The second cosmic speed is called also parabolic, or "the release speed". The body having insignificant weight in comparison with the mass of the planet is capable to overcome its gravitational attraction if to tell him this speed.
Instruction
1. The second cosmic speed – the size which does not depend on parameters of the "running-away" body, and is defined by the radius and mass of the planet. Thus, it is its characteristic size. The first cosmic speed needs to be given to a body that it became the artificial satellite. At achievement of the second - a space object leaves gravitational field of the planet and becomes the satellite of the Sun, like all planets of the solar system. For Earth the first cosmic speed is 7.9 km/s, the second – 11.2 km/s. The second cosmic speed of the Sun is equal to 617.7 km/s.
2. How to receive this speed theoretically? It is convenient to consider a task "since other end": let the body fly from an infinitely far point and falls to the Ground. Here the speed of "falling" also needs to be calculated: it needs to be reported to a body to save it from gravitational influence of the planet. Kinetic energy of the device has to compensate work on overcoming force of an attraction, exceed it.
3. So, when the body moves away from Earth, force of an attraction makes negative work, and as a result kinetic energy of a body decreases. But in parallel with it also the force of an attraction decreases. If energy of E is equal to zero before force of an attraction addresses in zero, the device "will plummet" back to Earth. According to the theorem of kinetic energy of 0 (mv^2)/2=A. Thus, (mv^2)/2=-A where m is the mass of an object, A is work of force of an attraction.
4. Work can be calculated, knowing the mass of the planet and a body, planet radius, value of gravitational constant G: A=-GmM/R. Now it is possible to substitute work in a formula of speed and to receive that: (mv^2)/2=-GmM/R, v= √-2A/m= √ 2GM/R= √ 2gR=11,2 km/s. From here it is visible that the second cosmic speed is more than first space by √2 times.
5. It is necessary to take into account the fact that the body interacts not only with Earth, but also other space bodies. Having the second cosmic speed, it does not become "truly free", but becomes the satellite of the Sun. Only having reported to the object which is near Earth, the third cosmic speed (16.6 km/s) it is possible to bring it and out of an action field of the Sun. So it will leave gravitational fields of both Earth, and the Sun, and in general will take off out of borders of the Solar system.