ASTR 101 Lab 3
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University of Victoria *
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Course
101
Subject
Astronomy
Date
Jan 9, 2024
Type
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5
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Feburary 16, 2023
ASTR 101 Lab 3 - Solar Rotation
Objective
The objective of this lab is to use the sun’s imperfections, the sunspots, to
estimate the different aspects of the Sun. This includes the solar radius, the distance to
the Sun, the composition, and mass. It’s apparent from the eight pictures of the
Sunspots that the Sun in fact rotates. Since Earth rotates and orbits the sun, it can be
tricky to see if the Sun actually moves or is completely stationary. While it’s possible to
factor in the Earth’s rotation and orbit for calculating the solar period and rotation speed,
for this lab I will assume the Earth is stationary.
Introduction
For many decades, it was believed that the Sun was perfect. It was flawless and
it had no imperfections. However, ancient Chinese astronomers had noticed the
presence of sunspots. At the time, this discovery was unusual because it contradicted
the well-known and accepted theory that the Sun was god-like. This observation was
supported and noted again when Greek philosopher Anaxagoras also saw dark spots
on the Sun back in 467 BC. In the early 17th century, Galileo Galilei invented the
telescope which was a game-changer in the world of observing the celestial heavens.
Notable figures who also documented the phenomenon of the sunspots using the
telescope include Thomas Harriot and Johannes Fabricius. They all contributed greatly
to this observation.
Despite having less powerful equipment and in the Chinese astronomers’ case,
no equipment, all of these astronomers were able to find out so much about the Sun
with great accuracy. The solar rotation, as well as many other aspects of the Sun, can
be measured with this information. It was because of these discoveries that we have a
better understanding of the solar system.
Procedure
The procedure of this lab is fairly simple. The equipment I used was an online
ruler, an online protractor, paper and pictures of the Sun that were taken for eight
consecutive days. First, I traced and sketched a picture of the Sun using my laptop
screen with maximum brightness. In order to represent the Sun’s curved surface, I drew
the line at the equator of the Sun and then a semi-circle. From there, I drew the
sunspots corresponding with all seven pictures representing each day of the second
week of April (April 10 - April 17). Thirdly, I drew a straight line that connected all seven
sunspots I traced a circle around each sunspot. Finally, I used an online protractor to
measure the angles of the sunspots' positions from the Sun's middle line. Figure 1 is the
sketch.
Figure 1: Diagram of Sun with Sunspots
Observations, Tables, and Graphs
Table 1: Angular Displacements of a Sunspot
DATE
ANGLE [deg]
CHANGE IN ANGLE [deg]
SOLAR PERIOD [days]
April 10
47
Start
-
April 11
61
14
25.71
April 12
73
12
30
April 13
84
11
32.73
April 14
96
12
30
April 15
108
12
30
April 16
120
12
30
April 17
133
13
27.69
Average Period & Uncertainty Period
29.45
± 1.16
Calculations
Solar Period
: 360/(Change in angle (delta angle)) x 1 day
Average Period
: (Sum of solar periods) / 7
29.45
Uncertainty Period
: (2nd highest solar period - 2nd lowest solar period) / 2
Mean: 30
2nd Lowest: 27.69
2nd Highest: 30
(30 - 27.69) / 2 = 1.155 =
1.16
Sidereal Period:
(360deg / ( Δ Angle + 1deg)) x 1 day
Average Sidereal Period
: (Sum of sidereal periods) / 7
27.21
Answers
1. Find the size of the sunspots
(1) Find the sun of diagram diameter:
(a) Using an online ruler, the diameter of the diagram’s sun is
14.50cm
(2) Find the sunspot of diagram diameter:
(a) Using the same ruler, the average diameter of the seven sunspots is
0.58cm
(0.60+0.50+0.60+0.70+0.60+0.50+0.60) / 7 =
0.58cm
(3) Find the size of sunspot:
(a) I need to find how much bigger the sun is compared to the sunspot.
