Escape velocity Definition and 220 Threads

We know that the escape velocity at the schwarzchild radius is c. Since the escape velocity is defined as the velocity needed to escape from the gravitational field, to reach a total energy of 0 at infinity: Doesn't this mean that an object falling from infinity starting at rest, to the...

Homework Statement What is the escape speed of a spaceship fired in space, far away from Earth but at the same distance from the sun as the Earth. Homework Equations Ve = (2GM/r)^0.5 The Attempt at a Solution The problem is that I don't know what the M or r is since it is fired...

Homework Statement A meteoroid with a velocity (when the effect of the Earth's gravity has been eliminiated) of 49.9 km/s when it is at a distance of 1.50x10^11m from the sun. (a) Using energy calculations show that this object has an open orbit and is therefore not restricted to our solar...

Hey guys so this question I'm kind of stuck on, Our solar system, starting from Saturn's orbit. So I know the formula is v = sqrt(2GM/r) But not sure what to put for the mass and radius, am i including saturn and planets like uranus and neptune only or all the satellites and stuff to like...

At 293K, helium atoms have a root mean square speed of about 1.35 km/s, whereas escape velocity at the Earth's surface is about 11km/s. Explain why is it nevertheless possible for helium atoms to escape from the Earth into space. Is it because near the top of the atmosphere the temperature...

Hi. I've been wondering, how could I calculate the escape velocity for a body of mass m which is a certain distance r from the center of the Earth to escape the entire solar system, assuming the distance from the center of mass (aprox. from the sun because it's about 99% of the mass of the solar...

Can anyone help me work out the energy required for a rocket powered craft to reach escape velocity. What I'm looking to find is the amount of fuel (in any measurement) that will need to be burned simultaneously to achieve this for a craft carrying a payload of 5 to 10kg. Any help/links to...

Need some help with solving bet Do spacecraft (so we're talking about powered object) have to reach escape velocity in any point of travel to leave Earth and if so, can you prove it by any scientific definition ?

Homework Statement The gravitational acceleration of the moon is 1.6 m/s^-2. Estimate its escape velocity and explain how you did this? Homework Equations v= square roots(2GM/r) The Attempt at a Solution I have absolutely no idea how to do this question at all

The escape velocity on Planet X is the speed the rocket needs in order to never fall back down again in a universe in which X is the only object. In order for the rocket to not fall back down, its velocity to never become negative, how far away does the rocket have to be when the velocity is 0...

Why is there an inherent presumption imbedded in the field of physics that gravitational force is exempt from the rules of relativity? The presumption is based on the non-relativistic expression for escape velocity: v=(2MG/r)^.5 Thus, with a very large mass or a very small radius...

Homework Statement The radius of Mercury (from the center to just above the atmosphere) is 2440 km (2440103 m), and its mass is 0.31024 kg. An object is launched straight up from just above the atmosphere of Mercury. (a) What initial speed is needed so that when the object is far from Mercury...

Well this question I've had since high school (first year mech), how would i calculate escape velocity of a gas if i know volume, diameter of the hole, pressure, temprature and mass.

1- F = mk/r^2 ... k is -ve value ...why ?? please in concise way 2- for escape velocity ... v( inital) = root ( 2gR )... with proof thank u

Hello, can you can tell me if this is correct? I thought the height would turn out close to where satellites orbit, but it comes out to about 5.5 million miles away! I was very surprised by this, that's about 20 times further than the moon. Here's what I used Escape velocity: Ve = sqrt(2GM/r)...

How are space shuttles accelerated to escape velocity? Would it be possible to build a rocket at home that would be capable of getting into space if it were to use liquid hydrogen and oxygen as fuel?

In a lot of calculus texts, there's an example of an application of differential equations involving escape velocity. They write acceleration is dv/dt but then write it as \frac{dv}{ds}\frac{ds}{dt} That just looks like an application of the chain rule but what is the meaning of dv/ds...

What is the escape velocity of nitrogen heated to 325 K?

I have a question on escape velocity. Would a planet with 60% of Earths gravity support a relatively thick atmosphere? It would contain nitrogen, oxygen, water vapor and carbon dioxide. This planet would get the same amount of solar radiation and luminousity the Earth does. Would the gases...

can someone please very briefly explain why the escape velocity of an object is given when the total mechanical energy (KE + potential energy) on an object is zero Thanks

Hi, A space probe is launched from the equator in the direction of the north pole of the Earth. During launch the energy given to the probe of mass m is E=(3GMm/RE) Deduce that the Space probe will not be able to travel into deep space. That is a past paper question my teacher gave...

Homework Statement Determine the escape velocity of a planetary body that has a radius 5 times greater than its Schwarzschild radius. Homework Equations Schwarzschild radius=(2GM)/c^2 escape velocity=√(2GM/r) The Attempt at a Solution v=√((2GMc^2)/(10GM))=√(c^2/5) Is this...

I apologise if this isn't the right place to post this. If I was to calculate the escape velocity of a body, e.g. the Earth which is approx. 11.2km/s, could this then be used as the delta-v in the ideal rocket equation to calculate the mass ratio needed? This would be for both a trip to...

Distance expansion and escape velocity ("thought experiment") If you care to, it would help if you would check my arithmetic. I may have made one or more mistakes. Thanks to anyone who can show the conclusion here is wrong. The question came up if you have a pair of kilogram masses and you...

What is escape velocity?

Why doesn't the escape velocity depend upon the mass of body?

Homework Statement In the Solar neighborhood, the Milky Way has a flat rotation curve, with V(r)= Vc where Vc is a constant, implying a mass desnity profile ρ(r) ~ r^-2 Assume there is a cutoff radius R beyond where the mass density is zero. Prove that the velocity of escape from the...

