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The earth rotates around the sun at speed of approximately $18.5$ miles per second. And the escape velocity of earth is $6.96$ miles per second. So the speed of rotation is greater than the escape velocity of earth. So why doesn't a object on earth escape away from earth's gravitational field?

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I think you are confusing speed necessary to escape from the Earth which you would want to compare with the speed an object has due to its rotation about the Earth's axis of rotation (through the poles) and speed necessary to escape from orbit around the Sun which you would want to compare to the Earth's orbital speed. Speed needed to escape the Sun is much higher. See this article for example.

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Velicity and speed are not absolute quantities but only relative to a specific reference frame. The escape velocity of Earth refers to the minimum speed of an object starting from the Earth's surface, allowing it to get an infinite distance. It is the speed in the Earth's reference frame.

The speed of Earth's rotation around the Sun is measured in the Sun's reference frame. Transforming the escape velocity from the terrestrial to the solar reference frame is possible. However, it would require considering the vector character of the velocity and is useless for practical applications.

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