| Solar_System_Dynamics Provides detailed information related to known bodies in orbit around the Sun. Ephemerides, physical parameters, Earth close-approaches, observer tools. |
| Solar_System_Ephemeris Providing ephemeris of a variety of Sun orbiting bodies. |
| The_Solar_System_in_Pictures Quizzes and images about all the bodies of our planetary system. |
| Solar_System_Simulator Online software that generates views of the bodies of our planetary system at any date from any artificial or natural point of observation. |
| Solar_System_Simulator Shows the position of Venus, Earth and Mars at any date from 1900-2100. |
| Stardate_Online__Guide_to_the_Solar_System Contains an outline of the formation and evolution of planets, comets, asteroids, and of their features and exploration. |
| Uranus,_Neptune,_and_Pluto Encyclopedia article about the outermost planets. |
| USGS_Astrogeology_Research_Program Features planetary imagery, research, GIS, mapping, and image processing software. The site provides information about the group and about the Solar System. |
| Virtual_Solar_System Images, facts and quizzes about the nine planets. Also includes a scale model. |
| Welcome_to_the_Planets Select images from NASA's planetary exploration program. |
| Windows_to_the_Universe Aimed at portraying Earth and Space Sciences in a fun way. Includes information about space weather, global space physics and a real time movie of current solar activity. |
| Alina_Simona_Rusu Researcher whose publications include coping strategies in mice, chemical communication in mammals and cognitive ethology. |
| Animal_and_Plant_Sciences Research conducted at University of Sheffield, United Kingdom, that includes evolution and behavior studies. |
| Animal_Behavior Daniel Mills and Gill Sheppard describe an evolutionary approach to the analysis, assessment and treatment of behavior problems. |
| Animal_Behavior_and_Sociobiology Lecture on sociobiological behavior based on experimental animal observation from McMaster University, Canada. |
| Animal_Behavior_Lab Overview of current research at Macquarie University, Australia, with detailed material on each project. |
| Archives_of_Ethology Archives of an unactive internet discussion group on animal behavior that span over an eight year period. |
| Baboon_and_Impala_Together Website discusses the intermingled relationship the two species share. Offers scientific observations and images. |
| Bee_World Uses modern technology to demonstrate the life cycle of bees in real time through the use of a live Internet feed. |
| Behavioral_Ecology_Research_Group Research on the evolution of social systems and social learning at the University of Queensland, Australia. |
| Biopsy Annotated links and other resources on animal behavior, behavioral endocrinology and evolutionary and biological psychology. |
| Bird_Behavior An interdisciplinary journal that publishes research on descriptive and experimental analyses of species-typical avian behavior. |
| Center_for_the_Integrative_Study_of_Animal_Behavior Information from Indiana University's program on animal behavior. |
| Chimpanzee_Cultures A searchable database of chimpanzee cultural behaviors. |
| Dolphin_Institute Dedicated to conservation of and education about dolphins and whales. Research projects include dolphin echolocation. |
| Encyclopedia_of_Psychology_-_Animal_Behavior Annotated links to resources on animal behavior and instincts. |
| Ethology Tables of contents, contacts and subscription information from this journal by Blackwell Publishing. |
| Fauna_Communications_Research Institute that researches bioacoustics and animal communication, especially of endangered species. |
| Feral_Cats Information on a study of feral cats in Portsmouth Naval Dockyard, United Kingdom, conducted by Jane Dards in the 1970s. |
| Honey_Bee_Research_at_the_University_of_Illinois Research in Gene E. Robinson's lab that studies the mechanisms of social behavior in honey bees. |
| Insect_Behavior_and_Chemical_Ecology_Lab Research interests of the University of California, Riverside, including evolution of insect mating signals. |
| Konrad_Lorenz_Institute_for_Ethology Austrian organization that investigates major unsolved problems in behavioral and evolutionary ecology. |
| Movie_Archives_of_Animal_Behavior An online animal behavior video database available in various formats. Most clips filmed in Japan. |
| Ontologies_for_Ethology Peter E. Midford's research in coding animal behavior descriptions, particularly ethograms using ontology. |
| Phenology Animal activity and growth responses to seasonal climatic changes. Discussion of phenology data on animal cycles of life. |
| Research_Station_Petite_Camargue_Alsacienne Affiliated with the University of Basel, Switzerland. Focuses on the behavioral ecology of passerines. |
| Slagsvold_Group A research group at the University of Oslo, Norway. Primary focus is on the study of sexual imprinting in small passerines. |
| University_of_Los_Andes_Frog_Research Group working on frog behavior and ecophysiology at Universidad de Los Andes, Bogota-Colombia. |
| Whiting_Lab Research conducted at Wits University in South Africa that focuses on the behavior and evolutionary ecology of lizards and cichlids. |
| Wolf_and_Wildlife_Studies Discusses ongoing field research concerning the behavioral habits of the Fishtrap wolf pack in northwest Montana. |
4-2-The rotation Equation:
Equation (1)
From
equation 1 and Kepler's laws:
Equation (2)
Where:
T=Sidereal rotation period of the large body (sec)
K=Moment of inertia factor of the large body.