Homework Statement We assume an asteroid with density similar to earth. An astronaut performs a spot jump of 1 meter. Which is the maximum radius of the asteroid in order to escape the astronaut from the asteroid? Homework Equations Vesc=√2GM/R=R√8ΠGρ/3 The Attempt at a Solution...

Homework Statement The acceleration of gravity on the surface of Mars is 0.38g. The radius of Mars is 2100 miles. Determine the velocity of a particle projected in a radial direction outward from Mars and acted upon by only the gravitational attraction of Mars by first modeling the motion...

I'm having some difficulty with a homework problem which states: A cannonball is shot straight up out of a very powerful cannon located at the South Pole and reaches a maximum height of one Earth radius above the surface of the Earth. What was its initial speed? How long did it take to reach...

So I looked at a neat derivation for what the minimun escape velocity is, and It was pretty clever. Because this is conserved: KE + PE = 1/2 *mv^2 + -GMm/r You can find what the velocity would have to be to get to infinity with zero velocity 1/2 *mvesc^2 + -GMm/r = 1/2 *m(0)^2 +...

can someone explain physically why escape velocity is independent of angle of projection.

Okay, in the Escape Velocity Equation, with the usual notations, v2=2gR2/r + (v02-2gR) a few articles like [PLAIN]"www.math.binghamton.edu/erik/teaching/02-separable.pdf"[/URL]give the following explanation: ... ... ...(implying that v0>=√2gR) That raises a few doubts in my mind...

: Derive a relation for the escape velocity of an object, launched from the center of a proto-star cloud. The cloud has uniform density with the mass of M and radius R... Ignore collisions between the particles of the cloud and the launched object. If the object were allowed to fall...

Homework Statement A satellite is in orbit around a planet with orbital speed determined to be 7080 m/s. Find the escape velocity from the planet from this position of its orbit. Homework Equations EV=sqrt(2GM/r) The Attempt at a Solution With a problem like this, I would just...

Earth's Escape velocity is approximately 11.2 km/s, which is derived from the equation v = (2GM/R)^1/2. I know that this equation is derived from energy conservation, K + U = 1/2mv^2 + (-GMm/r). My question is regarding the addition of other masses to this equation based on location...

Hi guys! I want to ask something about escape velocity. I know the definition of EV "escape velocity is the speed at which the kinetic energy plus the gravitational potential energy of an object is zero"(wikipedia). Can we approach the problem by equalling the attractive force to the...

Homework Statement A 20000kg spacecraft carrying 17000kg of fuel starts at the surface pf the earth, (Mass=6*1024kg, radius of 6.3*10^6 m). The liquid oxygen and kerosene rocket provides an exhaust velocity of 3500m/s. a.) How much high can the rocket go above the Earth's surface? b.)Once...

Homework Statement A scientist wants to put an 100kg experimental package in orbit around the Earth. The cost of deployment depends on the amount of extra energy it takes to get it into the required position i.e. how much more energy is used than just sending the rocket up there. a)...

Homework Statement A spherical asteroid has a density of 2600 kg/m^3. I throw a ball at the speed on 20 m/s. If the ball is to travel in a circular orbit, what is the largest radius of the asteroid possible to accomplish this? Homework Equations these are the equations I used.. escape...

Homework Statement An Object is fired vertically upward from the surface of the Earth ( of radius RE ) with an initial speed vi that is comparable to but less than the escape speed vesc Show that the object attains a maximum height h given by h=\stackrel{R_{E}v^{2}_{i}}{v^{2}_{esc}-v^{2}_{i}}...

I am trying to understand the existence of orbits apart from the elliptical one. I have used the following line of thought. Consider an object moving from infinity towards a planet. The object has kinetic energy alone at infinity. But it develops a potential energy as it comes closer to the...

I have a problem where it ask to find the period/time(using Kepler's 3rd law) of an unpowered spacecraft to move from Earth's orbit to Mars orbit using the transfer orbit approach. I found P/T using kepler's 3rd law but the second part ask to find how fast the spacecraft need to be moving at...

I tried finding the equation for terminal velocity in a broader attempt to understand planetary orbits better. According to wikipedia's two derivations (one of which i don't understand very well) I'm off by a factor of \sqrt 2 . I would greatly appreciate help in finding my thinking/math...

http://img682.imageshack.us/i/77482562.jpg/" I don't really understand these questions... Is there anyone who could tell me HOW to solve them? I don't ask about ONLY answers, I just want to understand how to solve these types of exercises. The things I know: 1. the centrifugal force =...

I have been told that there is no interaction between the gravitational fields of the sun and any planet, but the issue continues to stimulate my curiosity. If the Earth orbits the sun at 30km/s, how could anything achieve an orbital speed around Earth at greater than 30km/s without...

Homework Statement Three wires are made of same materials. Which wire will have the greatest elongation? wire1: length: 50cm, diameter: 0.5mm wire2: length: 100cm, diameter: 1mm wire3: length: 300cm, diameter: 3mm Homework Equations The Attempt at a Solution I know, the wire having greatest...

I was trying to understand the similarities and differences between electrostatics and standard Newtonian mechanics, in particular gravitational formulas. One thing I was curious about is escape velocity. For gravity I've learned that it's sqrt(2GM/R). But for electrostatics, suppose I was...

Homework Statement A certain spherical planet which is not rotating has a radius of 6.36 x 105 m and a mass of 1.89 x 1021 kg. At what minimum speed would a vehicle traveling along its surface just begin to leave the ground? Homework Equations FC = mv2/r FG = GMm/d The Attempt at a...

Homework Statement I'm having a hard time relating the escape velocity equations, sqrt(2GM/r) to sqrt(2gr) The Attempt at a Solution I know that both equations mean the same thing, but I can't figure out how to get from the first equation to the second