Final answer:
The formula for escape velocity is Vesc = √(2GM/R), where G is the gravitational constant, M is the mass of the body being escaped from, and R is its radius. This demonstrates the escape velocity is independent of the mass of the escaping object.
Step-by-step explanation:
The correct formula for escape velocity (Vesc) is derived from the principle that the total mechanical energy at the surface of an astronomical body should be equal to zero if an object is to escape its gravitational influence without further propulsion. Taking into account the gravitational constant (G), the mass (M) of the body being escaped from, and the radius (R) of the body, the formula for escape velocity is:
Vesc = √(2GM/R)
This equation indicates that the escape velocity does not depend on the mass (m) of the object attempting to escape. It only depends on the properties of the body being escaped from. As the energy an object needs to escape from a gravity well is purely based on the gravitational force exerted by the larger body (like a planet), the escape velocity is the same for all objects, irrespective of their mass.