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Kaxa2000
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Assuming a vacuum above the Earth's surface
The simplest thing to do is to use "conservation of energy". The gravitational force on the rocket is GMm/r2 where G is the universal gravitation constant, M is the mass of the earth, m is the mass of the spaceship and r is the distance from the center of the earth. The work necessary to "escape from earth" is the integral of that, with respect to r, from the surface of the Earth to an infinite distance away. Assuming that you start with initial speed v and apply no more force (not what a spaceship does but the standard way of computing "escape velocity", you must have that much kinetic energy to exchange for potential energy. Set that integral equal to (1/2)mv2 and solve for v. Notice that the mass of the space ship, m, appears on both sides of the equation and can be cancelled.Kaxa2000 said:Assuming a vacuum above the Earth's surface
Escape velocity is the minimum speed required for an object to break free from the gravitational pull of a larger body, such as a planet or star.
Escape velocity can be calculated using the formula v = √(2GM/R), where v is the escape velocity, G is the gravitational constant, M is the mass of the larger body, and R is the distance from the center of the larger body to the object.
The escape velocity from Earth is approximately 11.2 kilometers per second (km/s) or 6.95 miles per second (mi/s). This is the speed required for an object to escape the Earth's gravitational pull and enter into orbit around the Earth.
The escape velocity is directly proportional to the mass of the larger body. This means that the larger the mass of the body, the higher the escape velocity required for an object to break free from its gravitational pull.
Yes, it is possible for an object to exceed escape velocity. This would result in the object leaving the gravitational influence of the larger body and entering into an unbound trajectory. However, this would require additional energy to be expended, such as through a rocket or other propulsion system.