For the sake of simplicity, unless stated otherwise, we will assume that an object is attempting to escape from a uniform spherical planet by moving directly away from it along a radial line away from the center of the planet and that the only significant force acting on the moving object is the planet's gravity.
Escape velocity is actually a speed not a velocity because it does not specify a direction: no matter what the direction of travel is, the object can escape the gravitational field provided its path does not intersect the planet. The simplest way of deriving the formula for escape velocity is to use conservation of energy. 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, it will be an infinite distance away from the planet, and its speed will be negligibly small and assumed to be 0. Kinetic energy K and gravitational potential energy U g are the only types of energy that we will deal with, so by the conservation of energy,. The same result is obtained by a relativistic calculation, in which case the variable r represents the radial coordinate or reduced circuference of the Schwarzschild metric.
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. 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 planet or moon. On the surface of the Earth, the escape velocity is about However, at 9, km altitude in "space", it is slightly less than 7. The escape velocity relative to the surface of a rotating body depends on direction in which the escaping body travels.
The surface velocity decreases with the cosine of the geographic latitude, so space launch facilities are often located as close to the equator as feasible, e. The barycentric escape velocity is independent of the mass of the escaping object.
It does not matter if the mass is 1 kg or 1, kg, what differs is the amount of energy required. For a mass equal to a Saturn V rocket, the escape velocity relative to the launch pad is When the mass reaches the Andromeda Galaxy , Earth will have recoiled m away from the mutual center of mass. Ignoring all factors other than the gravitational force between the body and the object, an object projected vertically at speed from the surface of a spherical body with escape velocity and radius will attain a maximum height satisfying the equation [8].
If an object attains escape velocity, but is not directed straight away from the planet, then it will follow a curved path. Although this path does not form a closed shape, it is still considered an orbit. Assuming that gravity is the only significant force in the system, this object's speed at any point in the orbit will be equal to the escape velocity at that point due to the conservation of energy, its total energy must always be 0, which implies that it always has escape velocity; see the derivation above.
The shape of the orbit will be a parabola whose focus is located at the center of mass of the planet. How does propulsion work? What is an orbit? What causes an orbit to happen? What is gravity? What is a satellite? How do spacecraft use an orbit to move from planet to planet? What is thrust? Lee, Leeds UK There is a big difference between an object being aimed vertically upwards and shot out of a cannon and a powered rocket. The ball shot from the canon receives energy only as it passes through the barrel, from then on it is unpowered and slows down as it climbs through the earths gravitational field.
Escape velocity refers to this case, not a powered rocket. Incidentally the mass of the ball does not effect the escape velocity if there is no atmospheric friction, which means that an elephant and a mouse would both have to be given the same escape velocity if launched from the surface of the moon!
As such an object travels upwards it will of course be slowed by gravity, but at the same time an object that moves upwards from the earth the effect of gravity gradually dimishes. If you begin travelling upwards too slowly gravity will bring you back down to earth.
If you start out travelling fast enough, whilst gravity will slow you down it will not be sufficient to bring you back down to earth. The escape velocity is the break point between these two alternatives. The escape velocity is of course dependent upon the distance from the earth or indeed any large body , diminshing as you travel away.
Therefore if you started the earth's surface and travelled upwards at the escape velocity, although your velocity would diminish due to gravity it would still remain at what would be defined as the escape velocity.
You could of course escape from earth's gravity if you could continuously move at even a very low speed. The problem is maintaining this speed against the pull of gravity.
To do so you would need to introduce some other force, at which point the concept of escape velocity is no longer applicable. These values are at ground level. The greater the planet mass the greater the gravitational pull. To escape the sun it is around miles per second!
That is why light cannot even escape from the surface! If you're going at escape velocity you don't need any more energy to escape from the Earth, because your kinetic energy is already enough assuming you don't lose it; for example air drag. But you can go more slowly if you either spend more energy, or if you go ballistic from higher altitude. Ian Woollard, UK So how do you explain a helium filled balloon with no thrust and no persistent velocity, travelling at minimal speeds and still being able to leave Earth gravitational pull, assuming no gas is lost and the balloon remains in tact?
The technology exists and has been used to escape earth's atmosphere at a much slower speed. However, the technology is highly classified and is only available to a select few. One point nobody has made is that gravity is acceleration and to beat it you need opposite acceleration something your chair is doing at them moment , so you would be accelerating away from earth.
The closest Lagrange point areas of flat space-time of the moon would be the obvious target as you wouldn't then be pulled back to earth - because otherwise Earth's gravity will just take too long to reduce sufficiently - and anyway, you'd be stuck in deep space.
As the fuel weighs a considerable amount, and needs sizable containers, there are efficiency reasons for burning it all as quickly as possible while dumping spent containers en route - standard rocket style. However, your rocket wouldn't have to endure such huge tolerances, and I guess the structure could therefore be much lighter. Ok, now I might be making Mr Area 51 sound sensible but I'm beginning to see traction in a variant of the idea Perhaps someone could correct me, but if a rocket accelerated directly up not orbital acceleration as usual - I mean it's the same Newton requirement after all , burnt fuel reasonably quickly but never reaching anything like 25K, only enough to drift to a near stop at say L4, then couldn't we slingshot it on L4 is it possible to slingshot a convex Lagrange?
Surely it is. Or say if you're going to the moon, why provide more energy than the journey requires by insisting on reaching EV with a orbital route? Am I missing something here? David, Peterborough, United Kingdom This is a big question - Can a Space vehicle take say three weeks to get to the Moon but travelling at a far slower speed. What is the fuel required to do that and would it be possible? The high velocity used at the moment is get into orbit around the earth however if you wanted to travel to the moon couldn't you do it slower but over a longer period of time?
Obviously if you didnt go into orbit around the moon you would have to be able to slow down so that you wouldn't crash into it. It does seem that if you had more time you could do things at slower pace Roy, Cape Town South Africa Add your answer.
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