The velocity an object must travel to successfully exit the gravitational influence of a body.

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Escape velocity for Schwarzschild metric

I can't fill in the gaps in my solution to this and assistance or a reference would be appreciated. The question begins with the straightforward derivation of the EoM for a massive particle orbiting ...
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How can escape velocity be independent of the direction of projection of a body?

I read that the escape velocity of a body is independent of the direction of projection. For example, I could throw a ball at $11.2$ km/s velocity horizontally, and it would still leave earth. I am ...