Determination of Solar Rotation

Topic – Synodic and Sidereal Time Period of the
Sun using Sun spots
Submitted by :-
Name – Subhajit Pramanick
Exam Roll No. – 20419PHY097
Department of Physics, B.H.U.
Name – Shivani Gupta
Exam Roll No. – 20419PHY088
Department of Physics, B.H.U.

CONTENTS
 About the Sun
 Solar Properties
 What makes the Sun shine?
 Solar Activity
 Solar Cycle
 Sun Spots
 Properties of Sun Spots
 Why do Sun Spots appear in pair?
 Effect of Differential rotation of the Sun
 Butterfly Diagram
 Importance of Sun Spots
 Synodic and Sidereal Period of the Sun
 Video of Sun spots Animation
 Video of Solar Flare Emitted from Sun spots

About the Sun
 The star at the center of the Solar System.
Ordinary star amongst 1011 stars in our
Milky Way Galaxy.
 Nearly perfect sphere of the hot
plasma.
 About 90% are 𝐻+ and 10% are 𝐻𝑒2+ and
< 1% different 50 elements.
 Interior of Sun consists of 3 layers :
(A) Core, (B) Radiative Zone and
(C) Convective Zone.
 Atmosphere of Sun is also divided into 3
layers : (A) Photosphere, (B)
Chromosphere, and (C) Corona.
Capital of Knowledge

Solar Properties
The Moon’s orbit around the Earth would
easily fit within the Sun!
 Radius = 696,000 km
(100 times Earth)
 Mass = 2 x 1030 kg
(300,000 times Earth)
 Average Density = 1410 kg/m3
 Rotation Period =
24.9 days (equator)
36 days (poles)
 Surface temperature = 5780 K
 Age = 4.5× 109 years

What makes the Sun shine?
4 H
He
Nuclear Fusion
The Proton-Proton
Chain:
But where does the Energy come from?
E = m c 2
(c = speed of light)
 c2
is a very large number!
 A little mass equals a lot energy

BHU
Capital of Knowledge Solar Activity
The sun is a magnetic variable star that fluctuates on times scales ranging from a
fraction of a second to billions of years. Sun spots, Solar prominences, solar wind,
Solar flares etc. are all forms of solar activity. All solar activity is driven by the solar
magnetic field.
Solar Prominences Sun Spots
Solar Wind Solar Flares

Solar Cycle
 The Solar activity is measured by the number of Sun spots seen on the solar disc . It is
observed that the number of Sun spots varies periodically and it has a cyclic variation.
 The consecutive 2 maxima & 2 minima have a time period of 11 years. This is known as
Solar Cycle.
 The remarkable property of solar magnetic field is that its polarity is reversed after every
11 years . So, the complete period of magnetic reversal is of 2 cycles is 22 years.

Sun Spots
BHU
 Sunspots are cooler & darker regions seen on Solar disk. It appear darker because of
lower temperature compared to the surrounding solar surface.
 Sunspots often occur in groups; the sun may have 100’s or more at one time.
 Sunspots change their size and shape with time , they may fade out completely. A spot
may last from 1 to 100 days.

Properties of Sun Spots
BHU
 Size: typically 10,000 km: large enough for
the whole earth to be immersed.
 Magnetic Field: 3000 Gauss.
 The inner dark part is called the umbra, and
the outer, lighter part is called the
penumbra.
 In 1919 Hale discovered that the sunspots
always appear in pair having opposite
polarities.
 All the sunspot pairs in the northern
hemisphere have the same polarity. In the
southern hemisphere all the pairs have the
opposite polarity of the northern
hemisphere.

Why do Sun Spots appear in pair ?
BHU
Sunspots &
Magnetic Fields
 Sunspots are almost always in pairs
at the same latitude with each
member having opposite polarity.
 Magnetic field lines are coming out
from the surface of the Sun through
a Sun spot due to magnetic
buoyancy and as the magnetic field
lines are closed line, those lines will
terminate at the other sunspots with
opposite polarity.

