Escape velocity is the minimum speed required for an object to break free from the gravitational pull of a celestial body, such as a planet or moon.
Gravitational potential energy is the energy an object possesses due to its position within a gravitational field, such as the Earth's gravitational field.
Escape velocity can be calculated using the equation: Ve = √(2GM/r), where Ve is the escape velocity, G is the gravitational constant, M is the mass of the celestial body, and r is the distance between the object and the center of the celestial body.
Escape velocity is significant because it determines whether an object can break free from the gravitational pull of a celestial body and enter into orbit or continue on a trajectory into space.
The shape of a gravitational potential energy surface affects escape velocity because it determines how much energy an object must have to escape the gravitational pull of the celestial body. A steeper potential energy surface requires a higher escape velocity, while a shallower surface requires a lower escape velocity.