What is escape velocity?
“Escape velocity” is a misnomer, because it doesn’t refer to a velocity, but rather a speed. It is properly “escape speed”. The escape speed for a mass is the speed required to travel an infinite distance from said object. In other words (and taking Re to be the radius of the Earth), escape speed for Earth is the speed at r = Re such that speed at infinite r is 0. Obviously, that would take an infinite amount of time, but it is a useful theoretical exercise. As speed at infinite r is 0, kinetic energy is also 0. Gravitational potential energy is defined to be 0 at infinite distance, so at infinite distance, the total energy of the object is 0. Due to conservation of energy, that must be the energy of the object on the surface of the Earth. Therefore: E = (1/2)*m*v ^ 2 – (G*M*m)/Re = 0, when E is total energy, m is the mass of the object, v is the escape speed, G is the gravitational constant, M is the mass of the Earth and Re is as above. Solving for v, we find: v = sqrt( (2*G*M) / Re
Escape velocity is the velocity needed by a projectile on launch to exit the gravitational potential well of the object it is leaving. It is a mistake to think that escape velocity is needed to get to space. Actually much less is needed, since most of our space-destined objects are meant to stay in the gravity well of the Earth, in orbit, usually. Technically, since gravity is infinite in its reach, it takes an infinite time and energy to escape an objects pull. Practically, what needs to be done is to get an object away from the launching body enough that the launching body’s gravity becomes negligable. Even if you get off the Earth, you still have the sun’s gravity to overcome, so really we are in a hole in a bigger hole. To get away from the entire solar system has been done only twice, by the Voyager I and II spacecrafts. Incidentally, when a body is so dense it’s escape velocity (outside it’s surface) is the speed of light in a vacuum (3*10^8 m/s) it is, by definition, a “black ho
Escape velocity is the launch speed that is necessary for an object launched from the surface of an object (usually a planet) to escape the gravitational pull of that planet. For the earth, this speed is approximately 11 kilometers per second. That is to say, if you could launch something (a couch for instance) from the surface of the Earth at 11 km/s, it would escape the Earth’s gravity and continue on into space. Of course, this is ignoring wind resistance… so the real speed would have to be even faster.
Escape Velocity is quite a misnomer in that it has nothing to do with escaping a planetary body but has rather to do with entering orbit around it. The escape velocity is actually the speed required for any object to maintain orbit from a given altitude around a given mass. This escape (or orbit) velocity decreases with distance from the object and increases with the mass of the object or body . This term must have caused untold confusion over the years and should perhaps itself be projected away from the earth at whatever velocity it requires to escape it. As far as the velocity required to escape the earths atmosphere… well I hate to de-sensationalise this but walking speed would do just fine if maintained for an appropriate duration. If we explore this example, the misuse of the word ‘escape’ can perhaps be more easily excused: Maintaining a constant walking speed in the upwards direction would require constant power to be applied to the object. In reality, it iwould be more pract
Nothing ever escapes from gravity, any gravity. It’s the literal truth that you’re feeling the gravitational influence of Pluto right now, and it’s also sensing you — though not very much. So what really happens when something gets into orbit? You probably know that a bullet fired parallel to the earth starts falling as soon as it’s out of the muzzle, and falls to earth in a long curve. Suppose you were on a long, sloping hillside whose curve exactly matched the bullet’s descending curve. Now the bullet stays the same height above ground for as long as the slope continues (which can really happen). And for the time that it’s in flight, a bug traveling on it (ignore air resistance and any spin — maybe make it a cannon ball) would, after the initial bang, feel weightless. Since the cannon ball is falling freely (for as long as the ground falls away beneath it), the bug would have no sensation of weight, but would be like a passenger on one of those rides that just takes you up a tower
