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| {| class="infobox bordered" style="font-size: 100%" cellpadding=3
| | It begins by consuming in a pair of one's lovely island where your amazing peaceful village is part way through beaches and woods till the enemies known when your BlackGuard led by Lieutenant Hammerman invades your snowdonia. After managing to guard against a tiny invasion force, he proposes to avenge his loss using battle.<br><br>Use the web for help. Practically every game has its legion of devoted devotees, lots of which waste countless hours crafting wide-range maps and guides. Additionally there are newsgroups where you are speak one on one with other players. Benefit from this found diamond and it is possible to eventually get past that level of cla you have been stuck on forever.<br><br>Assuming you have little ones who experience video games, then you're aware challenging it really in order to use pull them out among the t. v.. Their eye can continually be stuck towards the maintain a record of for hours as they will play their preferred games. If you want aid regulating your little ones clash of clans Hack time, your own pursuing [https://Www.Google.com/search?hl=en&gl=us&tbm=nws&q=article&btnI=lucky article] has many ways for you.<br><br>Essentially clash of clans hack tool no survey encourages believe in among some people. Society is definitely powered by professional pressure, one of the particular most powerful forces during the planet. If you liked this post and you would like to obtain more data about [http://prometeu.net clash of clans hack apk] kindly check out our page. Considering that long as peer make utilizes its power as for good, clash of clans hack tool no survey will have its place in community.<br><br>Amongst the best and fastest establishing certifications by ECCouncil. Where a dictionary damage fails the computer cyberpunk may try a brute force attack, which is much more time consuming. Establishes the borders of everyone with non-editable flag: lot_border [ ]. The issue is this one hit people where it really hurts - your heart. These Kindle hacks continue to be keyboard shortcuts will help save you tons of time seeking and typing in repetitive things. Claire mentioned how she had started gain a (not trivial.<br><br>It's hard to select the required xbox game gaming procedure. In the beginning, you should associated with your standard requirements like a video game player, then check out the specs made available from just about every unit you are deciding on. Consider investigating on-line. Check consumer reviews to ascertain if other gamers have discovered complications with the unit. Ahead of buying a game process, you should know up to a whopping you are able to help regarding it.<br><br>So as to master game play near shooter video games, excel att your weapons. Have an understanding of everything there is recognize about each and each single weapon style in the. Each weapon excels while in certain ways, but tumbles short in others. When you know i would say the pluses and minuses of each weapon, you can use them to registered advantage. |
| |-
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| ! Body
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| ! ''μ'' (km<sup>3</sup>s<sup>−2</sup>)
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| |-
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| | [[Sun]]
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| | {{val|132712440018|(9)}}<ref name="Astrodynamic Constants" />
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| |-
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| | [[Mercury (planet)|Mercury]]
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| | {{val|22032}}
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| |-
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| | [[Venus]]
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| | {{val|324859}}
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| |-
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| | [[Earth]]
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| | {{val|398600.4418|(9)}}
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| |-
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| | [[Moon]]
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| | {{val|4902.8000}}
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| |-
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| | [[Mars]]
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| | {{val|42828}}
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| |-
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| | [[1 Ceres|Ceres]]
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| | {{val|63.1|(3)}}<ref name="Pitjeva2005" /><ref name="Britt2002" />
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| |-
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| | [[Jupiter]]
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| | {{val|126686534}}
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| |-
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| | [[Saturn]]
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| | {{val|37931187}}
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| |-
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| | [[Uranus]]
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| | {{val|5793939|(13)}}<ref name="Jacobson1992" />
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| |-
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| | [[Neptune]]
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| | {{val|6836529}}
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| |-
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| | [[Pluto]]
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| | {{val|871|(5)}}<ref name="Buie06" />
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| |-
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| | [[Eris (dwarf planet)|Eris]]
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| | {{val|1108|(13)}}<ref name="Brown Schaller 2007" />
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| |}
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| | |
| In [[celestial mechanics]], the '''standard gravitational parameter''' ''μ'' of a [[celestial body]] is the product of the [[gravitational constant]] ''G'' and the mass ''M'' of the body.
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| | |
| :<math>\mu=GM \ </math>
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| | |
| For several objects in the solar system, the value of ''μ'' is known to greater accuracy than ''G'' or ''M.'' The [[SI]] units of the standard gravitational parameter are [[Kilometre|km]]<sup>3</sup>[[second|s]]<sup>−2</sup>.
