Space Trajectories. Launch on Orbit

The mission of a launch vehicle is to transport a satellite from the Earth's surface to a specified orbit. The lowest stable orbits are at altitudes of at least 200 km, beyond the Earth's atmosphere, and the speed of satellite entry is of the order of 8 km/s. Reaction propulsion is the only way to reach these kinematic conditions, at the cost of large quantities of fuel. As most of the trajectory takes place in a vacuum, it is not possible to use oxygen from the air, as is the case with most aircraft. All the fuel has to be taken on board at lift-off, resulting in a very high total mass, on the order of 100 times that of the satellite. Conventional launchers are expendable, meaning that no components are recovered for the next flight. The priority objective is to reduce mass by optimizing configuration and trajectory.

The configuration is optimized for a reference mission defined by the payload mass and orbit to be reached. Design choices concern the number of stages and propulsion technologies. Qualification of the launcher and its subsystems requires several years of study and testing, and the qualified configuration will then be identical for all flights. The launcher's overall performance over a range of missions enables it to be compared with competing launchers.

The ascent trajectory from ground to orbit lasts around 30 minutes, including 2 minutes spent in the lower atmosphere below 50 km. This part of the flight is the most demanding, due to the aerodynamic loads involved. The nominal trajectory is optimized to reach orbit with the lowest possible fuel consumption, while respecting the launcher's mechanical and thermal capacities and limiting the risk of failure. In-flight guidance recalibrates the control system in response to any disturbances encountered, so as to reach the target orbit precisely. A propellant reserve guarantees successful flight with a probability of around 99%.

This article presents the modeling of the launcher and its dynamics, methods for optimizing the configuration and trajectory, and guidance principles.