What is Escape Velocity?
Escape velocity is the minimum velocity required for an object to break free from the gravitational pull of a planet, moon, or other celestial body without any additional thrust.
Derivation of Escape Velocity
To derive an expression for escape velocity, we can use the principle of conservation of energy.
- Let’s consider an object of mass ‘m’ at a distance ‘r’ from the center of the celestial body.
- The total mechanical energy of the object is the sum of its kinetic energy (KE) and potential energy (PE).
Using the equation for gravitational potential energy and kinetic energy, we get:
PE + KE = 0.5 * m * v^2 – G * (M * m) / r = 0, where M is the mass of the celestial body and G is the gravitational constant.
Solving for velocity ‘v’, we find the expression for escape velocity:
v = sqrt(2 * G * M / r).
Examples of Escape Velocity
On Earth, the escape velocity is approximately 11.2 km/s. This means that a rocket or spacecraft needs to reach this speed to escape Earth’s gravitational pull.
Case Study: Apollo Moon Missions
During the Apollo moon missions, the escape velocity from Earth was crucial for launching the spacecraft into lunar orbit and eventually landing on the moon.
Statistics on Escape Velocity
Escape velocities vary depending on the mass and radius of celestial bodies. For example, Mars has a lower escape velocity of 5 km/s compared to Earth.
