Fontem paginae Celeritas fugae inspicere

[[Fasciculus:Newton Cannon.svg|thumb|upright=1.3|“Canno Newtoni”, sive de celeritate fugae ab [[Isaacus Newtonus|Isaaco Newtono]] illustrata. A summa altissimi [[mons|montis]], [[canno]] quidam [[proiectile|proiectilia]] maiore maioreque velocitate explodit. Proiectilia A et B in terram denuo incidunt; proiectile C orbitam circularem sequitur; D autem sequitur [[ellipsis|ellipticam]]; demum proiectile E e planeta evadit.]]

[[Fasciculus:Newton's cannonball cropped.svg|thumb|upright=1|“Canno Newtoni” sicut in editione Anglica anni [[1728]] libri Newtoni {{Op|De mundi systemate}}.<ref>{{cite book
	| last = Newtonus
	| first = Isaacus
	| author-link = Isaacus Newtonus
	| date = 1728
	| title = A Treatise Of The System Of The World
	| url = https://archive.org/details/1728-newton-a-treatise-of-the-system-of-the-world/page/n35/mode/2up
	| location = [[Londinium|Londinii]]
	| publisher = F. Fayram
	| page = 6
}}.</ref>]]

{{Res|Celeritas fugae}}{{Convertimus}} seu {{Res|plene=Celeritas effugiendi|effugiendi}}{{Convertimus}} in {{Creanda|en|Celestial mechanics|d|Q184274|mechanica caelestis|mechanica caelesti}} est minima [[celeritas]] cuidam corpori necessaria ut e contactu vel ex [[orbita]] circum aliud corpus evadat, dummodo:

* {{Creanda|en|Trajectory|d|Q193139|traiectoria}} sit {{Creanda|de|Wurfparabel|d|Q10281355|motus parabolicus|ballistica}} ({{*ie}} nullae aliae [[vis|vires]] corpus agunt, ne {{Creanda|en|Propulsion|d|Q2583685|propulsio}} nec {{Creanda|en|Friction|d|Q82580|frictio}} quidem)
* ulla ailia notabilis [[massa]] circum corpus fugiens absit

Etiamsi ambo verba ''celeritatis'' et ''velocitatis'' vulgo adhiberi solent, casus vocabulo ''celeritatis'' melius descirbitur, cum [[velocitas]] sit [[vector]] (i.e. {{Creanda|en|Direction (geometry)|d|Q2151613|directio|directionem}} habeat), sed fugae celeritas eadem sit praeter directionem.

Massā corporis fugientis neglectā et corporibus inter se tangentibus, haec [[aequatio]] celeritatem describit fugae {{Eodem versu|(<math>c_f</math>)}},

: <math>c_f = \sqrt{\frac{2GM}{d}}</math>

ubi:

* <math>G</math> est [[constans gravitatis]]
* <math>M</math> est massa alterius corporis
* <math>d</math> est [[spatium]] inter amborum corporum [[Centrum (geometria)|centra]]

[[Energia]] quam fuga requirit {{Eodem versu|(<math>E_f</math>)}} sic computatur,

: <math>E_f = \frac{GMm}{d}</math>

ubi <math>m</math> est massa corporis effugientis.

Si autem corpus est in orbita [[circulus|circulari]], magnitudo velocitatis orbitalis eius (<math>|\mathbf{v_o}|</math>) totiens celeritati fugae congruit quotiens numerus [[unus|unius]] radici congruit numeri [[2|duorum]], i.e.:

: <math>c_f = \sqrt{2}\;|\mathbf{v_o}| \approx 1.414\;|\mathbf{v_o}|</math>

== Celeritates fugae planetarum systematis solaris, Lunae Solisque ==

{| class="wikitable" 
! rowspan="2" | '''Corpus''' 
! colspan="3" | '''Celeritas fugae a [[superficies|superficie]]'''
|-
! [[metrum|m]]/[[secundum|s]] !! [[chiliometrum|km]]/[[secundum|s]] !! [[chiliometrum|km]]/[[hora|h]]
|-
| [[Sol]] || 617 300 || 617.3 || 2 222 280
|-
| [[Mercurius (planeta)|Mercurius]] || 4 435 || 4.435 || 15 966
|-
| [[Venus (planeta)|Venus]] || 10 400 || 10.4 || 37 440
|-
| [[Tellus]] || 11 200 || 11.2 || 40 320
|-
| [[Luna]] || 2 300 || 2.30 || 8 280
|-
| [[Mars (planeta)|Mars]] || 5 000 || 5.00 || 18 000
|-
| [[Iuppiter (planeta)|Iuppiter]] || 59 600 || 59.6 || 214 560
|-
| [[Saturnus (planeta)|Saturnus]] || 35 500 || 35.5 || 127 800
|-
| [[Uranus (planeta)|Uranus]] || 21 300 || 21.3 || 76 680
|-
| [[Neptunus (planeta)|Neptunus]] || 23 300 || 23.3 || 83 880
|-
| [[Ceres (planetulus)|Ceres]] || 510 || 0.51 || 1 836
|-
| [[Pluto (planetulus)|Pluto]] || 1 200 || 1.20 || 4 320 
|-
| [[Eris (planetulus)|Eris]] || 2 700 || 2.70 || 9 720 
|}

== Notae ==
<references />

{{NexInt}}
* [[Astrophysica]]
* [[Constans gravitatis]]
* [[Fluctus gravitatis]]
* [[Gravitas (physica)]]
* [[Isaacus Newtonus]]
* [[Relativitas generalis]]
* [[Systema solare]]
* [[Vis aestualis]]

{{physica-stipula}}
{{Myrias|Physica}}

[[Categoria:Mechanica caelestis]]
[[Categoria:Notiones in physica]]
[[Categoria:Physica]]
[[Categoria:Astronomia]]