Approximate Methodology for Design Ballistic Calculation of Two-Stage Launch Vehicles

At the initial stage of building new models of rocket and space systems, so-called design ballistic calculations are usually performed. Due to the problems of deep space exploration and the creation of low-orbit satellite constellations with small spacecraft, the relevance of the tasks of design ballistics of launch vehicles has noticeably increased. The most cost-effective way to deliver small satellites to target orbits is to launch them using two-stage ultra-light launch vehicles powered by liquid propellants. To solve the problems of design ballistics of a two-stage launch vehicle, we expanded the technique of design ballistic calculation of the first stages of launch vehicles and tackled the problems of analytical determination of the characteristic velocity losses of the last stages of multistage launch vehicles. As a result, we introduce an approximate method for ballistic design calculation on the active part of the trajectory of two-stage launch vehicles when the payload is injected into a low Earth orbit with an arbitrary inclination. The paper considers the application of the developed technique on a specific example of injecting a payload into a circular polar orbit.

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