# What is Escape velocity: Definition and 219 Discussions

In physics (specifically, celestial mechanics), escape velocity is the minimum speed needed for a free, non-propelled object to escape from the gravitational influence of a massive body, that is, to eventually reach an infinite distance from it. Escape velocity rises with the body's mass (body to be escaped) and falls with the escaping object's distance from its center. The escape velocity thus depends on how far the object has already traveled, and its calculation at a given distance takes into account the fact that without new acceleration it will slow down as it travels—due to the massive body's gravity—but it will never quite slow to a stop.
A rocket, continuously accelerated by its exhaust, can escape without ever reaching escape velocity, since it continues to add kinetic energy from its engines. It can achieve escape at any speed, given sufficient propellant to provide new acceleration to the rocket to counter gravity's deceleration and thus maintain its speed.
The escape velocity from Earth's surface is about 11,186 m/s (6.951 mi/s; 40,270 km/h; 36,700 ft/s; 25,020 mph; 21,744 kn). More generally, escape velocity is the speed at which the sum of an object's kinetic energy and its gravitational potential energy is equal to zero; 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 asymptotically approach zero speed as the object's distance approaches infinity, never to come back. Speeds higher than escape velocity retain a positive speed at infinite distance. 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 acceleration or extraneous deceleration (for example from thrust or from gravity of other bodies), which would change 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

v

e

=

2
G
M

r

{\displaystyle v_{e}={\sqrt {\frac {2GM}{r}}}}
where G is the universal gravitational constant (G ≈ 6.67×10−11 m3·kg−1·s−2), M the mass of the body to be escaped from, and r the distance from the center of mass of the body to the object. 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

V

{\displaystyle V}
greater than the escape speed

v

e

,

{\displaystyle v_{e},}
the object will asymptotically approach the hyperbolic excess speed

v

,

{\displaystyle v_{\infty },}
satisfying the equation:

v

2

=

V

2

v

e

2

.

{\displaystyle {v_{\infty }}^{2}=V^{2}-{v_{e}}^{2}.}
In these equations atmospheric friction (air drag) is not taken into account.

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1. ### Escape Velocity from Earth starting from its Centre

What is the minimum velocity (theoretically) of an object located at the CENTER of the Earth to move it outside its gravitational field?
2. ### I Balloon experiment - Classical Physics vs. Statistical Physics

While reading a similar and deservedly closed post a contradiction came to my mind. The supposed contradiction is related to Statistical Physics where my understanding is only conceptual so correct me where I might be wrong. I remember reading that lightweight gasses can escape Earth's...
3. ### Escape velocity question - constant is wrong....

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4. ### Rocket Escape Velocity from the Earth-Sun system

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5. ### Escape velocity of solar system

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7. ### Fields (Gravitational fields) -- Escape Velocity from the Moon

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8. J

### I Does Escape Velocity depend on a rocket's direction away from Earth?

He explain escape velocity in example where rocket goes straight up,isnt escacpe velocity ,velocity where centrifugal forces and gravity are equal,so refers only when rocket going in circle/orbit? Can rocket really leave Earth in straight line like he show in video once reach this velocity and...
9. ### Escape Velocity Question: Why is the final kinetic energy = 0?

So Ekf-Eki+Epf-Epi=0. I understand that the final potential energy is 0 (distance away approaches infinity), but don't get why the final kinetic energy becomes 0. If the final kinetic energy was 0, wouldn't that mean the object no longer has any velocity and would start being effected by the...
10. ### I Derive Escape Velocity GR: Source for Schwarzschild Metric

I was surprised to read that the formula for escape velocity — at least for a spherical mass like the Earth — is the same in relativity as it is in classical physics: v_e = (2GM/r)^{1/2} I'm wondering if someone can give me a good source for deriving this. (I assume one takes a radial...
11. ### Finding r of a Jovian-synchronous orbit and escape velocity

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12. ### A mistake in the derivation of escape velocity

In the last step of the derivation of escape velocity, the two sides of the equation seem to have opposite signs. $$-1/2mv_0^2=-mgR_e^2\,\lim_{r\to\infty}(1/r-1/R_e)$$ $$-1/2mv_0^2=mgR_e^2 \frac{1}{R_e}$$ Since the mass and the square of the velocity are positive, the left side of the equation...
13. ### Exploring the Logical/Geometrical Explanation of Escape Velocity

If you derive the equation for orbital velocity you get $$v_{orbit} = \sqrt{\frac{GM}{R}}$$ and for escape velocity you get $$v_{escape} = \sqrt{\frac{2GM}{R}}=\sqrt{2}\,v_{orbit}$$ I'm wondering if there is a logical/geometrical...
14. ### Escape Velocity depends on the Radius of the Earth?

We have 2 different formulas for escape velocity. and . If we look at the first formula we see that escape velocity is inversely proportional to the square root of Radius of Earth. While in the second formula, escape velocity is directly proportional to the square root of Radius of Earth. We...
15. ### Find the escape velocity from 2 point charges

Below is the work I've attempted. I used 2 PE b'c there were 2 point charges, and only one KE b'c only the proton is moving. The final equation in case it's hard to see is V(esc) = sqrt (4kQq / mr). I'm not sure if I did it right. Did I set up this equation right? and I am also not sure what...
16. ### What is the kinetic energy when an object reaches escape velocity?

