Roland BONINSEGNA
Centre de Dépaysement et de Plein Air de Fleurus-Sivry (B)Abstract
This laboratory exercise uses some ready made slides. The students will have to observe and draw on a screen the different positions of a solar spot along several days. A simple construction on paper will permit to show the movement of the spot on the surface of the Sun and compute the value of the solar rotation. That exercise can be organised in a way that several groups of students are each busy with one different spot, in order to obtain several values, which could be averaged. Other ways of presenting that laboratory is also presented.
I) Introduction
Galileo first discovered the rotation of the Sun in 1611. On his telescope, the surface of our star was smeared by dark spots. At first considered as interfering clouds, Galileo proved that these spots were related to the solar surface itself. Later, they were also used to measure the Sun rotation.
The exercise presented here is a method that was in use as soon as it was possible to photograph our Sun during XIX Th century. It can be adapted using drawings made by projection from a telescope.
II) Examining the slides.
The slides presented here are from J. -P. Rosenstiehl and prepared by the French association CLEA (Comité de Liaison Enseignants et Astronomes) under the designation D7.
First of all, let us examine a set of slides presenting the evolution of the solar features during several days. These documents are all oriented in the same way: north is at the top of the images as if you were looking directly at the Sun at the moment of solar midday.
Can you identify some same spots on the different images? Are they staying at the same place? No! Could you evaluate the movement direction? Be careful to use the same reference frame in that case. The spots seem to move more or less from east to west if we use the terrestrial point of view. But if we look at the Sun as we do with geographical map (view from space), we have to change our reference frame: the spots seem to move from the Westside to the eastside, the same as our planet rotation. The rotation of the Sun and the Earth is both counterclockwise, but they appear to be different if observed solely from the geocentric point of view (See figures 1 and 2). From now on, we shall refer to the direction on the Sun as we do with geographical maps, as seen from space.
Is the spots movement (from west to east) due to the earth revolution around the Sun? No! The earth is moving around the Sun in a direct way (counter clockwise), so the spots would appear to move apparently from east to west. Moreover, our planet moves a little less than one degree per day around its complete orbit, so the westward shift would appear quite trivial even on a week basis. It is clear that the displacements we can see are due to the solar rotation itself.
Are the spots keeping the same shape all along the period of observation? More or less. That will raise a little difficulty in the measurements we are going to do.
The sunspots appear quite dark when compared to the disk of the Sun. They are in fact cooler zones of the photosphere where magnetic phenomena are taking place. The normal photosphere temperature is around 6300 K, whereas that of a sunspot is around 4000 K. The edge of the solar disk seems also darker. See especially the two slides in positive normal light. This limb darkening effect is due to a particular visual consequence: the radiation coming from the edge is much more absorb due to the quantity of solar atmosphere to be crossed to be viewed by the observer. Only the light emitted by higher and, thus, cooler layers reach the observer.
III) Marking the sunspots.
On a sheet of paper (A4 format), draw a circle 15 cm in diameter. Parallel at the bottom of the sheet, draw, breadth wise, several lines spaced by 2 to 5 mm (see figure 3).
Project the first slide onto the prepared sheet of paper in a way that the Sun image must just fit inside the pre-defined circle. Keep also in mind that the global orientation must be the same for each slide: just maintain the inferior border of the image, parallel to the reference lines at the bottom.
Use a slide projector with a normal lens (85-100 mm of focal length) placed around 50 to 100 cm from the prepared sheet of paper. Be careful and verify that the projector is parallel and at the same height as the screen. If the projector is installed on a moving table, it could be easier to move it back and forth, right to links to project the image exactly into the circle. The screen, sheet of paper, can also be maintained on a movable panel, perpendicularly to the projector. A magnetic white board is doing well especially if it is movable. In that way, you can adjust the size and the orientation of the image in moving the projector and/ or the screen or the sheet of paper.
When a perfect alignment is obtained, we can begin our first position measurement of one spot. Mark on the prepared paper, its first position. Use for that, a pencil, a marker, a roller or stick a black dot. Repeat this for each slide where the sunspot remains visible, always respecting image size and orientation. Finally, you will obtain a complete view of the apparent displacement of the sunspot.
You can organise in your classroom several group of students, each devoted to a particular spot. See figure 4 showing two examples of position and identification.
IV) Sunspots and the solar rotation.
First of all, choose in a set of an identified spot, two positions separate by, at least, five to six days. Normally, as seen from Earth, the spots appear to move in straight lines only when our planet crosses the plane of the solar equator. It happens only twice in a year: in early June and December (see figure 7). At these moments, both the Sun poles are situated exactly on the limb. In figure 4 it is clear that the spots paths are not straight lines but ellipse arcs. Nevertheless, we can use the chord between two positions: for example, draw a straight line “a” between spot positions 1 and 9. The line intersects the circle in “A” and “B”. For better determination, use compasses to find the midpoint between “A” and “B”. Trace a line “b” which will join this midpoint and the centre of the circle: the solar rotation axis. You will notice the inclination of that axis compared to our geographical one. What is the value of that inclination? It varies from –26° to +26° in a year (see figure 7). In March 1982, its value was around –25° (or +335°), at the same time, the solar North Pole was invisible for us (see figure 5).
