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Questions tagged [escape-velocity]

The velocity an object must travel to successfully exit the gravitational influence of a body.

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Answering simple questions about black holes to someone not knowing GR

In the Newtonian description of a black hole, it is a gravitating astrophysical object for which the escape velocity exceeds the speed of light in vacuum ($c$). But what does this actually mean for a ...
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What if we set the exact equality $u^2=\frac{2GM}{R}$? Escape or not?

Let an object of mass $m$ is thrown up with an initial velocity $u$ from a spherical gravitating body $A$ of mass $M$ and radius $R$. Let us assume that when it reaches a height $h$ its velocity ...
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How does General Relativity explain escape velocities?

In general relativity, objects follow the shortest possible path through curved space-time called a geodesic and that there exists no such force of gravity which pulls objects, it is just because ...
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510 views

What is the escape velocity of a neutron particle (not neutron star)

I'm not sure if this question makes sense (if not maybe you can explain why) But if the neutron has mass and have a size, then it should have a escape velocity in the "surface" right? I know the ...
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1answer
55 views

Gravitation and escape speed [closed]

I applied conservation of energy at the surface and at the centre of earth which brought me to equation $$- \frac{GMm}{R} =\frac{1}{2} m v^2$$ Having asked my sir, he said that gravitational potential ...
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1answer
54 views

Escape velocity of Kerr black Hole [duplicate]

Do the event horizon of Kerr black Hole have escape velocity is equal to the speed of light same Schwarzschild black hole?
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46 views

Could a rover drive to orbital velocity?

Could a rover, assuming it is on a perfectly smooth sphere in space, eventually reach orbital velocity? Would there be a limit on the possibile speed?
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70 views

At what velocity will the moon be able to escape the earth's orbit?

I haven't found an answer to this question online so correct me if I am wrong. This is the escape velocity equation: $v_{esc} = \sqrt{\frac{2GM}{r}}$ and by plugging the known values, this is the ...
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2answers
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What would happen if a planet's escape velocity exceeded the speed of light?

What would happen if a planet's escape velocity exceeded the speed of light? Would it also collapse into a black hole (by Heisenberg's uncertainty principle and Pauli's exclusion principle) or would ...
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5answers
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I don't understand why escape velocity is necessary [duplicate]

I have read multiple explanations of escape velocity, including that on Wikipedia, and I don't understand it. If I launch a rocket from the surface of the Earth towards the sun with just enough force ...
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1answer
76 views

Does space expansion mean the escape velocity at a black hole event horizon is strictly less than $c$?

The title pretty much sums it up. I could ask this question slightly differently; does the expansion of space cause the effective event horizon to shrink below what it would be for flat space? If so,...
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6answers
141 views

How is it possible to escape a gravitational body? [duplicate]

The velocity required to escape a gravitational body is termed escape velocity. But how is it possible for any object to escape a body if it's gravitational field acts over an infinite range, so the ...
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4answers
153 views

Why is escape velocity independent of direction of projection?

However, for any body projected with a velocity less then the escape velocity, the final maximum height will vary with variation in angle of projection. But why is this not the case in case of ...
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2answers
117 views

Relativistic kinetic energy has no upper bound, so why is there a Schwarzschild radius?

Schwartzschild radius is the distance from the center of a body at which, the escape velocity will be equal to the speed of light, i.e. when $\frac{2GM}{R} = c^2$. However, here it is assumed that the ...
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5answers
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What is $R$ in the formula for escape velocity?

From the escape velocity formula $$v_e = \sqrt \frac {2GM}R.$$ Some sources say it is the distance between two objects with mass $M$ and $m$. Some examples I have read, only used radius of the $M$. ...
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2answers
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Why are the dimensions of escape velocity correct?

How does this formula work, from a dimensional analysis perspective? $$ v_\text{escape} = \sqrt{\frac{2GM}{R}}$$ The way I'm thinking about it is that $G$ is in units $\text{N} \cdot \text{m}^2/\...
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What if I throw a ball downward with velocity greater than but near to escape velocity of earth [closed]

As escape velocity does not depend on the angle of projection what if I throw a ball downward with velocity greater than but near to escape velocity of earth, will escape earth gravitational field.
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What is the difference between orbital velocity and critical velocity? Are their values similar or not?

