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Can someone explain me what is escape velocity? why cant a bird with enough energy (super bird) fly into space?

Qmechanic
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Austin Rojers
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    Does the explanation in Wikipedia help? If not, you might want to mention what parts of it you don’t understand, so that answers can focus on those parts. – G. Smith Mar 05 '20 at 04:39
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    The “enough energy” itself is where the 11.2 km/s comes from! – Superfast Jellyfish Mar 05 '20 at 04:49
  • I couldn't get you traveller – Austin Rojers Mar 05 '20 at 05:23
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    please explain ' A rocket, continuously accelerated by its exhaust, need not reach ballistic escape velocity at any distance since it is supplied with additional kinetic energy by the expulsion of its reaction mass. It can achieve escape at any speed, given a suitable mode of propulsion and sufficient propellant to provide the accelerating force on the object to escape' as in wikipedia – Austin Rojers Mar 05 '20 at 05:31
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    The article explains that “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 achieve an infinite distance from it.” If the object is being propelled by a force (say, the thrust of a rocket engine) greater than the gravitational attraction toward Earth, then it doesn’t need to reach escape velocity. – G. Smith Mar 05 '20 at 07:21
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    Also see https://physics.stackexchange.com/q/29779/123208 It's important to keep in mind that escape velocity applies to a ballistic object. That is, it gets shot upwards with the escape velocity but it has no further upwards propulsion after that initial impulse. (And it ignores air resistance). – PM 2Ring Mar 05 '20 at 15:21
  • Thanks every body, now I have got a nice picture of escape velocity – Austin Rojers Mar 14 '20 at 03:24

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What happens when you throw a ball up? It goes up to some height where it loses all its kinetic energy and then falls back. Now if you throw it harder, it’s velocity is higher and it reaches a greater height before falling back.

Now if you throw so hard that the height after which it’ll fall back is infinity, then it will never fall back. And the initial velocity at such a situation is the escape velocity which for earth turns out to be $11.2$ km/s

The object will start falling back when the kinetic energy is zero, so if somehow you manage to maintain the kinetic energy above zero at all times, then you don’t really need to reach escape velocity at any instant.

To understand this, consider our example of throwing the ball again. Except this time there’s a person above you and a person above them and so on. enter image description here So all you have to do is throw hard enough to reach the next person and they have to do the same and so on.

Superfast Jellyfish
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    I'll point out that the 11.2 km/s ignores air friction. – MaxW Mar 05 '20 at 08:10
  • But how can this height become infinity? If initial speed is $v$, after time $t$ it will be $v-gt$ (where $g=GM/R^2$), so it will stop after time $t=v/g$ and then you say it will start falling back. Presumably it cannot go to infinite height in finite time $t$, right? – მამუკა ჯიბლაძე Mar 05 '20 at 14:02
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    @მამუკაჯიბლაძე It never has to get to infinite height at any specific time, but you can mathematically prove that it will continue to move towards infinite height. The thing you're missing is that the force of gravity decreases with distance. Intuitively, if you're moving straight up, gravity is always decreasing your velocity (trying to pull you down). The higher up you are, the less gravity affects you. At some velocity, you cross a boundary where gravity will never be able to slow your velocity to zero. We call that the escape velocity, and for Earth, it happens to be 11.2 km/s. – Josh Eller Mar 05 '20 at 14:15
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    @JoshEller I see, thanks. So actual equation of motion is quite complicated then. It is something like $r'(t)=v_0-kt/r(t)^2$. It must not be easy to say for which $v_0$ will $r(t)$ keep growing forever – მამუკა ჯიბლაძე Mar 05 '20 at 15:17
  • @მამუკაჯიბლაძე yes. That’s the differential equation. But one need not solve that to get the $v_0$ for which it’ll grow forever. Energy equations are enough. – Superfast Jellyfish Mar 05 '20 at 15:19
  • Do you mean the equations from the answer by @NayanDave? Because there also $r$ is taken to be radius of earth, not distance from earth – მამუკა ჯიბლაძე Mar 05 '20 at 15:21
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    If you consider $r=\infty$ as your zero potential energy, then the energy at radius of earth will be negative. And since you want the object to stop at infinity, the final kinetic energy is also zero. So final total energy is zero. Then initial total energy must also be zero. So you get the equation given in that answer. – Superfast Jellyfish Mar 05 '20 at 15:30
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    Aha now it's completely clear to me, many thanks! – მამუკა ჯიბლაძე Mar 05 '20 at 15:35
  • ...except my equation was wrong, sorry. It should be $r''(t)=-k/r(t)^2$ with $r(0)=r_0$, $r'(0)=v_0$. – მამუკა ჯიბლაძე Mar 06 '20 at 08:39
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Any projectile launched from Earth is slowed by interaction with the atmosphere. Most of this interaction is caused by friction. If we can talk about launching without worrying about the drag caused by friction, the discussion is easier. We can use the idea of conservation of energy to discover the velocity needed to escape the Earth's gravitational pull.

If the energy of motion (kinetic energy) of a projectile just equals the pull of gravitational (potential) energy, the projectile can barely escape the Earth.

enter image description here

Notice that the mass of the projectile can cancel on both sides of the equation. This is why the escape velocity is independent of the mass of the projectile.

enter image description here

Both SuperBird and a rocket must each obtain an escape velocity of 11.2 km/s to escape the Earth(Because It doesn't depend on Object's weight at all)

But SuperBird (if you consider living) can't achieve this because of Breathing problem while achieving that velocity even if we neglect that it will be burnt to ashes because of Air Resistance.

Nayan Dave
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To fly free of earth and off into space, you have to perform work against gravity as you climb upwards. This requires energy. A moving body possesses kinetic energy, and because of this you can solve for the speed that the moving body would have to possess in order to climb far enough upwards that the earth's gravity won't be able to pull you back. That speed is called the escape velocity and is equal to 11.2 km/sec.

niels nielsen
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Escape velocity is the minimum velocity required for a body to escape from the gravitational pull of the earth and move to outer space.

If your "super bird" could fly with a velocity of 11.2 km/s or its provided with a constant acceleration greater than g it would have moved to outer space.

This is the answer for what you have questioned, for the derivation search the internet as you also need to give some effort to clear your concepts.

Abhirup Adhikary
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    A super bird can go to space even without reaching 11.2 kn/s. This is the core or the Q and any correct answer. This one isn't wrong just because it asserts something true. The reasoning behind it can be deeply wrong. See @Austin Rojers comment. – Alchimista Mar 05 '20 at 08:48