Effect of Differential Rotation of the Sun
BHU
 Consider rotation of the sun. It does not rotate like a solid body. Equatorial region rotate
with higher angular velocity than polar regions. It takes 36 days at poles and 27 days at
equator to complete a full rotation. It is called differential rotation of the Sun.
 This differential rotation will stretch the field lines. Thus the rotation produces strong mag.
fields in the toroidal direction. Parts of the toroidal fields may then become buoyant &
produce bipolar magnetic region (i.e., pair of large Sun spots) by piercing through the solar
surface.

Butterfly Diagram
BHU
A graph on which the latitudes of sunspots are plotted against time. It shows how spots
migrate from higher latitudes (30–40° north or south) towards the equator (latitude 5° or so)
throughout each sunspot cycle. The shape of the distributions, when plotted for both
northern and southern hemispheres, resembles the wings of a butterfly.

Importance of Sun Spots
BHU
 The presence of Sun spots is an
explicit proof of solar activity.
 Sun spots play host to solar flares
and hot gassy ejections from the
sun’s corona.
 Many climate scientists agree that
sunspots and solar wind could be
playing a role in climate change. But
the effect is negligible.
 We can determine the Synodic and
Sidereal time period of the Sun by
tracing Sun spots.
coronal mass ejections captured by SOHO
Animation of Solar Flare

Synodic & Sidereal Period of the Sun
BHU
Sidereal Time Period :
In reality earth is also moving
about its own axis as well as
around the Sun which takes
about 365.25 days. That’s why
the time period of the Sun
measured from its own frame,
is called “Sidereal Time
Period”.
Synodic Time Period :
If we observe the Sun from
the earth assuming the earth
to be stationary, then the
measured value of the time
period of rotation of the Sun is
called “Synodic Time Period”.
If 𝑻𝒔 is the Synodic
period, then the
Sidereal period is:
𝜌 =
𝑇𝑠 × 365.25
𝑇𝑠 + 365.25

BHU
Capital of Knowledge Video of Sun spots Animation

BHU
Video of Solar Flare Emitted from Sun spots

CONTENTS
 Learning goals or aim
 Prerequisite
 Sun spots and Solar rotation
 Galileo’s Telescope
 Images of Sun spots
1. From Telescopic Observation
2. From SOHO
3. From GONG
 Tracing paper
 Mathematica Software
 Result and Discussion
 Conclusion

Learning Goals
After this experiment you should be able to:
1. State the direction of rotation of the sun as seen from the
earth.
2. Explain how rate of rotation of the sun can be determined
from observations of sunspots.
3. The Synodic and Sidereal period of rotation of the Sun.
Prerequisite
Before experiment we should have some basic knowledge about:
1. Synodic and sidereal rotation period of sun and relation between
them.
2. Differential rotation of the sun .
3. Sunspots.
4. Mathematica software to plot graph between number of days and latitude .
BHU

Sunspot and solar rotation
Galileo Galilei was one of the first to publish a series of observation of sunspots
that he made with the telescope in 1613.
He observed that the spots were marking on the visible surface of the sun ,and
that they moved as sun rotates.
In the 1860’s ,Richard Christopher Carrington used sunspot to determine that
the period of rotation of the sun depends on latitude.
The rotation period is about 25 days at the equator, 28 days at latitude 40°, and
36 days at latitude 80°. We call this behavior differential rotation.
To determine the solar rotation rate from sunspot you need to time how fast
a spot takes to go once around the sun , or perhaps some fraction of the
distance around the sun.
BHU

2 June To 8July,1613
Galileo’s Telescope
BHU

Images of the sunspots
• We have to capture images of sunspot for at least ten
consecutive days .
• The time interval between two consecutive images should
be constant preferably 24 hours or a day.
Casualties:
• Takes a lot of time.
• Sunspots may not be available at time of observation or
the present one may not survive for 10 days.
• Failed to capture images due to bad weather conditions
Telescopic observation:
BHU

