Using the Equation of a Line to Determine the
Rotational Rate of the Sun
Project Overview
At what rate does the sun rotate? There are several ways to approximate this.
In this project students will estimate the rotational rate of the sun using real-time
sunspot data and the equation of a line. Students will record the coordinates of a
sunspot over several days and will create a graph based on the time the data
was recorded and the longitude of the sunspot. Students will then determine the
equation of this line and use this to find the rotational rate of the sun.
Sunspots typically last for several days and appear black because they are much
cooler than the surrounding area. It is believed that Galileo was one of the first
people (at least in Europe) to have observed sunspots and made sketches of
them.
This project is best suited for a Beginning Algebra course, an Intermediate
Algebra course, or an appropriate science course that has algebra as a
prerequisite. It is meant to supplement a section on graphing and equations of
lines. Prior knowledge of graphing lines, finding slope of a line, and finding the
equation of a line is necessary.
The documents for this RWLO can be found by navigating the folders in the
frame to the left.
1
Student Learning Objectives
For this RWLO, the student will be able to:




Find the ordered pair for a point.
Create ordered pairs from real-time data and plot these points on a
Rectangular (Cartesian) Coordinate System.
Calculate the slope of a line and the equation of a line.
Determine the rotational rate of the sun using the slope of the equation of
a line.
2
Procedure
Time: Approximately 30 minutes after collection of data. Data will need to be
collected on three separate days.
Materials: Pencil, paper, ruler (straightedge), and computers with internet
access.
Implementation: This RWLO is recommended as a project that is done outside
of class as homework, with a suggested in-class introduction to the project.
However, this project could be done entirely as an in-class project. Students
may discuss their procedures with other students, but it is recommended that
each student goes through each step and does his/her own calculations.
Steps:
1. Print off and show students an example of a SOHO MDI Continuum
Image. Point out a sunspot.
2. Print off a copy of the sun longitude and latitude grid and review latitude
and longitude with students. Students will need to print off a copy of the
sun longitude and latitude grid for themselves or you may provide copies
for them (you may consider giving students a transparency of the sun
longitude and latitude grid).
3. Review a copy of the sunspot data worksheet with students. They will
need to print off a copy of the sunspot data worksheet or you may provide
them with copies.
4. You may want to suggest students follow more than one sunspot in case
the sunspot "disappears" from view.
5. On the sunspot data worksheet, students should fill in the data, graph a
line, and answer the questions.
6. Approximately one week after assigning the project, collect the sunspot
data worksheet along with sun longitude and latitude grid (which should
have some points on it) and three copies (for three days) of SOHO MDI
Continuum Images.
3
Content Material
Student Directions:
1. Find the solar coordinates of a sunspot:
o Print off the latest SOHO MDI Continuum Image. Note the
sunspots on this orange image are black spots or clusters.
o Pick a sunspot that you will follow for a few days (one on the
left side of the image may be best so that it does not spin out
of view before you get a chance to record it two more times).
o Get a copy of the sun longitude and latitude grid from your
instructor or print off the sun longitude and latitude grid. The
origin is labeled. You will need to label the axes. The
horizontal axis is longitude and the vertical axis is latitude
(use 15intervals).
o Place the sun longitude and latitude grid over the SOHO
MDI Image and plot a point where the center of the sunspot
is (you may have to hold the paper up to a light source).
Estimate the coordinates of the sunspot to the nearest
degree (longitude, latitude).
2. Obtain a copy of the sunspot data worksheet or print off a copy. Fill
in the date, time, and longitude information on the sunspot data
worksheet.
3. Repeat this process two more times within the same week. Make
sure you are using the same sunspot each day. It should follow
a horizontal route from left to right. It is recommended that you
print off SOHO MDI Continuum Image at the same time each day.
This way the interval between each day will be whole numbers. If
necessary, round to the nearest 1/4 of a day.
4. Fill in the rest of the table and plot the points that you have
recorded in the table on the graph provided on the sunspot date
worksheet. Draw a line through the points
5. Answer the remaining questions on the second page of the
worksheet.
Referenced URLs:
o
SOHO website: http://sohowww.nascom.nasa.gov
Solar rotation (NASA’s Solar Physics page):
http://science.nasa.gov/ssl/pad/solar/sunturn.htm
4
Assessment
Approximately one week after assigning the project, collect the sunspot data
worksheet along with sun longitude and latitude grid (which should have some
points on it) and three copies (for three days) of SOHO MDI Continuum Images.
The following link will provide you with a possible form of assessment for this
project (point values for each part are in red): assessment of sunspot data
worksheet.
5
Links to Course Competencies
This RWLO could be applied in the following courses: Beginning Algebra,
Intermediate Algebra, Science, and others. Specifically, this RWLO meets the
following course competencies:







Utilize mathematical formulas to solve a real world problem.
Express answers in a written format.
Computer/internet awareness.
Find and sketch the graph of the solution set for linear equations.
Graph points and lines on the rectangular coordinate system.
Find the slope of a line.
Find the equation of a line.
6
Supplementary Resources
Sun Related Websites:




SOHO website
Stanford Solar Center
NASA's Solar Physics Page (solar rotation)
Galileo
Math Related Websites:



Ask Dr. Math
Help with Slope
Help with Equations of Lines
7
Recommendations
Recommendations for Integration:
This problem-solving based RWLO can be used in a beginning algebra course,
an intermediate algebra course, or in a science course that has algebra as a
prerequisite. This project will be used to discover the rotational rate of the sun
and to reinforce the basic algebra skills of finding slope and the equation of a
line. Students will need to be familiar with using ordered pairs to graph a line,
finding slope, and finding the equation of a line.
Back-up:
If the SOHO website (where students get the SOHO MDI Continuum Images) is
unavailable, it is unlikely that it would be down for an entire week. Students
could always check back the next day. They just need three images of the same
sunspot within one week (and they could get by with just two images). However,
just to be safe, print out SOHO MDI Continuum Images for a single sunspot on
three different days (approximately the same time of day) within the same week.
You can access archived images at the Search SOHO Realtime Data site by
choosing MDI Continuum and the dates you would like to look at. If necessary,
students can use copies of these images. If you are unable to access MDI
Continuum Images, students could use other images that are available at the
SOHO website, in particular, MDI Magnetogram images. Also, print out the other
materials students will need: sun longitude and latitude grid and the sunspot
data worksheet. You can provide copies of these materials to students if
needed.
8