As critical velocity is the minimum velocity required to put a satellite into orbit. And orbital velocity is the velocity required to keep a satellite moving in an orbit.The value of critical velocity ...
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2answers
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Is this derivation for schwarzschild radius for a black hole of mass $M$ correct?

Consider a body of mass $M$. We know that light can’t escape a black hole. Speed of light being the highest possible could be set as the escape velocity.(??) Then $$\text{Escape velocity}^2=(2GM/r)$$ ...
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1answer
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What is the escape velocity in the Kerr metric? [duplicate]

In the non-rotating Schwarzschild metric there is a straightforward expression for the escape velocity in the radial direction, defined from the point of view of a stationary observer at that radius, ...
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6answers
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Can a massive object have an escape velocity close to $c$ and not become a black hole?

It is well-documented that a given body has a well-defined Schwarzschild radius, defining a minimum radius for its volume, given its mass, before it becomes a black hole. It is clearly true, also, ...
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4answers
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Formula of escape velocity

While establishing relation of escape velocity and radius , I confronted a problem . (i) $$v_e=\sqrt{\frac{2GM}{R}}$$ This states that $v_e$ is inversely proportional to the square root of radius ....
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1answer
287 views

Length contraction in GR

In general relativity, $\sqrt{1-v_{e}^2}$ (with $v_e$ the escape velocity as a fraction of the speed of light) is the factor by which time is dilated in a gravitational field. Is it also the factor by ...
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3answers
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What could force Earth to leave the Solar System? [closed]

Is it theoretically possible? I'm thinking of some possible ways, e.g 1) large enough asteroid hitting Earth; 2) asteroid, with bigger mass than Earth, with a high velocity passing very near Earth.
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6answers
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Why is $v=\sqrt{\frac{GM}{r}}$ not a valid equation for escape velocity?

Firstly, I know that the equation for the escape velocity is $$v_{\text{escape}}=\sqrt{\frac{2\,GM}{r}}\tag{1}$$ and understand it's derivation. The following is such a simple derivation; for a test ...
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3answers
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Is this definition of “escape velocity” correct? [duplicate]

According to Wikipedia: In physics, escape velocity is the minimum speed needed for an object to escape from the gravitational influence of a massive body. But, say, I have a spaceship in low ...
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2answers
265 views

Is this the correct equation for Gravitational Potential Energy in Relativity?

If I understand correctly the equation for kinetic energy in relativity is $$ E_k= mc^2 \left(\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1\right) \;,$$ and the equation for escape velocity in General ...
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Escape velocity [duplicate]

I don't understand what escape velocity is. I know escape velocity from the earth is 11,186m/s. If a rocket is launched from the surface of the earth with initial speed of 11,186m/s, does it escape ...
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1answer
202 views

What are the conditions for an orbiting satellite of the earth to escape into space? [closed]

I am confused whether the increase in its velocity is enough for it to escape. Also, will the satellite escape if suddenly stopped moving in its orbit or fall back to the earth?
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3answers
117 views

Is the weight of an object moving at escape velocity equal zero?

If an object would be accelerated to the escape velocity would it's weight be equal to zero? Say I throw a ball from Earths surface (assuming frictionless atmosphere) upwards at 11.186km/s is it's ...
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2answers
379 views

Is Speed of light the Escape velocity of the Universe?

If speed of light is the escape velocity of a Black Hole, Why cannot it be assumed that it is the escape velocity of this Universe OR that we live inside a Black Hole?
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Does escape velocity require you to cross Moon's orbit?

Escape velocity is the velocity required to project an object from an object's (here, the Earth's) surface so that it "escapes" the gravity of that object (or in our case, the Earth's gravity). Now, ...
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1answer
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Escape velocity for an arbitrary metric in General Relativity

It's a known calculation how to derive the escape velocity of a system following the Schwarschild Metric. It comes out to be, if I am not wrong $$v = c\sqrt{2GM/Rc^2 - (2GM/Rc^2)^2}$$ So, is there a ...
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1answer
905 views

At what temperature will the hydrogen molecules escape from earth's surface? [duplicate]

At what temperature will the hydrogen molecules escape from the earth's surface?
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1answer
561 views

Escape velocity of the solar system?