G=Gravitational constant.
M=Large body mass (kg)
Re=
Equatorial radius for the large body (meter)
a=Semimajor axis of the mass center of all satellites that orbit
large body (meter)
m=Total mass of all satellites that orbit the large body (kg)
re =Equatorial
radius of all satellites that orbit large body (meter)
rp =Polar
radius of all satellites that orbit large body (meter)
P=Rotation period of the moons's mass center
that orbit the large body (sec.)
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
*Bsc, 1981
Mechanical engineering, Egypt, Email:
saeles@yahoo.com
4-3-Solar
system data sources.
All
parameters according to NASA fact sheets (Ref.1)
http://nssdc.gsfc.nasa.gov/planetary/factsheet/index.html
4-4-The
equation results:
4-4-1-Determination
of Earth rotation period:
The Earth has one
satellite (the Moon)
K=0.329865
current value =0.3308
M=5.9736E+24 (kg)
Re= 6.3781E+6 (meter)
a=3.844E+8 (meter)
m=7.35E+22 (kg)
re =1738100 (meter)
rp =1736000 (meter)
From the
rotation Equation, the rotation period of Earth=23.93 hr
4-4-2-The
Earth rotation is going to be faster:
The Earth
rotation period is going to be faster as a result of increasing Earth- Moon
distance.
From the
rotation equation, the Earth is fastening it's rotation period by -0.428 milliseconds/century (3.82
cm/year)
A negative
leap second may be inserted every 233 000 year
The lower
the rotation period of the large body, the higher the orbital one of it's
moon.
The
rotation period was equal the orbital one= 54.7 hr at a distance of 73 500
000 meter, it is now 384 400 000
4-4-3-Determination
of Mars rotation period:
K=0.3581
current value =0.366
M=6.4185E+23 (kg)
Re= 3397000 (meter)
There are two
satellites orbit Mars
m= Total mass of
all satellites that orbit the large body Mars (kg)
= m1 (Phobos)+m2 (Deimos) =1.3E+16
a=semimajor axis
of the center of mass of all satellites that orbit Mars (meter)
=(m1 a1
+m2 a2 )/(m1 +m2 )=1.1977E+7 (meter)
re= Equatorial radius of the total
satellites (meter)
re=[(r1)3+(r2)3]^0.3333=[(13400)3+(7500)3)]^0.3333=14128
(meter)
rp= Polar radius of the total
satellites (meter)
rp=[(r1)3+(r2)3]^0.3333=[(9200)3+(5200)3)]^0.3333=9714
(meter)
From the
rotation Equation, the rotation period of Mars=24.62 hr
4-4-4-Mars
rotation is going to be slower:
Mars rotation
period is going to be slower as a result of decreasing the distance of it's
moons' mass center.
From the rotation
equation, Mars is slowing it's
rotation period by 0.67
second/century (1.8 meter/year)
A positive 0.67
leap second may be inserted every 100 year
The lower the
rotation period of the large body, the higher the orbital one of it's moon.
The rotation
period was equal to the orbital one= 20.2 hr at a distance of 17 880 000
meter, it is now 12 000 000
4-4-5-Determination
of Jupiter, Saturn, Uranus, Neptune, Pluto and sun rotation period:
By the same way,
we can calculate their rotation periods from the rotation equation.(table-1)
All moons of small
masses are negligible according to the equation results.
4-5-Conclusion:
1-The slower the
rotation period of the large body, the faster the orbital one of it's moon.
2-The slower the
rotation period of the large body, the smaller the distance of it's moon.
3-The slower the
rotation period of the large body, the higher it's density (D)
4-The slower the
rotation period of the large body, the smaller of it's moon density (d)
5-The slower the
rotation period of the large body, the smaller of it's moment of inertia
factor value (k)
6-Jupiter, Uranus
and Neptune may have the same moment of inertia factor approximately.
7-The moment of
inertia of Pluto is very close to that of Saturn.
5-Acknowledgements
I express my
deep-felt gratitude to Meta Ottevanger, for helping me to compose this page
Thanks to Franz J.
Heeke; (Germany) for his useful
internet web.
Thanks to Jerald
Lee ; (USA) for his useful internet
discussion.
6-Appendix
Title Rotation of sun and
planets
AUTHOR Sami Esmaeil
Keywords Rotation, Sun, Planets, Moment,
Inertia, Leap, Second, Mass, Radius
7-References
1-David R. Williams, 2006.
