The body put to circular orbit of the planet and which is, in fact, its satellite has the first cosmic speed. Overcoming attraction force, it will horizontally move over the surface of the planet, without falling and without reducing a trajectory.
Instruction
1. Let's consider the object which is already the artificial Earth satellite, that is making the movement on a circle. Such motion is not neither uniform, nor ravnoperemenny. The vector of speed of v is sent to each timepoint on a tangent, and a vector of acceleration of a – to the center of the planet. It is natural that during the movement these vectors constantly change the directions. But modules of sizes remain invariable.
2. It is convenient to consider the movement of a body concerning Earth, i.e. in a noninertial reference system. In this case the body is affected already by two forces: the gravity seeking to "skhlopnut" a body with Earth, and centrifugal, kind of pushing out to the external environment. Remember how "takes out" you when you ride a carousel. So, as the satellite does not fall and moves from a constant on the module speed, it is necessary to accept equality two these silt.
3. The gravity directed "inside" is calculated under the gravitational law: F (drafts) =GMm/R^2 where G is a gravitational constant, M – the mass of the planet, m – the mass of the satellite, R – planet radius. Centrifugal force is connected with centrifugal acceleration and body weight: F (center) =ma, at the same time acceleration can be calculated as a=(v^2)/R. Here v is the required speed, the first space. Thus, the total equation has an appearance: GMm/R^2=m(v^2)/R. From here it is easy to express speed: v= √ (GM/R).
4. Having substituted all known numerical data in result, you receive that the first cosmic speed of Earth is km/s v=7.9. Cosmic speeds can be calculated as well for other planets and celestial bodies. So, for the Moon it is 1.680 km/s. It is curious to notice that cosmic speed does not depend on the mass of the satellite in any way unless a dimensional object will need more fuel for achievement of it.
5. The collected as the designer, space rocket consists of several levels. Each of steps is equipped with own engine and fuel reserve. The first step, the heaviest, has the most powerful engine with the maximum volume of the fuel tank. Exactly thanks to it the rocket gathers necessary dispersal. After fuel of level is spent, the step "comes unfastened". It is so possible to save on transportation of empty containers very strongly. Then the following levels get into gear, and the last will take out the device into an orbit where that will be able to fly long enough without any fuel expenses.