[Physics] Is escape velocity the same for all objects

Question

Would a lighter-than-air craft in the mid atmosphere at 80,000 feet altitude need to achieve the same velocity to escape earth gravity as the space shuttle?

Answer 1

Yes. Escape velocity does not depend on the flying object's mass, but only on that of the earth. The precise formula is given by

$$v_e=\sqrt{\frac{2GM}{R}},$$

where $G$ is the gravitational constant, $M$ the mass of the earth and $R$ the object's distance from the center of the latter.

This is of course only true if one ignores the interaction between the atmosphere and the vehicle.