## Escape velocity |

In **escape velocity** is the minimum speed needed for a free object to escape from the gravitational influence of a massive body.

The escape velocity from Earth is about 11.186 km/s (6.951 mi/s; 40,270 km/h; 36,700 ft/s; 25,020 mph; 21,744 kn)^{[1]} at the surface. More generally, escape velocity is the speed at which the sum of an object's ^{[nb 1]} an object which has achieved escape velocity is neither on the surface, nor in a closed orbit (of any radius). With escape velocity in a direction pointing away from the ground of a massive body, the object will move away from the body, slowing forever and approaching, but never reaching, zero speed. Once escape velocity is achieved, no further impulse need be applied for it to continue in its escape. In other words, if given escape velocity, the object will move away from the other body, continually slowing, and will ^{[2]} Speeds higher than escape velocity have a positive speed at infinity. Note that the minimum escape velocity assumes that there is no friction (e.g., atmospheric drag), which would increase the required instantaneous velocity to escape the gravitational influence, and that there will be no future sources of additional velocity (e.g., thrust), which would reduce the required instantaneous velocity.

For a spherically symmetric, massive body such as a star, or planet, the escape velocity for that body, at a given distance, is calculated by the formula^{[3]}

where *G* is the universal *G* ≈ 6.67×10^{−11} m^{3}·kg^{−1}·s^{−2}), *M* the mass of the body to be escaped from, and *r* the distance from the ^{[nb 2]} The relationship is independent of the mass of the object escaping the massive body. Conversely, a body that falls under the force of gravitational attraction of mass *M*, from infinity, starting with zero velocity, will strike the massive object with a velocity equal to its escape velocity given by the same formula.

When given an initial speed greater than the escape speed the object will asymptotically approach the *hyperbolic excess speed* satisfying the equation:^{[4]}

In these equations atmospheric friction (*M*.

- overview
- escape velocity in various situations
- trajectory
- multiple bodies
- list of escape velocities
- deriving escape velocity using calculus
- see also
- notes
- references
- external links

The existence of escape velocity is a consequence of

For a given

The simplest way of deriving the formula for escape velocity is to use conservation of energy. For the sake of simplicity, unless stated otherwise, we assume that an object is attempting to escape from a uniform spherical planet by moving away from it and that the only significant force acting on the moving object is the planet's gravity. In its initial state, *i*, imagine that a spaceship of mass *m* is at a distance *r* from the center of mass of the planet, whose mass is *M*. Its initial speed is equal to its escape velocity, . At its final state, *f*, it will be an infinite distance away from the planet, and its speed will be negligibly small and assumed to be 0. *K* and *U _{g}* are the only types of energy that we will deal with, so by the conservation of energy,

*K _{ƒ}* = 0 because final velocity is zero, and

where μ is the

The same result is obtained by a *r* represents the *radial coordinate* or *reduced circumference* of the ^{[6]}^{[7]}

Defined a little more formally, "escape velocity" is the initial speed required to go from an initial point in a gravitational potential field to infinity and end at infinity with a residual speed of zero, without any additional acceleration.^{[8]} All speeds and velocities measured with respect to the field. Additionally, the escape velocity at a point in space is equal to the speed that an object would have if it started at rest from an infinite distance and was pulled by gravity to that point.

In common usage, the initial point is on the surface of a

The escape velocity is independent of the mass of the escaping object. It does not matter if the mass is 1 kg or 1,000 kg; what differs is the amount of energy required. For an object of mass the energy required to escape the Earth's gravitational field is *GMm / r*, a function of the object's mass (where *r* is the radius of the Earth, *G* is the *M* is the mass of the *M* = 5.9736 × 10^{24} kg). A related quantity is the

Other Languages

Alemannisch: Fluchtgeschwindigkeit

العربية: سرعة الإفلات

asturianu: Velocidá d'escape

বাংলা: মুক্তিবেগ

беларуская: Другая касмічная скорасць

беларуская (тарашкевіца): Другая касьмічная хуткасьць

български: Втора космическа скорост

català: Velocitat d'escapament

čeština: Úniková rychlost

dansk: Undvigelseshastighed

eesti: Paokiirus

Ελληνικά: Ταχύτητα διαφυγής

español: Velocidad de escape

Esperanto: Liberiga rapido

euskara: Ihes-abiadura

فارسی: سرعت گریز

français: Vitesse de libération

Gaeilge: Luas éalaithe

galego: Velocidade de escape

한국어: 탈출 속도

հայերեն: Երկրորդ տիեզերական արագություն

हिन्दी: पलायन वेग

hrvatski: Brzina oslobađanja

Bahasa Indonesia: Kecepatan lepas

italiano: Velocità di fuga

עברית: מהירות מילוט

ಕನ್ನಡ: ವಿಮೋಚನ ವೇಗ

қазақша: Екінші космостық жылдамдық

latviešu: Otrais kosmiskais ātrums

lietuvių: Antrasis kosminis greitis

magyar: Kozmikus sebesség

македонски: Втора космичка брзина

मराठी: मुक्तिवेग

Bahasa Melayu: Halaju lepas

Nederlands: Ontsnappingssnelheid

日本語: 宇宙速度

norsk: Unnslipningshastighet

norsk nynorsk: Unnsleppingsfart

occitan: Velocitat de liberacion

oʻzbekcha/ўзбекча: Ikkinchi kosmik tezlik

ਪੰਜਾਬੀ: ਇਸਕੇਪ ਗਤੀ

Piemontèis: Andi d'evasion

polski: Prędkość ucieczki

português: Velocidade de escape

română: Viteză cosmică

русский: Вторая космическая скорость

Scots: Escape velocity

Simple English: Escape velocity

slovenčina: Úniková rýchlosť

slovenščina: Ubežna hitrost

српски / srpski: Друга космичка брзина

srpskohrvatski / српскохрватски: Brzina oslobađanja

suomi: Pakonopeus

svenska: Flykthastighet

தமிழ்: விடுபடு திசைவேகம்

татарча/tatarça: İkençe ğälämi tizlek

తెలుగు: పలాయన వేగము

ไทย: ความเร็วหลุดพ้น

Türkçe: Kurtulma hızı

українська: Друга космічна швидкість

اردو: فراری سمتار

Tiếng Việt: Tốc độ vũ trụ cấp 2

吴语: 宇宙速度

中文: 宇宙速度