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| The '''tug of war''' in astronomy is the ratio of planetary and solar attractions on a [[natural satellite]]. The term was coined by [[Isaac Asimov]] in ''The Magazine of Fantasy and Science Fiction'' in 1963. <ref name="Asimov"> Isaac Asimov: ''Asimov on Astronomy'' Coronet Books,1976, ISBN 0-340-20015-4 pp125-139</ref>
| | My name is Louisa (27 years old) and my hobbies are Inline Skating and Bonsai.<br><br>Feel free to surf to my site [http://tinyurl.com/pkup9lo http://tinyurl.com/pkup9lo] |
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| == Law of universal gravitation ==
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| According to [[Isaac Newton]]'s [[law of universal gravitation]]
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| :<math> F= G\cdot \frac{m_1 \cdot m_2} {d^2}</math>
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| In this equation
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| :'''F''' is the force of attraction
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| :'''G''' is the [[gravitational constant]]
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| :'''m<sub>1</sub>''' and '''m<sub>2</sub>''' are the masses of two bodies
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| :'''d''' is the distance of separation between the two bodies
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| The two main attraction forces on a satellite are the attraction of the [[sun]] and the [[primary (astronomy)|primary]] (the planet around which the satellite revolves) Thus the two forces are
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| :<math> F_p= \frac{G \cdot m \cdot M_p} {d_p^2}</math>
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| :<math> F_s= \frac{G \cdot m \cdot M_s} {d_s^2}</math>
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| where the subscripts p and s represent the primary and the sun respectively.
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| The ratio of the two is
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| :<math> \frac{F_p}{F_s} = \frac{M_p \cdot d_s^2}{M_s \cdot d_p^2} </math>
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| == Example ==
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| [[Callisto (moon)|Callisto]] is a satellite of Jupiter. The parameters in the equation are <ref>Thomas Arny: ''Explorations'', Mc Graw Hill, ISBN 0-07-561112-0 pp.543-545 </ref> | |
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| *Callisto-Jupiter distance (d<sub>p</sub>) is 1.883 · 10<sup>6</sup> km.
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| *Mass of Jupiter (M<sub>p</sub>) is 1.9 · 10<sup>27</sup> kg
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| *Jupiter-Sun distance (ie, mean distance of Callisto from the Sun, m<sub>s</sub>) is 778.3 · 10<sup>6</sup> km.
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| *The solar mass (M<sub>s</sub>) is 1.989 · 10<sup>30</sup> kg
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| :<math> \frac{F_p}{F_s} = \frac{1.9 \cdot 10^{27} \cdot (778.3)^2}{1.989 \cdot 10^{30} \cdot(1.883)^2} \approx 163 </math>
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| == The table of planets ==
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| Asimov lists tug of war ratio for 32 satellites (then known in 1963) of Solar system. The list below shows one example from each planet.
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| {| class="sortable wikitable"
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| !Primary
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| !Satellite
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| !Tug of War ratio
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| |-
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| |[[Neptune]]||[[Triton (moon)|Triton]]||8400
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| |-
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| |[[Uranus]]||[[Titania (moon)|Titania]]||1750
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| |-
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| |[[Saturn]]||[[Titan (moon)|Titan]]||380
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| |-
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| |[[Jupiter]]||[[Ganymede (moon)|Ganymede]]||490
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| |-
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| |[[Mars]]||[[Phobos (moon)|Phobos]]||195
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| |-
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| |[[Earth]]||[[Moon]]||0.46
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| |}
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| == The special case of the Moon ==
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| Unlike other satellites of the solar system solar attraction on the Moon is more than that of its primary. According to Asimov, the Moon is a planet moving around the Sun in careful step with the Earth.<ref name="Asimov"/>
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| == References ==
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| <references/>
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| [[Category:Moons]]
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| [[Category:Gravitation]]
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| [[Category:Astronomical dynamical systems]]
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My name is Louisa (27 years old) and my hobbies are Inline Skating and Bonsai.
Feel free to surf to my site http://tinyurl.com/pkup9lo