Escape velocity earth confusion

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SUMMARY

The escape velocity on Earth is definitively 11 km/s, which is the minimum speed needed for an object to break free from Earth's gravitational pull without further propulsion. This velocity is measured relative to the Earth, and while the Earth's rotation contributes a surface speed of approximately 0.464 km/s at the equator, it does not affect the escape velocity itself. When launching a rocket eastward, the initial velocity provided by Earth's rotation reduces the required fuel to achieve orbital or escape velocity. Understanding these dynamics clarifies why the atmosphere does not escape Earth's gravity despite the high velocities of some molecules.

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  • Understanding of gravitational forces and escape velocity concepts
  • Basic knowledge of kinetic and potential energy equations
  • Familiarity with Earth's rotational dynamics
  • Awareness of orbital mechanics and satellite trajectories
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AakashPandita
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If escape velocity on Earth is 11 km/s and velocity of Earth is 30 km/s how is that the atmosphere doesn't escape the pull of earth.
Is the escape velocity with reference to Earth ? I don't think so because when finding the formula we add kinetic and potential energy and then equate to zero. If it is not then doesn't everything on Earth has velocity greater than escape velocity...
Please help me out.
 
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The escape velocity on Earth is relative to the earth. In the outer fringes of the atmosphere, a very tiny percentage of molecules will randomly end up with >= escape velocity. Escape velocity from the solar system, is relative to the Sun (with some effect from orbiting planets). There are a few satellites that have exceeded escape velocity from the solar system. A list of them from wiki:

http://en.wikipedia.org/wiki/List_of_artificial_objects_escaping_from_the_Solar_System
 
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If the escape velocity is relative to Earth then why is it that( i read in my book) that projectiles are projected in the direction of rotation of Earth ?
 
AakashPandita said:
If the escape velocity is relative to Earth then why is it that( i read in my book) that projectiles are projected in the direction of rotation of Earth ?
It's relative to the Earth centered non-rotating frame.
 
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AakashPandita said:
If escape velocity on Earth is 11 km/s and velocity of Earth is 30 km/s
At the equator, the surface speed of the Earth relative to it's center of mass is about 0.464 km/s. As posted by A.T., the escape velocity from the Earth is not affected by the Earth rotation, but by launching a rocket to the east at the equator the rocket would start with 0.464 km/s speed relative to the center of mass of the earth, reducing the fuel it would need to reach orbital or escape velocity speeds.
 
Thanks. It makes sense to me now,
 

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