Escape Velocity Formula:
The escape velocity (vₑ) is determined by:
vₑ = √(2GM/r)
Where:
* G is the gravitational constant
* M is the mass of the celestial body (e.g., planet, star) the particle is escaping from
* r is the distance from the center of the celestial body to the particle
Explanation:
Notice that the formula for escape velocity doesn't include the mass of the particle (m). This means that a feather and a bowling ball, if launched from the same distance on Earth, would require the same escape velocity to escape Earth's gravitational pull.
Why doesn't the particle's mass matter?
The escape velocity is the minimum speed needed to overcome the gravitational pull of a celestial body. This means the particle has to have enough kinetic energy to counteract the potential energy from the gravitational force.
While a more massive particle has more kinetic energy at a given speed, it also experiences a stronger gravitational force. These two factors perfectly balance each other out, resulting in the mass of the particle not affecting the escape velocity.
