will give you the Doppler shift in angstroms. Record your value in Table 3. Table 2 (4 points)
Fraunhofer Line Position Upper (mm) Position Lower (mm) Shift (mm) 6290.971 6297.801 6301.509 6302.502
Rod Lee & Bob Ewing | Table 3
(4 points)
Average shift Doppler shift (in mm) = [Average Shift] / 2 Spectrum scale Doppler shift (in Å)
7) The formula for calculating velocity from the shift in wavelength of radiation from a moving source is:
ݒ
ܿ
=
߂ߣ
ߣ
where ǻȜ
is the Doppler shift (in Å), Ȝ
o is the wavelength as measured from a stationary source, and c is the speed of light. We will take the speed of light c to be 3 x 10
8 m/s and the average wavelength (the approximate center of the spectra) Ȝ
o to be 6300 Å. The formula for the tangential speed (the speed at the outmost portion of a rotating circle) of a rotating body is ݒ
=
2
ߨܴ
ܶ
Setting these two formulae equal to each other and solving for the period of rotation T yields the equation: ܶ
=
2
ߨܴߣ
ܿ ή οߣ
where R
= radius of the circle at 15
q
latitude from the sun
’
s equator =
6.723 x 10
8 m. 8) This will give us the period of rotation of the sun in seconds. To convert to days, we divide this result by 86,400 seconds/day. Æ
One rotation of the Sun __________seconds Æ
__________days (2 points)
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Rod Lee & Bob Ewing | General Questions
(1 point each (#3 has two parts) = 4 points)
1) How does this value for the rotation of the Sun you just calculated compare to the value you obtained in Part I? Calculate a percent difference. % ܦ݂݂݅݁ݎ݁݊ܿ݁
=
#
ିௌ
#
#
ݔ
100
2) What factors might cause the answers from the sunspot method (Part I) and the spectra method (Part II) to be different? Hint: consider the differential rotation of the Sun. 3) The Sun actually takes about 25 days to rotate once at the equator and 30 days near the poles. We will assume an average of 28 days for this question. How close did you come to this value in Part I and Part II? % Difference (Part I) = ௧
ூ
௩ିଶ଼
ௗ௬௦
ଶ଼
ௗ௬௦
ݔ
100
= _______________________________ % Difference (Part II) = ௧
ூூ
௩ିଶ଼
ௗ௬௦
ଶ଼
ௗ௬௦
ݔ
100
= ______________________________
Rod Lee & Bob Ewing | Figure 1 Sunspots (APOD) August 8-16, 1999 (upper half of the Sun represents 8 days; the bottom half represents 6 days)
Rod Lee & Bob Ewing | Figure 2
Sunspots at Noon from December 13, 1999 to December 17, 1999
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Rod Lee & Bob Ewing | Figure 3
Spectra for Measuring the Sidereal Period of the Sun’s Rotation