How would I calculate the escape velocity from the earth?

In summary, to calculate the escape velocity for a spaceship from Earth's surface, one can use conservation of energy by setting the integral of the gravitational force equal to the kinetic energy and solving for the initial speed. This equation takes into account the universal gravitation constant, the mass of the Earth, the mass of the spaceship, and the distance from the center of the Earth. The mass of the spaceship can be cancelled out in the equation.
  • #1
Kaxa2000
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Assuming a vacuum above the Earth's surface
 
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  • #2
Kaxa2000 said:
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.
 
  • #3
What do you mean when you say the work is the integral of that with respect to r?
 
  • #4
Can you just set the KE of the object equal to the Gravitational force and solve for v? Wouldnt that give you the escape v?
 

FAQ: How would I calculate the escape velocity from the earth?

What is escape velocity?

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.

How is escape velocity calculated?

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.

What is the escape velocity from Earth?

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.

How does the mass of an object affect escape velocity?

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.

Can escape velocity be exceeded?

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.

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