(b) (0.58cm / 14.50cm) = 0.04 x 100 =
4.00%
(c) The size of the sunspot is
4.00%
of the sun
(d) Now compare it with the diameter of the actual sun
(e) Size of sunspot: (1392500km x 0.04) =
55,700.00km
2.
Assumptions
For this lab, I assumed that the sunspots are in fixed positions, just as Galileo
assumed. The sunspots on the diagram are also in a fixed position. This is observed by
the fact that the sunspots have a straight line going through them and connecting all of
them. They move in correlation to the Sun’s rotation. There are no jagged lines or
fluctuations between any of the sunspots. Therefore, the positions of the sunspots are
fixed.
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3. Differential Rotation
The sun rotates slower at its north and south poles while it’s faster at the equator.
From the diagram (Figure 1), we can observe that all seven of the Sun spots are very
near to the equator. Because of how close the sunspots are to the equator, the speed of
the rotation is almost 26 days as that is the speed of the Sun's rotation at the equator.
Had the sunspots been anywhere else, it would have affected my calculations. If the
sunspots appeared closer to the poles of the Sun, then the speed of the rotation would
have been perceived to have 30 or more day periods.
4. Ptolemaic/Greek Perfection
The Greeks and Ptolemaic believed that everything in the celestial heavens was
perfect and had no flaws. And that included the Sun which was initially believed to have
no imperfections and was god-like. That mindset was challenged when sunspots were
spotted on the surface of the Sun. This observation contradicted what the Greeks and
Ptolemaics believed in. Astronomy was advanced thanks to this discovery. From it came
the heliocentric model and that everything in the heavens was not orbiting around the
Earth.
5. Correction
(1) Sidereal period = (360deg / ( Δ Angle + 1deg)) x 1 day
(2) Then I took the sum of the sidereal periods using the formula above and divided
it by seven to find the average: 27.2111 =
27.21
.
(3) The original solar period was 29.45 days. If I subtract 27.21 from 29.45, then the
solar period was
2.24
days off.
Discussion
This lab has shown me that people of today can learn a lot from history and old
theories. It was thanks to the contradiction of the Greek and Ptolemaic beliefs that
astronomers found out more aspects of the Sun and the entire solar system. I also
learned that you can study a lot about the celestial heavens from Earth by simply
observing. And while having advanced equipment like a telescope will provide clearer
and more accurate images, you can also look into the sky with enough patients and
observe the same thing. My results could have been better. There were some factors
that might of led to some inaccurate data. For example, I used an online protractor and
ruler. Using an actual ruler and protract would have gotten more accurate results. And
tracing a picture off a laptop screen onto a piece of paper was quite tricky especially
since my artistic skills are below average. Since there were eight pictures, the size of
the image on my laptop for all might not have been the same. For this lab, I assumed
that the Earth is in a fixed position and was not rotating. While the Earth’s rotation has
an effect on how we perceive the solar period, I only took into account that the sunspots
were enough.
Conclusion
Through this lab, I learned to mathematically calculate the change in angles, the
solar periods and the uncertainty period. Although there were some factors and
assumptions that lead to a less accurate result. Factors being that it was assumed that
the Earth was completely stationary and the sunspots only appeared along the equator
of the Sun. While doing the lab, I did some research of my own to better understand
how differential rotation on the Sun works. Before, I didn’t know that the rotation speed
of the Sun is different in different areas of it. I also learned the difference between the
Synodic and Sidereal periods. This lab has expanded my knowledge on the topic.
References
“Solar Rotation Varies by Latitude”, in
Nasa
. [Online]. Available:
https://www.nasa.gov/mission_pages/sunearth/science/solar-rotation.html
[Accessed: January 22, 2013]
“Difference Between Sidereal and Synodic”, in DifferenceBetween. [Online]. Available:
https://www.differencebetween.com/difference-between-sidereal-and-vs-syno
dic/
[Accessed: June 4, 2011]