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| | |
| == Small body orbiting a central body ==
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| {{Properties_of_mass}}
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| Under standard assumptions in astrodynamics we have:
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| : <math>m \ll M \ </math>
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| where ''m'' is the mass of the [[orbiting body]], ''M'' is the mass of the [[central body]].
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| | |
| For all [[circular orbit]]s around a given central body:
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| : <math>\mu = rv^2 = r^3\omega^2 = 4\pi^2r^3/T^2 \ </math>
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| where ''r'' is the orbit [[radius]], ''v'' is the [[orbital speed]], ''ω'' is the [[angular speed]], and ''T'' is the [[orbital period]]. | |
| | |
| The last equation has a very simple generalization to [[elliptic orbit]]s:
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| : <math>\mu=4\pi^2a^3/T^2 \ </math>
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| where ''a'' is the [[semi-major axis]]. (See [[Kepler's laws of planetary motion#Kepler's third law|Kepler's third law]]).
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| | |
| For all [[parabolic trajectory|parabolic trajectories]] ''rv''<sup>2</sup> is constant and equal to 2''μ''. For elliptic and hyperbolic orbits ''μ'' = 2''a''|''ε''|, where ''ε'' is the [[specific orbital energy]].
| |
| | |
| == Two bodies orbiting each other == <!-- This section is linked from [[Alpha Centauri]] -->
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| | |
| In the more general case where the bodies need not be a large one and a small one (the [[two-body problem]]), we define:
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| * the vector '''r''' is the position of one body relative to the other
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| * ''r'', ''v'', and in the case of an [[elliptic orbit]], the [[semi-major axis]] ''a'', are defined accordingly (hence ''r'' is the distance)
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| * ''μ'' = ''Gm''<sub>1</sub> + ''Gm''<sub>2</sub> = ''μ''<sub>1</sub> + ''μ''<sub>2</sub>, where ''m''<sub>1</sub> and ''m''<sub>2</sub> are the masses of the two bodies.
| |
| | |
| Then:
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| * for [[circular orbit]]s, ''rv''<sup>2</sup> = ''r''<sup>3</sup>''ω''<sup>2</sup> = 4π<sup>2</sup>''r''<sup>3</sup>/''T''<sup>2</sup> = ''μ''
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| * for [[elliptic orbit]]s, 4π<sup>2</sup>''a''<sup>3</sup>/''T''<sup>2</sup> = ''μ'' (with ''a'' expressed in AU; ''T'' in seconds and ''M'' the total mass relative to that of the Sun, we get ''a''<sup>3</sup>/''T''<sup>2</sup> = ''M'')
| |
| * for [[parabolic trajectory|parabolic trajectories]], ''rv''<sup>2</sup> is constant and equal to 2''μ''
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| * for elliptic and hyperbolic orbits, ''μ'' is twice the semi-major axis times the absolute value of the [[specific orbital energy]], where the latter is defined as the total energy of the system divided by the [[reduced mass]].
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| | |
| == Terminology and accuracy ==
| |
| | |
| Note that the [[reduced mass]] is also denoted by <math>\mu.\!\,</math>.
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| | |
| The value for the [[Earth]] is called the '''geocentric gravitational constant''' and equals {{val|398600.4418|0.0008|u=km<sup>3</sup>s<sup>−2</sup>}}. Thus the uncertainty is 1 to {{val|500000000}}, much smaller than the uncertainties in ''G'' and ''M'' separately (1 to {{val|7000}} each).
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| | |
| The value for the [[Sun]] is called the '''heliocentric gravitational constant''' or
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| ''geopotential of the sun'' and equals {{val|1.32712440018|e=20|u=m<sup>3</sup>s<sup>−2</sup>}}.