BHU
Capital of Knowledge Our Telescope

Observations in Space
Solar and Heliospheric Observatory:
• The Solar and Heliospheric Observatory (SOHO) was launched on December 2,
1995, to study the sun.
• It began normal operations in May 1996. It is a joint project between the European
Space Agency (ESA) and NASA.
• In addition to its scientific mission, it is a main source of near-real-time solar data
for space weather prediction.
Website:
sohowww.nascom.nasa.gov
BHU

01-11-2021 to 06-11-2021
BHU

Global Oscillations Network Group:
• The Global Oscillation Network Group (GONG) is a worldwide
network of six identical telescopes, designed to have 24/7
observations of the Sun.
• The network serves multiple purposes, including the provision of
operation data for use in space weather prediction, and the study of
solar internal structure and dynamics using helioseismology.
Website:
https://gong.nso.edu
BHU

Tracing Paper
• Next, we take a tracing paper with an image of circle on which latitude
and longitude must present.
• Open image of sun and arrange with proper percentage so that image of
sun and image of circle match easily .
• Trace sunspot from left to right , make a table for no. of days,
latitude and longitude.
BHU

Tracing Paper
Lab Computer:118%
BHU

Mathematica software
This software is used to plot a curve between number of days and longitude.
You can plot curve between number of days and longitude in mathematica by given
format:
Fit [ { { x 1 , y 1} , { x 2 , y 2 }…………...{ x n , y n } }, {1 , x}, x ]
where, x i = day ; y i = longitude ; i =1 to n
Press “shift + enter” , you will find a line:
y = mx + c
Where , the slope of curve, ‘ m’ is angular speed of the sun .
Unit: degree per day
Synodic time period:
T s =
360∘
𝑚
days
To plot this curve in mathematica :
Click on “plot fit” ,given just below your output , you will get a straight line.
Note : mathematica is case sensitive
BHU

• Determination of the daily variation of longitude of
sunspot at fixed time
• We performed above practical for two sunspots from 25 sep 2017 to
05oct 2017 at 9:00 pm.
Result and discussion
BHU

TABLE:-
S. no. Date No. of
days
Longitude (in degree) Latitude (in degree)
Sunspot1 Sunspot 2 Sunspot1 Sunspot 2
1 25/09/2017 1 -75.00 -69.38 13.50 -13.50
2 26/09/2017 2 -57.50 -55.00 11.25 -14.50
3 27/09/2017 3 -53.75 -36.18 09.75 -15.75
4 28/09/2017 4 -41.47 -26.84 09.00 -17.25
5 29/09/2017 5 -29.21 -13.57 07.50 -18.00
6 30/09/2017 6 -16.58 -0.71 06.75 -18.00
7 01/10/2017 7 3.57 12.14 06.00 -18.00
8 02/10/2017 8 9.29 26.05 06.75 -17.25
9 03/10/2017 9 22.10 38.82 06.75 -17.25
10 04/10/2017 10 35.29 52.50 07.50 -16.50
11 05/10/2017 11 47.50 65.63 08.25 -15.00
BHU

Day v/s longitude plot:
SUNSPOT 1: SUNSPOT 2:
BHU

Synodic and sidereal time period of sun
Using formula,
Synodic time period , Ts =
360∘
𝑚
days, m = slope of the plot
Sidereal time period , 𝜌 =
𝑇𝑠×365.25
𝑇𝑠+365.25
days
We got the following results:
Sunspot 1 :
Sunspot 2 :
Synodic period of rotation of sun , Ts = 29.43 days.
Sidereal period of rotation of sun , 𝝆 = 27.24 days.
Synodic period of rotation of sun , Ts = 27.09 days.
Sidereal period of rotation of sun , 𝝆 = 25.22 days.
BHU

Conclusion:
1. Synodic time period of the rotation of sun is longer than
sidereal time period.
2. The average time period of rotation of sun near equator is 25 -27 days
(sidereal).
3. As we move away from the equator time period increases ,
indicating that sun rotate faster at equator and slower at
poles.
BHU

Determination of Solar Rotation

Determination of Solar Rotation

More Related Content

What's hot

Similar to Determination of Solar Rotation

Recently uploaded

Determination of Solar Rotation