Step 1: Understanding the Concept:
Escape velocity is the minimum velocity an object needs to break free from the gravitational attraction of a massive body.
It is derived by equating the kinetic energy of the object at the surface to the gravitational potential energy holding it there.
Step 2: Key Formula or Approach:
Kinetic Energy = Gravitational Potential Energy
$\frac{1}{2} m v_e^2 = \frac{GMm}{R}$
where $m$ is the mass of the object, $M$ is the mass of the earth, $R$ is the radius of the earth, and $G$ is the gravitational constant.
Solving for escape velocity $v_e$: $v_e = \sqrt{\frac{2GM}{R}}$.
Step 3: Detailed Explanation:
Looking at the derived formula $v_e = \sqrt{\frac{2GM}{R}}$:
$G$ is the universal gravitational constant.
$M$ is the mass of the planet (Earth).
$R$ is the radius of the planet (Earth).
The mass of the object being projected ($m$) cancels out during the derivation.
Therefore, whether launching a small satellite or a massive spaceship, the escape velocity from Earth remains the same (approximately $11.2 \text{ km/s}$).
It explicitly does not depend on the mass of the object to be projected.
Step 4: Final Answer:
It does not depend on the mass of the object to be projected.