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| | |
| == References ==
| |
| | |
| {{reflist
| |
| | refs =
| |
| | |
| <ref name="Astrodynamic Constants">
| |
| {{cite web
| |
| | title = Astrodynamic Constants
| |
| | date = 27 February 2009
| |
| | publisher = [[NASA]]/[[Jet Propulsion Laboratory|JPL]]
| |
| | url = http://ssd.jpl.nasa.gov/?constants
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| | accessdate = 27 July 2009
| |
| }}
| |
| </ref>
| |
| | |
| <ref name="Pitjeva2005">
| |
| {{cite journal
| |
| | doi = 10.1007/s11208-005-0033-2
| |
| | author = E.V. Pitjeva
| |
| | year = 2005
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| | title = High-Precision Ephemerides of Planets — EPM and Determination of Some Astronomical Constants
| |
| | url = http://iau-comm4.jpl.nasa.gov/EPM2004.pdf
| |
| | journal = [[Solar System Research]]
| |
| | volume = 39
| |
| | issue=3
| |
| | pages=176
| |
| | bibcode = 2005SoSyR..39..176P
| |
| }}
| |
| </ref> | |
| | |
| <ref name="Britt2002"> | |
| {{cite book
| |
| | author = D. T. Britt, D. Yeomans, K. Housen, G. Consolmagno
| |
| | year = 2002
| |
| | chapter = Asteroid density, porosity, and structure
| |
| | title = [http://www.lpi.usra.edu/books/AsteroidsIII/download.html Asteroids III]
| |
| | editor = W. Bottke, A. Cellino, P. Paolicchi, R.P. Binzel
| |
| | page = 488
| |
| | publisher = [[University of Arizona Press]]
| |
| | url = http://www.lpi.usra.edu/books/AsteroidsIII/pdf/3022.pdf
| |
| }}
| |
| </ref> | |
| | |
| <ref name="Jacobson1992"> | |
| {{cite journal
| |
| | doi = 10.1086/116211
| |
| | author = R.A. Jacobson, J.K. Campbell, A.H. Taylor, S.P. Synnott
| |
| | year = 1992
| |
| | title = The masses of Uranus and its major satellites from Voyager tracking data and Earth-based Uranian satellite data
| |
| | journal = [[Astronomical Journal]]
| |
| | volume = 103
| |
| | issue = 6
| |
| | pages = 2068–2078
| |
| | bibcode = 1992AJ....103.2068J
| |
| }}
| |
| </ref> | |
| | |
| <ref name="Buie06"> | |
| {{cite journal
| |
| | doi = 10.1086/504422
| |
| | author = M.W. Buie, W.M. Grundy, E.F. Young, L.A. Young, S.A. Stern
| |
| | year = 2006
| |
| | title = Orbits and photometry of Pluto's satellites: Charon, S/2005 P1, and S/2005 P2
| |
| | journal = [[Astronomical Journal]]
| |
| | volume = 132
| |
| | pages = 290
| |
| | bibcode = 2006AJ....132..290B
| |
| | arxiv = astro-ph/0512491
| |
| }}
| |
| </ref> | |
| | |
| <ref name="Brown Schaller 2007"> | |
| {{cite journal
| |
| | doi = 10.1126/science.1139415
| |
| | author = M.E. Brown, E.L. Schaller
| |
| | year = 2007
| |
| | title = The Mass of Dwarf Planet Eris
| |
| | journal = [[Science (journal)|Science]]
| |
| | volume = 316
| |
| | issue = 5831
| |
| | pages = 1586
| |
| | bibcode = :2007Sci...316.1585B
| |
| }}
| |
| </ref>
| |
| | |
| <!--
| |
| <ref name="Lunar Constants and Models Document">
| |
| {{cite web
| |
| | title = Lunar Constants and Models Document
| |
| | date = 23 September 2005
| |
| | publisher = [[NASA]]/[[Jet Propulsion Laboratory|JPL]]
| |
| | url = http://www.hq.nasa.gov/alsj/lunar_cmd_2005_jpl_d32296.pdf
| |
| | accessdate = 1 April 2013
| |
| }}
| |
| </ref>-->
| |
| | |
| }}
| |
| | |
| == See also ==
| |
| | |
| * [[Astronomical system of units]]
| |
| * [[Planetary mass]]
| |
| | |
| {{orbits}}
| |
| | |
| [[Category:Orbits]]
| |
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Use the web for help. Practically every game has its legion of devoted devotees, lots of which waste countless hours crafting wide-range maps and guides. Additionally there are newsgroups where you are speak one on one with other players. Benefit from this found diamond and it is possible to eventually get past that level of cla you have been stuck on forever.
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