# Spacecraft Dynamics Employing a General Multi-tank and Multi-thruster Mass Depletion Formulation

## Abstract

Using thrusters for either orbital maneuvers or attitude control change the current spacecraft mass properties and results in an associated reaction force and torque. To perform orbital and attitude control using thrusters, or to obtain optimal trajectories, the impact of mass variation and depletion of the spacecraft must be thoroughly understood. Some earlier works make rocket-body specific assumptions such as axial symmetric bodies or certain tank geometries hat limit the applicability of the models. Other earlier works require further derivation to implement the provided equations of motion in simulation software. This paper develops the fully coupled translational and rotational equations of motion of a spacecraft that is ejecting mass through the use of thrusters and can be readily implemented in flight dynamics software. The derivation begins considering the entire closed system: the spacecraft and the ejected fuel. Then the exhausted fuel motion in free space is expressed using the thruster nozzle properties and the familiar thrust vector to avoid tracking the expelled fuel in the simulation. Additionally, the present formulation considers a general multi-tank and multi-thruster approach to account for both the depleting fuel mass in the tanks and the mass exiting the thruster nozzles. General spacecraft configurations are possible where thrusters can pull from a single tank or multiple tanks, and the tank being drawn from can be switched via a valve. Numerical simulations are presented to perform validation of the model developed and to show the impact of assumptions that are made for mass depletion in prior developed models.

## Keywords

Variable mass systems Equations of motion Spacecraft dynamics## Notes

### Acknowledgments

This work was supported by the Italian Space Agency (ASI) in collaboration with the Cultural Association of Italians at Fermilab (CAIF).

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