Escape velocity is the minimum velocity an object needs to attain in order to escape the gravitational pull of a celestial body, such as a planet, moon, or star, without any further propulsion. It is the speed required for an object to overcome the gravitational attraction and achieve an unbound trajectory, essentially allowing it to "escape" from the gravitational field.
To understand why simply going very slowly for a very long time wouldn't allow you to escape gravity, it's important to consider the relationship between gravitational potential energy and kinetic energy.
When an object is near the surface of a celestial body, such as the Earth, it has a certain amount of potential energy due to its position in the gravitational field. As the object falls towards the center of the celestial body, it converts potential energy into kinetic energy. If the object were to slow down or come to a stop, all of its kinetic energy would be converted back into potential energy, bringing it back to its original position.
If you were to travel slowly, you would not have enough kinetic energy to overcome the gravitational pull and escape the celestial body's influence. No matter how long you travel at a slow speed, gravity will continue to pull you back until you eventually come to a stop and fall back towards the celestial body.
To escape the gravitational field, you need to reach a velocity that allows you to have enough kinetic energy to counteract the gravitational potential energy. This is why a specific minimum velocity, known as escape velocity, is required. By achieving escape velocity, you can overcome the gravitational pull and continue moving away from the celestial body without being pulled back.
It's worth noting that escape velocity depends on the mass and radius of the celestial body. For example, the escape velocity from Earth is about 11.2 kilometers per second (km/s), while the escape velocity from the Moon is much lower, around 2.4 km/s, due to its lower mass and weaker gravity.