What is the kinetic energy equal to during the escape velocity? Henceforth, what is exactly happening at the escape velocity in terms of gravity?
17. ### Escape velocity and gravitational freefall

Is an object with escape velocity in gravitational freefall?
18. ### Calculating Escape Velocity for Earth: Where Am I Going Wrong?

I really cannot understand where this is going wrong... Plugging in the constants, I get vescape=Sqrt(2(6.67x10^-11)(5.976x10^24kg)/6378). (6.67x10^-11)(5.976x10^24kg) gives me 3.99x10^14, and multiplied by 2 gives me 7.97x10^14. 7.97x10^14/6378=1.25x10^11. The square root of 1.25x10^11 would...
19. ### I Escape Velocity, Gravitational Velocity & Time Dilation

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20. ### Escape velocity of an iron asteroid

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21. ### Unusual escape velocity derivation

Is it possible to derive escape velocity say using momentum and force balance considerations? or using angular momentum consideration? Namely, any other approach then energy consideration that utilizes gravitation potential energy and kinetic energy?
22. ### When would a rocket return that was at escape velocity

we all know escape velocity is a velocity in which a body can escape orbit around the Earth and fly off into space. this needs to happen in space our just out of our atmosphere, due to drag that could bring an object back into orbit and cause it's velocity to degrade to a point where it would...
23. ### Question About the Escape Velocity from Different Mass Planets

Hi! I have a question about escape velocity. If a planet is bigger and have a greater escape velocity than another planet. Do this effect the density of the bigger planet in any way? Or do we have to know the mass of the bigger planet to know if the density is larger or lower for this planet?
24. ### I Escape Velocity: Newtonian vs Relativistic

Hi, Do we obtain the same escape velocity equation: Ve = sqrt(2GM/r) using both Newtonian and Relativistic approach?
25. ### Escape Velocity and the Motion of Two Massive Bodies

Hey there, If body 1, mass M1 has escape velocity V_e1 = (2GM1/r)**.5 but M2 is more massive than M1 is this relation still valid? In this case, the subordinate body really isn't the subordinate body so does this still hold? And r (distance b/t the two) changes not only due to the motion of M2...
26. ### Escape velocity when the rocket's mass is not small compared to the asteroid

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27. ### Find the speed of a satellite at a distance R from Earth

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28. ### Escape Velocity and Centripetal/Centrifugal Acceleration

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30. ### Escape velocity and kinetic energy of the Earth

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31. ### Intuition for why escape velocity doesn't depend on angle

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32. ### I Can a plane escape Earth's gravity with a powerful engine and no air?

If I drive a plane and the force of engine is bigger than force of gravity of it , if the engine is turn on always ,and assuming no air , will the plane continue moving up and escape from the gravity ?
33. ### GPE and Escape Velocity: Understanding the Relationship for Moving Objects

Is it necessary to be the kinetic energy greater than gpe to move ( I don't talk about in orbits) Example : Is it will be harder to move an object has a bigger gpe ( same mass but bigger hight from ground). And thanks.
34. G

### KE+PE when a rocket's speed is less than escape velocity?

Hey people, I just want to ask that what will happen to the total mechanical force of the rocket if its speed is less than escape velocity? a. KE+PE=0 b. KE+PE>0 c. KE+PE<0 d. Depends upon initial speed of the rocket Pick one. And Why??
35. ### Pytels Dynamics 12.8: Missile dynamics, acceleration and escape velocity

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36. ### B Escape Velocity from Relativistic Sphere: Derivation & Intuition

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37. ### B An exercise related to the mass of the Milky Way, sort of.

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38. ### Need help finding energy for escape velocity

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39. ### Trip to Space -- Can ship with 1g acceleration escape Earth?

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40. ### Need help calculating acceleration out of a gravity well

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41. ### Is the usual Escape Velocity eqn an approximation?

Text books ordinarily give the escape velocity of a mass-M body (in the center of mass frame of the system of the body and the escaping projectile, whose mass I'll label m) as (*) v2 = 2GM/r where r is the distance between the body and the escaping projectile. it doesn’t seem to me that (*)...
42. ### How come escape velocity isn't imaginary?

Going through several definitions, it appears that escape velocity is equal to the potential energy. That is:$$\frac{1}{2}m v^2=-\frac{G M m}{r}$$but if I solve for velocity, $v$, I get:$$v=\sqrt{-2\frac{G M}{r}}$$So how do I get an escape velocity that isn't imaginary?
43. ### Escape Velocity of a Neutron Star: Relativistic Calculation

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44. ### Rocket Launch: Achieving Escape Velocity w/ Fuel-Mass Ratio of 300

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45. ### B What does a black hole look like from the inside?

According to this video, , if a black hole is large enough you could actually travel for some time within the event horizon without dying because the event horizon is so far from the actual singularity. So, assuming that's true, what would you see while you were inside the black hole? Here's...
46. ### Escape Velocity: Unraveling the Mysteries of Kinetic & Potential Energy

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47. ### B Escape Velocity & Black Holes: Can Something Escape?

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48. ### D.E. Littlewood's comments about escape velocity

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49. ### Angular Acceleration and Moment Arm

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50. ### Escape velocity and kinetic energy

is it right to say, "when all the potential energy is converted in kinetic energy the object is moving at the escapevelocity. and "when the change in potential energy and kinetic energy is constant at the same time it is laying still on the ground or in a perfect circulair orbit. and the last...