I'm having a lot trouble with this problem. I need the minimum escape velocity for the (earth sun) solar system. I can't simply integrate the potential with respect to radius since this changes with ...
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1answer
105 views

Escape velocity given at an angle [duplicate]

We know that the escape velocity of Earth is about 11.2Km/s but what if we give that same velocity to an object at any angle let's just take 30° will it still escape from Earth's gravitational field ...
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Escape velocity from a rotating black hole

Under Newton, the escape velocity is $$v_{esc} = \rm c \ \sqrt{r_s/r}$$ where $\rm r_s=2 \ GM/c^2$. In the nonrotating relativistic case (the Schwarzschild case) the radial escape velocity is the ...
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Shouldn't the escape velocity of earth (with respect to earth) be less than $\sqrt{\frac{2GM}{R}}=11.2\,\mathrm{km/s}$

We know that the escape velocity of earth is, $$\sqrt{\frac{2GM}{R}}=11.2\,\mathrm{km/s}$$ Where $G=6.67×10^-11$ $M=\text{mass of earth}$ $R=\text{radius of earth}$ So if throw a object ...
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Escaping the Gravity well of the Moon

How much energy would it take to get 1 kg from the Moon's surface to Earth? Would You aim for Lagrange Point 1 or would you launch in the opposite direction that the moon is orbiting?
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Question on Escape Speed derivation

Reading lecture notes, I have some questions on this derivation's assumptions. - It must gain GMEm/RE in Gravitational Potential Energy (where ME is mass of the earth and RE is radius of the Earth)? ...
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2answers
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Mathematical relationship between escape speed and orbital speed

I am a high school student in AP Physics C. We are currently on our gravitation unit, and one of my homework questions goes like this: Show that the escape speed, $v_e$, from a planet is related ...
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1answer
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Upper limit of gravity

Now I don't mean maximum gravity because there is no maximum gravity. What I mean is what is the escape distance? In other words, how far would I have to be from a mass to get away from its gravity? ...
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4answers
230 views

Escaping from a supermassive black hole

At a supermassive black hole's event horizon the escape speed is, of course, the speed of light. At the same time, Newton's Law of Gravitation $F=G* m1*m2/r^2$ would predict that the gravitational ...
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1answer
347 views

Speed to throw something into space

I'm new here because I think I need some help. Our teacher gave us the task to find out how fast you would have to throw something upwards (friction and mass are not considered) to get it to leave the ...
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3answers
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Why doesn't hydrogen gas exist in Earth's atmosphere?

The root mean square velocity of hydrogen gas at room temperature is: Gas constant: $R=8.31\ \mathrm{J\ K^{-1}\ mol^{-1}}$ Molar mass of hydrogen gas: $M=2.02\times10^{-3}\ \mathrm{kg/mol}$ $$\begin{...
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1answer
2k views

Trajectory of the body when it is projected with greater than escape velocity

I know that if we project a body with velocity equal to escape velocity the body will fly to infinity but after reaching there it would have no energy as such, so it is the minimum velocity in fact to ...
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4answers
366 views

Where is gravity “potential energy” gone when object has escape velocity?

If an object leaves Earth with the escape velocity, meaning it'll never fall back on Earth, where does the energy go? You can't say it's converted to "potential energy" anymore because the object will ...
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1answer
120 views

Exit Velocity (sort of) [closed]

Why can't a vehicle just fly into outer space at a constant velocity of, say, 50 mph instead of having to achieve "exit velocity"?
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178 views

Why do we get 2 different answers for escape velocity, when we apply different laws to calculate it?

To measure the escape velocity, if I use the equation - $$\frac{-GMm}{r^2}=\frac{v.dv}{dr} $$ and I put my final distance to be $\infty$ , then I get the answer, $$u = \sqrt\frac{2GM}{R} \;. \...
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How come escape velocity isn't imaginary?

There's gotta be a simple explaination for this. 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 ...