Let the total residual mass of the rocket be m, and according to the conservation of momentum: mdv+vcdm = 0, so dv =-(vc/m) dm, integral, from 0 to v on the left and from m+p to m on the right, so v =-vc * ln [m/(m+p)] = vc * ln [(m+p)/.
Rocket use
At present, the rocket is the only vehicle that can make an object reach the speed of the universe, overcome or get rid of the gravity of the earth and enter space. The speed of the rocket is obtained by the operation of the rocket engine.
As early as 1903, tsiolkovsky derived the ideal velocity formula of a single-stage rocket: v = ω lnmo/MK, which is the so-called Tsiolkovsky formula. Ω is the injection speed of the engine, and Mo and Mk are the initial mass of the rocket and the mass when the engine is turned off (the propellant is used up) respectively. Mo/Mk is called the mass ratio of the rocket.
According to this formula, the rocket speed is directly proportional to the jet speed of the engine, and increases with the increase of the rocket mass ratio, that is, the rocket speed will increase when the engine mass decreases. Even with the best liquid hydrogen and liquid oxygen propellants, the injection speed of the engine can only reach 4.3 ~ 4.4 km/s.
Therefore, a single-stage rocket cannot send an object into space orbit, and a multi-stage rocket must be used to complete the space launch mission, that is, a rocket based on the relay principle can send a spacecraft into space orbit.
Launch vehicle structure
Whether it is a solid launch vehicle or a liquid launch vehicle, whether it is a single-stage launch vehicle or a multi-stage launch vehicle, its main components include a structural system (also known as an arrow structure), a power plant system (also known as a propulsion system) and a control system. These three systems are called the main system of the launch vehicle, and the reliability of the main system will directly affect the success or failure of the launch vehicle flight.
In addition, there are some systems on the launch vehicle that do not directly affect the success or failure of flight, which are composed of on-board equipment and ground equipment, such as telemetry system, external ballistic measurement system, safety system and aiming system.