NASA Planetary fact sheet .
http://nssdc.gsfc.nasa.gov/planetary/factsheet/index.html
2-Franz J.
Heeke, 2007 ,Shaker Effects in Celestial Mechanics
http://www.surf2000.de/user/f-heeke/article1.html
3-Paul
D. Jose, 1965.Sun's Motion and Sunspots. The Astronomical Journal, Vol. 70,
Number 3, April 1965; P. 193-200
9-Tables
and figures
Large body properties
Small body properties
Rotation
Grav.
Equatorial
Moment
Semi.Maj.
Equatorial
Polar
Observed
Calculated
Const.
Mass
Radius
of
inertia
Mass
Axis
Radius
Radius
T
G
M
Re
K
m
a
re
rp
hr
hr
Kg
meter
Kg
meter
meter
meter
Earth
23.9345
23.9344
7E-11
6.0E+24
6.38E+06
0.329864
7.349E+22
3.84E+08
1.74E+06
1.74E+06
Moon
7.35E+22
3.84E+08
1.74E+06
1.74E+06
Mars
24.6230
24.6230
7E-11
6.4E+23
3.40E+06
0.358103
1.30E+16
1.20E+07
1.41E+04
9.72E+03
Phobos
1.06E+16
9.38E+06
1.34E+04
9.20E+03
Deimos
2.40E+15
2.35E+07
7.50E+03
5.20E+03
Jupiter
9.9250
9.9354
7E-11
1.9E+27
71492000
0.257
3.93E+23
1.10E+09
3.47E+06
3.47E+06
Io
8.93E+22
4.22E+08
1.82E+06
1.82E+06
Europa
4.82E+22
6.71E+08
1.56E+06
1.57E+06
Ganymede
1.48E+23
1.07E+09
2.63E+06
2.63E+06
Callisto
1.08E+23
1.88E+09
2.41E+06
2.40E+06
Saturn
10.656
10.6586
7E-11
5.7E+26
60268000
0.189
1.40E+23
1.23E+09
2.63E+06
2.62E+06
Enceladus
1.08E+20
2.38E+08
2.56E+05
2.45E+05
Tethys
6.18E+20
2.95E+08
5.36E+05
5.26E+04
Dione
1.10E+21
3.77E+08
5.60E+05
5.60E+05
Rhea
2.31E+21
5.27E+08
7.64E+05
7.64E+05
Titan
1.35E+23
1.22E+09
2.58E+06
2.58E+06
Iapetus
1.81E+21
3.56E+09
7.18E+05
7.18E+05
Uranus
17.24
17.2380
7E-11
8.7E+25
25559000
0.2562
9.12E+21
4.24E+08
1.10E+06
1.10E+06
Miranda
6.60E+19
1.29E+08
2.40E+05
2.33E+05
Ariel
1.35E+21
1.91E+08
5.81E+05
5.78E+05
Umbriel
1.17E+21
2.66E+08
5.85E+05
5.85E+05
Titania
3.52E+21
4.36E+08
7.89E+05
7.89E+05
Oberon
3.01E+21
5.84E+08
7.61E+05
7.61E+05
Neptune
16.11
16.1088
7E-11
1.0E+26
24764000
0.2719
2.14E+22
3.55E+08
1.35E+06
1.35E+06
Triton
2.14E+22
3.55E+08
1.35E+06
1.35E+06
Pluto
153.282
153.3778
7E-11
1.3E+22
1159000
0.2293
1.62E+21
1.96E+07
5.93E+05
5.93E+05
Charon
1.62E+21
1.96E+07
5.93E+05
5.93E+05
Sun
609.12
609.1094
7E-11
2.0E+30
6.96E+08
0.059447
2.67E+27
1.13E+12
8.51E+07
7.88E+07
Mercury
3.30E+23
5.79E+10
2.44E+06
2.44E+06
Venus
4.87E+24
1.08E+11
6.05E+06
6.05E+06
Earth
5.97E+24
1.50E+11
6.38E+06
6.36E+06
Mars
6.42E+23
2.28E+11
3.40E+06
3.38E+06
Jupiter
1.90E+27
7.79E+11
7.15E+07
6.69E+07
Saturn
5.68E+26
1.43E+12
6.03E+07
5.44E+07
Uranus
8.68E+25
2.87E+12
2.56E+07
2.49E+07
Neptune
1.02E+26
4.50E+12
2.48E+07
2.43E+07
Pluto
1.30E+22
5.91E+12
1.16E+06
1.15E+06
Table (1)
The rotation equation results and solar system parameters.
Download the
full calculations from the Excel sheet
http://www.geocities.com/saeles/Rotation.xls
geovisit();
