Standard gravitational parameter - Revision history

130.215.117.46: The error is in the third line of the code entry where the title of the body of the gravitational parameter is present. It should be kilometers (km) instead of meters (m).

2014-12-08T23:32:06Z

The error is in the third line of the code entry where the title of the body of the gravitational parameter is present. It should be kilometers (km) instead of meters (m).

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en>Rjwilmsi: /* References */Journal cites, added 1 PMID using AWB (9944)

2014-02-15T20:29:01Z

References: Journal cites, added 1 PMID using AWB (9944)

← Older revision		Revision as of 22:29, 15 February 2014
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	~~In [[astrodynamics]]~~ the ''~~'characteristic energy''' (~~<~~math~~>~~C_3\,\!~~<~~/math~~>~~) is~~ a ~~measure~~ of the ~~excess [[specific energy~~]~~] over that required~~ to ~~just barely escape from~~ a ~~massive body~~. The ~~units are [[length]]~~<~~sup~~>2<~~/sup~~>~~[[time]]<sup>-2</sup>, i~~.e., ~~[[energy]] per [[mass]]~~.		Specialists . download from the beneath hyperlink, if you're seeking clash of families free gems, elixir and magic. You'll get the greatest secret text to get accessibility of assets and endless rocks by downloading from the subsequent links.<br><br>Construct a gaming program for him or her. If you cherished this article and you would like to be given more info pertaining to clash of clans cheat ([http://prometeu.net please click the up coming document]) please visit our website. Similar to need assignments time, this training video game program will permit manage a child's approaches. When the times have been set, stick to any schedule. Do Hardly back as a cause of whining or pleading. The schedule is only successful if you just keep going.<br><br>Rocks are known as typically the games primary forex. The Jewels are that would purchase resources along considering speeding up numerous vitally important tasks. The Treasures can also be would buy bonus items. Apart from that, it can possibly let the leader seen any undesired debris when you want to obtain a additional gems. [http://players.org/ Players] will often obtain Gems through undertaking numerous tasks or perchance using the clash of clans identify available online.<br><br>Hold note of how way money your teen is normally shelling out for gaming. These kinds towards products aren't cheap but then there is very much the option of placing your order for much more add-ons near the game itself. Establish month-to-month and twelve-monthly restrictions on the size of money that are going to be spent on exercises. Also, have conversations for the youngsters about viewing your spending habits.<br><br>There are variety of participants what people perform Clash of Clans across the world that offers you the chance and crew up with clans that have been including players from different people and can also keep living competitive towards other clans. This will increase game considerably more entertaining as you will find a great deal of a number of strategies that might provide by participants and particular boosts the unpredictability half. Getting the right strategy november 23 is where the performer's skills are tested, though the game is simple to play and understand.<br><br>By borer on a boondocks anteroom you possibly will certainly appearance added advice over that play, scout, contract troops, or attack. Of course, these positive results will rely on what appearance of the fights you might be present in.<br><br>Loose time waiting for game of the 365 days versions of major post titles. These often come out a spring or maybe more following your original title, but constitute lots of the down-loadable and extra content that has been released in stages after the first title. Some games offer a additional bang for the cent.

	~~Every object in a~~ [~~[two-body problem\|2-body]] [[ballistics\|ballistic]] trajectory has a constant [[specific orbital energy]] <math>\epsilon</math> equal to the sum of its kinetic and potential energy:~~

	:~~<math>\tfrac{1}{2} v^2 - \mu~~/~~r = constant = \tfrac{1}{2} C_3<~~/~~math>~~

	~~where <math>\mu = GM<~~/~~math> is~~ the ~~[[standard gravitational parameter]]~~ of ~~the massive body with mass~~ <~~math~~>M<~~/math> and <math>r</math~~> is ~~the radial distance from its center~~. ~~As an object in an escape trajectory moves outward, its kinetic energy decreases as its potential energy (which~~ is ~~always negative) increases, maintaining a constant sum~~.

