Escape velocity

Push hard enough and a body leaves for good, coasting away and never returning. The threshold is escape velocity:

v_escape = √(2μ / r)

That is exactly √2 ≈ 1.41 times the circular speed at the same distance. Below it you are bound in an ellipse; at or above it your path opens into a parabola or hyperbola and you are gone.

Escape velocity depends only on where you start and how massive the attractor is — not on which direction you fire (as long as you clear the surface). It also does not depend on the mass of the escaping object: a pebble and a spaceship need the same speed to break free.