lähdänopeus

Lähdönopeus, also known as escape velocity, is the minimum speed an object must attain to break free from the gravitational pull of a celestial body, such as a planet or moon, without further propulsion. It is a fundamental concept in orbital mechanics and astrophysics.

The formula for escape velocity is derived from the principle of conservation of energy. An object needs enough kinetic energy to overcome its gravitational potential energy. At the escape velocity, the object's total energy is zero, meaning it can travel infinitely far away from the body and will have zero velocity as it reaches an infinite distance.

The escape velocity depends on the mass of the celestial body and the distance from its center. For a spherical body of mass M and radius R, the escape velocity (v_e) is given by the equation v_e = sqrt(2GM/R), where G is the gravitational constant. This means that more massive bodies and smaller distances from their center result in higher escape velocities.

For Earth, the escape velocity at the surface is approximately 11.2 kilometers per second (about 25,000 miles per hour). This is why spacecraft need to reach such high speeds to leave Earth's atmosphere and enter space. The Moon has a lower escape velocity due to its smaller mass and radius. The Sun's escape velocity is significantly higher. Understanding escape velocity is crucial for designing spacecraft trajectories, calculating the orbital mechanics of satellites, and comprehending the dynamics of star systems.