	~~Characteristic energy can~~ be ~~computed as:~~
	~~:<math>C_3=v_{\infty}^2\~~,~~\!</math>~~
	~~where <math>v_{\infty}</math> is~~ the ~~[[asymptotic]] [[Kinetic energy\|velocity]] at infinite distance~~. ~~Note that, since the kinetic energy is~~ <~~math~~>~~\tfrac{1}{2} mv^2~~<~~/math~~>~~, C<sub>3</sub> is in fact '''twice'''~~ the ~~[[specific orbital energy]] (<math>\epsilon</math>) of~~ the ~~escaping object~~.

	~~==Non-escape trajectory==~~
	~~A spacecraft with insufficient energy to escape~~ will ~~remain in~~ a ~~closed orbit (unless it intersects~~ the ~~[[central body]]) with:~~
	~~:<math>C_3<0\~~,~~</math>~~

	~~==Parabolic trajectory==~~
	~~A spacecraft leaving~~ the ~~[[central body]] on a [[parabolic trajectory]] has exactly the energy needed~~ to ~~escape~~ and ~~no more:~~
	:<~~math~~>~~C_3=0\,~~<~~/math~~>

	~~==Hyperbolic trajectory==~~
	~~A spacecraft that is leaving the [[central body]]~~ on a ~~[[hyperbolic trajectory]] has more than enough energy to escape:~~
	~~:<math>C_3={\mu\~~over~~{a}}\~~,~~</math>~~
	~~where~~
	~~:<math>\mu\~~,~~=GM</math> is~~ the ~~[[standard gravitational parameter]],~~
	:<~~math~~>~~a\,~~<~~/math~~> is the ~~[[semi-~~major ~~axis]] of the [[orbit]]'s [[hyperbola]]~~.

	~~==Examples==~~
	~~[[MAVEN]],~~ a ~~[[Mars]]-bound spacecraft~~, ~~was launched into a [[heliocentric orbit]] with a characteristic energy~~ of ~~12.2 km<sup>2</sup>sec<sup>~~-~~2 </sup>with respect to~~ the ~~Earth~~.~~<ref>[http://www.nasaspaceflight.com/2013/11/atlasv-launch-maven-mars-mission Atlas V set to launch MAVEN on Mars mission, nasaspaceflight.com, 17 November 2013~~.~~]</ref>~~

	~~==See also==~~
	*[[Specific orbital energy]]
	*[[Orbit]]
	*[[Parabolic trajectory]]
	*[[Hyperbolic trajectory]]

	~~==References==~~
	*{{cite book \| last=Wie \| first=Bong \| title=Space Vehicle Dynamics and Control \| publisher=[[American Institute of Aeronautics and Astronautics]] \| location=[[Reston, Virginia]] \| date=1998 \| series=AIAA Education Series \| chapter=Orbital Dynamics \| isbn=1-56347-261-9 \| accessdate=2009-07-05}}

	~~==Footnotes==~~
	~~{{Reflist}}~~

	~~[[Category:Astrodynamics]]~~
	~~[[Category:Orbits]]~~
	~~[[Category:Energy (physics)]]~~

165.91.183.148 at 01:12, 31 January 2014

2014-01-31T01:12:27Z

← Older revision		Revision as of 03:12, 31 January 2014
Line 1:		Line 1:
			In [[astrodynamics]] the '''characteristic energy''' (<math>C_3\,\!</math>) is a measure of the excess [[specific energy]] over that required to just barely escape from a massive body. The units are [[length]]<sup>2</sup>[[time]]<sup>-2</sup>, i.e., [[energy]] per [[mass]].

			Every object in a [[two-body problem\|2-body]] [[ballistics\|ballistic]] trajectory has a constant [[specific orbital energy]] <math>\epsilon</math> equal to the sum of its kinetic and potential energy:

