Proceeding of the 2011 IEEE International Conference on Space Science and Communication (IconSpace)
12-13 July 2011, Penang, Malaysia
Acceleration due to Gravity Changes during Solar
Eclipse Phases
Mohd. Zambri Zainuddin1, Noorul – Aini Ambak2, Mohd. Sahar Yahya3, Mohd. Hafiz Mohd. Saadon1
1
Physics Departments, Faculty of Science, University of Malaya, 50603, Kuala Lumpur, Malaysia.
2
Sekolah Menengah Kebangsaan Sri Aman (P), Seksyen 14, Petaling jaya, Selangor, Malaysia.
3
Centre for Foundation of Studies in Science, University of Malaya, 50603, Kuala Lumpur, Malaysia.
E-mail: [email protected], [email protected]
Generally, the idea of gravity is whereby every celestial
object should have an influence upon each other. For example,
the Sun attracts the Earth to make the planet stays in its orbit
and so does the Earth to the Moon. These three bodies are
actually causing a great influence on all objects on the surface
of the Earth such as the existence of atmosphere and sea tide.
Abstract—Every celestial bodies including our Earth having their
own gravity field which causing the attractive force towards the
object near them. By assuming that the Earth is symmetrical
sphere, the strength of the gravity field at any point on the
surface of Earth should be proportional to the mass of the planet
and inversely proportional to the square root of two of the
distance from the center of the planet. The strength of
gravitational force can be equalized with the acceleration of any
mass in the influence of gravity and the value on the Earth
surface, denoted as g, is approximated with standard average
value g = 9.8 m/s2. Experiment conducted during two different
solar eclipses, Total Solar Eclipse 2009 and Annular Solar
Eclipse 2010. For 2009 experiment, the increment from preeclipse to the totality is about 18.92%. For the first and second set
of experiment in 2010, showing the percentage increase of gravity
acceleration from pre-eclipse to the annularity is about 7.51%
and 8.59% respectively. This difference in gravity acceleration
may cause chicken egg able to stand during the maximum phase
of eclipses.
Nevertheless, during solar eclipses, the Moon, Earth and
Sun , which having a gravity force of 1.625 m/s2, 9.81 m/s2
and 274.1 m/s2 respectively, is forming a straight line so that
even the shadow of the Moon is falling on the Earth. In order
to study the effect on the line formation of those main bodies
within our solar system, we conducted a simple pendulum
experiment determining the magnitude of acceleration due to
gravity [3].
II.
A pendulum is a simple system with a weight suspended
from a pivot so that the weight can swing freely. When a
pendulum is swinging from its equilibrium position during at
rest, it is actually having a restoring force caused by gravity to
bring it back to the previous position of equilibrium. As the
pendulum is release, the gravity will cause the pendulum to
oscillate surpassing the equilibrium position back and forth. A
period is the time taken for a complete cycle of oscillation that
is moving from left to right and back to left [4] [5].
Keywords-Solar eclipse, Newton’s Gravitational Law, simple
pendulum, oscillation, local gravity
I.
INTRODUCTION
This Gravity is one of the fundamental forces that creating
our universe and affecting movement of every celestial bodies.
From Newton to Einstein, gravity inspired them in interpreting
the mechanism of the movement on every mass in the universe
and its influence on the others.
A crude makeshift pendulum (Fig. 1) consists of a massive
bob with mass less cord suspended from a pivot, which is
acting as point of swinging. The length of the cord and time of
oscillation is measure using a long ruler and stopwatch
respectively.
Starting up with an English mathematician, Sir Isaac
Newton defined a force that causes an apple to fall straight on
his head. Hence, he stated that every point of mass is attracting
another point of mass by a force projected along a straight line
connecting to both points [1]. Then, he put the force
mathematically as in (1) [2].
F~
m1 m2
d2
978-1-4577-0564-9/11/$26.00 ©2011 IEEE
METHODOLOGY AND INSTRUMENTATION
Oscillation period for a simple pendulum is actually
depending on the length of the cord, gravity oscillation and
maximum angle from vertical line, θo, is the amplitude. A
period T for a simple pendulum with small amplitude is
express as
(1)
T ≈ 2π
170
L
g
θo << 1
(2)
Where L is the length of the cord and g is the local
gravitational acceleration.
