Speed determines the possible trajectories around the Earth
If a rocket is launched from the surface of the Earth, it needs to reach a speed of at least 7.9 kilometres per second in order to reach space. This speed of 7.9 kilometres per second is known as the orbital velocity, referred to in German as the 'first cosmic velocity' – it corresponds to more than 20 times the speed of sound. At the start of the space age, Russian scientists applied the term 'cosmic velocities' to certain velocities that are important for space exploration. The 'first cosmic velocity', known as the orbital velocity, will bring a rocket or other projectile into orbit around the Earth. A slower projectile will fall back to Earth.
The 'second cosmic velocity' is the so-called escape velocity from the Earth: 11.2 kilometres per second. This is the speed a rocket should attain in order to be able to escape from the Earth’s gravitational field and fly to other planets. It follows from the laws of orbital mechanics that the escape velocity (11.2 km/s) is equal to the orbital speed (7.9 km/s) multiplied by 1.414 (i.e. by the square root of 2).
If a spacecraft travels fast enough it is also possible to leave the Milky Way behind
The 'third cosmic velocity' is the speed that a spacecraft needs to attain in order to be able to leave our solar system. This solar system escape velocity is about 42 kilometres per second (or 0.014 percent of the speed of light in a vacuum). Again, this is the product of the orbital velocity and the square root of 2. However, the orbital velocity now refers to the speed at which the Earth revolves around the Sun: about 30 kilometres per second multiplied by the square root of 2 equals about 42 kilometres per second. The ‘fourth cosmic velocity’ is the escape velocity from our galaxy - the Milky Way. It corresponds to about 320 kilometres per second.
It is important to bear in mind that these cosmic velocities are idealised values. For instance they do not take into account the loss of speed due to air resistance when a rocket is launched. Moreover, the values mentioned above are specific to the Earth and our solar system, and they do not apply to other parts of the universe.