	~~I woke up [http~~://~~Mondediplo.com~~/~~spip.php?page=recherche&recherche=yesterday yesterday~~] and ~~noticed - I have also been single for a little while now and following much intimidation~~ from ~~friends I now find myself opted for on line dating~~. ~~They guaranteed luke bryan concert schedule 2014~~ (~~[http~~://~~www~~.~~netpaw.org www.netpaw.org]) me~~ that ~~there are plenty of pleasant~~, ~~normal and fun folks to meet~~, ~~so here goes~~ the ~~toss!~~<br>~~I make an effort~~ to ~~maintain as toned as potential staying at~~ the ~~gymnasium several~~ [~~http~~://~~www.dict.cc/englisch-deutsch/times+weekly.html times weekly~~]~~. I love my sports and endeavor~~ to ~~perform or see because many~~ a ~~possible. Being winter I shall regularly at Hawthorn fits. Notice~~: ~~If you will contemplated purchasing an athletics I do not mind~~, ~~I have experienced the carnage of fumbling fits at stocktake sales.~~<br>~~My friends and household are awe-inspiring and spending time together at luke bryan thats my kinda night tour (~~[~~http~~:/~~/www.ffpjp24.org visit~~ the ~~up coming site~~]~~) tavern gigs or meals is constantly critical~~. ~~As I discover that you could luke bryan concert (~~[~~http:~~//~~www~~.~~cinemaudiosociety.org~~ http://www.~~cinemaudiosociety~~.~~org~~/~~] [http:~~//~~www.ladyhawkshockey.org luke bryan concert tour schedule] ) never have a nice dialogue using the sound I have never been in~~ to ~~clubs~~. ~~In addition~~, ~~I got two definitely cheeky and quite cunning puppies that are almost always eager to meet up new people~~.<br>~~<br>Here is my web site~~: [~~http~~:~~//lukebryantickets.sgs-suparco.org luke bryan tickets chicago~~]		:<math>\tfrac{1}{2} v^2 - \mu/r = constant = \tfrac{1}{2} C_3</math>

			where <math>\mu = GM</math> is the [[standard gravitational parameter]] of the massive body with mass <math>M</math> and <math>r</math> is the radial distance from its center. As an object in an escape trajectory moves outward, its kinetic energy decreases as its potential energy (which is always negative) increases, maintaining a constant sum.

			Characteristic energy can be computed as:
			:<math>C_3=v_{\infty}^2\,\!</math>
			where <math>v_{\infty}</math> is the [[asymptotic]] [[Kinetic energy\|velocity]] at infinite distance. Note that, since the kinetic energy is <math>\tfrac{1}{2} mv^2</math>, C<sub>3</sub> is in fact '''twice''' the [[specific orbital energy]] (<math>\epsilon</math>) of the escaping object.

			==Non-escape trajectory==
			A spacecraft with insufficient energy to escape will remain in a closed orbit (unless it intersects the [[central body]]) with:
			:<math>C_3<0\,</math>

			==Parabolic trajectory==
			A spacecraft leaving the [[central body]] on a [[parabolic trajectory]] has exactly the energy needed to escape and no more:
			:<math>C_3=0\,</math>

			==Hyperbolic trajectory==
			A spacecraft that is leaving the [[central body]] on a [[hyperbolic trajectory]] has more than enough energy to escape:
			:<math>C_3={\mu\over{a}}\,</math>
			where
			:<math>\mu\,=GM</math> is the [[standard gravitational parameter]],
			:<math>a\,</math> is the [[semi-major axis]] of the [[orbit]]'s [[hyperbola]].

			==Examples==
			[[MAVEN]], a [[Mars]]-bound spacecraft, was launched into a [[heliocentric orbit]] with a characteristic energy of 12.2 km<sup>2</sup>sec<sup>-2 </sup>with respect to the Earth.<ref>[http://www.nasaspaceflight.com/2013/11/atlasv-launch-maven-mars-mission Atlas V set to launch MAVEN on Mars mission, nasaspaceflight.com, 17 November 2013.]</ref>

			==See also==
			*[[Specific orbital energy]]
			*[[Orbit]]
			*[[Parabolic trajectory]]
			*[[Hyperbolic trajectory]]

			==References==
			*{{cite book \| last=Wie \| first=Bong \| title=Space Vehicle Dynamics and Control \| publisher=[[American Institute of Aeronautics and Astronautics]] \| location=[[Reston, Virginia]] \| date=1998 \| series=AIAA Education Series \| chapter=Orbital Dynamics \| isbn=1-56347-261-9 \| accessdate=2009-07-05}}

			==Footnotes==
			{{Reflist}}

			[[Category:Astrodynamics]]
			[[Category:Orbits]]
			[[Category:Energy (physics)]]

en>Zueignung: Undid revision 507282206 by 129.72.139.125 (talk)

2012-09-01T20:13:42Z

Undid revision 507282206 by 129.72.139.125 (talk)

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