Therefore, according to the equation, by knowing the value
of L and T, we could determine the gravitational acceleration,
g, if there are any changes on the parameter during solar
eclipse.
⎛T 2
g = 4π 2 ⎜⎜
⎝ L
⎞
⎟⎟
⎠
(3)
Hence, a crude makeshift pendulum had been set a few
hours before the start of the eclipse during Total Solar Eclipse
2009. The string with marking of fixed various length in unit
of centimeter, the pendulum is swung for 20 cycles of
oscillation and the time taken for the completed 20 cycles is
recorded in unit of seconds. In order to gets an average reading,
the reading taken twice. The experiment start before the eclipse
and for every stage of eclipse phases, a set of reading are taken
such as the various length of string, and two set of time for 20
oscillation for various length.
Figure 2. A simple pendulum suspended from a pivot that had been set
during Annular Solar Eclipse 2010 in Maldives.
In order to improve the research outcome of China
experiences, we had prepared two sets of simple pendulum of
laboratory standard (Fig. 2) for the Annular Solar Eclipse
2010.
The experimental results were tabulated and the value of
acceleration due to gravity g is calculated using the formula in
equation 3. Plotting graphs for values of g correspond to each
phase will show the changing pattern within the whole process
of eclipse. Microsoft® Excel software was used for plotting
graphs.
Simple gravity pendulum experiments were done
accordingly to the phases of eclipse during Total Solar Eclipse
2009 in China and Annular Solar Eclipse 2010 in Maldives.
Solar eclipse is dividing into five phases according to the
moon disk in contact with the sun disk as the following:
Phase 1: Before first contact (Before eclipse)
Figure 1. (Right) A crude makeshift pendulum that was uesd during Total
Solar Eclipse 2009 in China. (Left) The weight used.
Phase 2: First contact to second contact
Phase 3: Second contact to third contact (During totality or
annularity)
Phase 4: Third contact to fourth contact
Phase 5: After fourth contact (After eclipse)
171
TABLE I.
Coordinate
Contact I
A CHRONOLOGY ILLUSTRATED PHASES OF TOTAL SOLAR ECLIPSE 2009 IN CHINA
Longitude: 120° 02.900’ E
Latitude: 30° 10.033’ N
Contact II
Maximum
Contact III
Contact IV
Events
China
Time
Sun
Altitude
08:21
09:34
09:36
09:39
10:59
38.8°
54.5°
55.1°
55.6°
72.0°
TABLE II.
Coordinate
Contact I
A CHRONOLOGY ILLUSTRATED PHASES OF ANNULAR SOLAR ECLIPSE 2010 IN MALDIVES
Longitude: 073° 31’ 33.7”E
Latitude: 04° 11’ 43.4” N
Contact II
Maximum
Contact III
Contact IV
Events
Maldivian
Time
Sun
Altitude
10:15:29.3
12:20:28.7
12:25:52.3
12:31:14.3
14:23:20.6
51.2°
64.6°
64.5°
64.4°
49.7°
III.
RESULTS
After the experiments have been analyzed, there are a
pattern that showing the changes in acceleration due to gravity
through the phases. It is indicate in Fig. 3, Fig. 4 and Fig. 5.
Figure 4.
Figure 3.
A plot of local acceleration due to gravity, g (m/s2) by phase at
Total Solar Eclipse 2009, Hangzhou, China.
172
A plot of local acceleration due to gravity, g (m/s2) by phase at
Annular Solar eclipse 2010, Hulhule Island, Maldives.
eggs able to stand on the narrow oval shape on a flat surface as
shown in Fig. 6. The phenomenon had to do with the changes
in magnitude of the acceleration due to gravity. The data
obtained from the experiments exhibit, the change of
acceleration due to gravity of the Earth, g, during solar eclipse.
For total solar eclipse, the percentage of change is higher with
18.92% than during annular eclipse with the average of
8.05%. Table III gives the summary of the experimental result.
The differences are due to the position of the Moon during
total and annular eclipses.
The result confirmed our
hypothesis about acceleration due to gravity changes during
solar eclipses. Furthermore solar eclipses can only happen
during astronomical new moon or conjunction. Therefore it is
possible egg can be making to stand during conjunction or
astronomical new moon. However only during solar eclipses
we can observed the conjunction or astronomical new moon
with naked eye.
Gravity by Phases
10.8
10.71
10.6
2
GRAVITY (m/s )
10.4
10.2
10
9.94
9.86
9.8
9.87
9.82
9.6
9.4
9.2
1
Figure 5.
2
3
4
5
A plot of local acceleration due to gravity, g (m/s2) by phase at
Annular Solar eclipse 2010, Hulhule Island, Maldives.
The experiments that have been done during both Total
Solar Eclipse 2009 and Annular Solar Eclipse 2010, local
acceleration due to gravity has been seen changing in every
phase and taking a shape of a hill with its peak occurred
during totality or annularity.
TABLE III. Results of acceleration due to gravity in Hangzhou, China and
Hulhule Island, Maldives during total and annular solar eclipses.
Place
Experiment results (Fig. 3) during Total Solar Eclipse
2009, the local acceleration due to gravity before first contact
give reading 8.16 m/s2 before the eclipse start. At the first to
second contact, its read 9.97 m/s2. During second to third
contact, the reading gives 12.6 m/s2. At the third to fourth
contact, it read 11.18 m/s2. Finally, after the fourth contact or
after eclipse end it read 9.75 m/s2. The increment from preeclipse to the totality is about 18.92%. The result is based on a
crude makeshift simple pendulum as shown in Fig. 1.
1
Phase 2
Phase
Phase 4
Phase 5
)
(m/s2 )
3/maximum
(m/s2
(m/s2
±0.1
±0.1
(m/s
2
)
±0.1
)
)
±0.1
±0.1
During Annular Solar Eclipse 2010 in Maldives Island, we
had conducted two set of experiments for simple pendulum.
The first set of experiment (Fig. 4) reveals that the local
acceleration due to gravity gives reading at phase 1 is 9.388
m/s2 that are before the eclipse begins. At phase 2, the reading
is 9.570 m/s2. During phase 3, the reading is 10.093 m/s2.
While for phase 4, reading is 9.288 m/s2. Finally, at phase 5
the reading is 9.290 m/s2 that are after the eclipse end. The
percentage increase of acceleration due to gravity from preeclipse to the annularity however is about 7.51%. While the
second set of experiment graph 2b, produced results as 9.862
m/s2, 9.939 m/s2, 10.710 m/s2 , 9.870 m/s2 and 9.817 m/s2
respectively. The changes calculated prior to first contact to
annularity is about 8.59 %. Both results conclusively show
that the magnitude of acceleration due to gravity increases
during solar eclipses particularly annular and totality.
Hangzhou,1
8.12
9.97
12.6
11.18
9.78
Hulhule,2a
9.388
9.570
10.093
9.288
9.290
Hulhule,2b
9.862
9.939
10.710
9.870
9.817
Figure 6. Standing eggs experiments during both solar eclipses.
REFERENCES
[1]
[2]
[3]
IV.
Phase
(m/s2
CONCLUSION
This is the first attempt of measuring acceleration due to
gravity during totality and annularity eclipses. This idea come
about when during the past eclipses in 1998 at Mersing, Johor,
1999 at Volklingen, Germany and 2006 at Antalya, Turkey we
conducted chicken egg standing experiments during the solar
eclipse phases. The chicken eggs able to stand with human
assist during annularity and totality phases. Here the chicken
[4]
[5]
173
Newton, I (1846). Mathematical Principles of Natural Philosophy. 45
Liberty Street, New York.
Hewitt, P. G. (2005) Conceptual Physics. 10th edition. Addison-Wesley,
Massachusetts.
Windows Team. Can an Eclipse Change Gravity? (1999)
http://www.windows.ucar.edu/tour/link=/headline_universe/gravity_ecli
pse.html Accessed on 11 February 2010.
Elizabeth, B. C. (n.d.). Using a Pendulum to Measure Gravity’s
Acceleration. Science Experiments on File Revised Edition, 6.33: 1 - 4
Facts On File Inc., New York.
Yoshida, K., Kawabe, H., and Kawanishi, K. (1996). Stabilizing Control
for a Single Pendulum by Moving the Center of Gravity – An
investigation by numerical Experiment. Proceeding of the 35th
Conference on Decision and Control, Kobe, Japan. pp.1039 – 1040.