The straight line AB is in fact the projection chord of the sunspot’s path onto the apparent solar disk. Compare the space between spot positions one day apart: see, for instance positions 1, 2 and 4, 5 of set B on figure 4? What have you noticed? Repeat the verification between other spot positions and with two days separation: for example use positions 6, 7 of set A and positions 5, 6 of set B. The spots are passing more rapidly from west to east when they are near the centre of the apparent disk and more slowly when they are near the edges. This is a consequence of the flat vision of a spherical globe. To have an idea of the correct rotation without using trigonometry, we must convert that flat vision into a 3D one, in transforming graphically the straight line AB into a circle (see figure 6).
Draw, on a sheet of squared or graph paper, the line AB breadth wise. On that line, mark the position of the set B spot at the moments 1 and 9. Trace also the centre “D” of the line and use compasses to draw a circle whose diameter is equal to AB. Projects, perpendicularly to AB the points 1 and 9 onto the circle, name these new points “E” and “F” respectively. These points represent the spot position at the moments 1 and 9 on the circular surface of the Sun. The point “D” is the solar North Pole as seen from “above”. Our planet stands far away below this figure. From EDF, measure the angle . This angle shows us the apparent rotation of the Sun as seen from the moving Earth on a 10.08 days interval. The value must be very near of 132°. Compute the synodic rotation by using the equality:
/ t9 –t1 = 360° / S
where S is the synodic period, t1 and t9 are the dates of sunspot position 1 and 9. We obtain:
S = 10.08 x (360/132) = 27.5 days
That value is very near of the adopted synodic value of 27.3 days, which is representative for a 16° latitude. The differential rotation is slower at higher latitude.
The synodic period is the solar rotation period as seen from a moving Earth around the Sun. We must eliminate that movement to compute the sidereal period using that formula:
P = S x E / (S + E)
Where P is the sidereal period, E is the Earth sidereal year (365.26 days). We obtain:
P = 27.5 x 365.26 / (27.5 + 365.26) = 25.6 days
It is better to organise several groups of students, each devoted to one spot. All the values could then be averaged. The slides set D7 from CLEA contains other pictures made in July 1982. You can also choose to use photographs, as the Sky and Telescope Laboratory Exercise LE014 suggests. The measurements are made more difficult due to the weakness of the solar limb. On the contrary, the 1951 pictures where made in late May early June when the sunspots’ path looks almost as a straight line.
You can decide also to record your own observations directly from a scope, using the safe method of projecting the solar image on a prepared sheet of paper (see figure 3). That method is more difficult to carry on, but opens to more discoveries. See the chapter devoted to the solar observation using telescopes elsewhere in this book.
Solar rotation
N
W E
S
horizon
E S W
Earth rotation direction
S
Figure 1: Sun and Earth rotation as seen from the geocentric point of view: the Sun appears to rotate in the opposite direction as the Earth.
Figure 2: Sun and Earth rotation as seen from “above” the solar system plane: the Sun and the Earth rotate in the same direct sense (counter clockwise).
Figure 3: Paper model used for projecting a solar image from a slide or from a telescope
A (top)B (bottom)
Figure 4: Sunspots sets A and B, positions and identifications
Date / Time / A / B13/03/1982 / 11h48 / 1
14/03/1982 / 09h18 / 2 / 1
15/03/1982 / 09h13 / 3 / 2
16/03/1982 / 09h08 / 4 / 3
17/03/1982 / 11h12 / 5 / 4
18/03/1982 / 11h55 / 6 / 5
20/03/1982 / 11h45 / 7 / 6
22/03/1982 / 12h11 / 7
23/03/1982 / 12h08 / 8
24/03/1982 / 11h18 / 9
Figure 5: First steps of the reduction. Choosing the chord between two distant observations of a sunspot. Determining the Sun rotation axis.
1 D 9
A B
F
E
EARTH
Figure 6: Transformation of the apparent linear movement of one spot into a circular movement. In that case, the spot has moved circularly along the surface of the Sun from “E” to “F“, describing the angle . The point “D” represents the North Pole of the Sun, which is seen from “above”. Our planet is situated below.
January 5 /
February 8 /
March 7 /
April 8 /
May 5 /
June 5
July 7 /
August 13 /
September 8 /
October 11 /
November 9 /
December 7
Figure 7: Due to the Earth revolution and axis inclination, the position angle of the Sun’s axis is varying all along the sidereal year. The value of this angle is near zero around Earth perihelion and aphelion. The distance of the Sun’s rotational poles from the limb has been exaggerated: at maximum the shift reaches 7°. We can only see the sunspots’ paths as straight lines in early June and December.
Bibliography.
Rosenstiehl J. -P., CLEA D7 slides set (Taches solaires et rotation du Soleil),
Gingerich O. and Tresch-Fienberg R., 1982, Laboratory Exercises LE014,
Martres M.J.et al., 1987, Astronomie le guide de l’observateur, tome 1,17
Martres M.J.et al., 1994, The observer’s guide to astronomy, volume 1,1, Cambridge Univ. Press
Gray B.J., 2002, Guide 8 software,
For those who prefer to download recent pictures of the Sun I suggest you this site, which offers you access to different observatories presenting their up-to-date pictures: